research a concept paper

Concept Papers in Research: Deciphering the blueprint of brilliance

Concept papers hold significant importance as a precursor to a full-fledged research proposal in academia and research. Understanding the nuances and significance of a concept paper is essential for any researcher aiming to lay a strong foundation for their investigation.

Table of Contents

What Is Concept Paper

A concept paper can be defined as a concise document which outlines the fundamental aspects of a grant proposal. It outlines the initial ideas, objectives, and theoretical framework of a proposed research project. It is usually two to three-page long overview of the proposal. However, they differ from both research proposal and original research paper in lacking a detailed plan and methodology for a specific study as in research proposal provides and exclusion of the findings and analysis of a completed research project as in an original research paper. A concept paper primarily focuses on introducing the basic idea, intended research question, and the framework that will guide the research.

Purpose of a Concept Paper

A concept paper serves as an initial document, commonly required by private organizations before a formal proposal submission. It offers a preliminary overview of a project or research’s purpose, method, and implementation. It acts as a roadmap, providing clarity and coherence in research direction. Additionally, it also acts as a tool for receiving informal input. The paper is used for internal decision-making, seeking approval from the board, and securing commitment from partners. It promotes cohesive communication and serves as a professional and respectful tool in collaboration.

These papers aid in focusing on the core objectives, theoretical underpinnings, and potential methodology of the research, enabling researchers to gain initial feedback and refine their ideas before delving into detailed research.

Key Elements of a Concept Paper

Key elements of a concept paper include the title page , background , literature review , problem statement , methodology, timeline, and references. It’s crucial for researchers seeking grants as it helps evaluators assess the relevance and feasibility of the proposed research.

Writing an effective concept paper in academic research involves understanding and incorporating essential elements:

How to Write a Concept Paper?

To ensure an effective concept paper, it’s recommended to select a compelling research topic, pose numerous research questions and incorporate data and numbers to support the project’s rationale. The document must be concise (around five pages) after tailoring the content and following the formatting requirements. Additionally, infographics and scientific illustrations can enhance the document’s impact and engagement with the audience. The steps to write a concept paper are as follows:

1. Write a Crisp Title:

Choose a clear, descriptive title that encapsulates the main idea. The title should express the paper’s content. It should serve as a preview for the reader.

2. Provide a Background Information:

Give a background information about the issue or topic. Define the key terminologies or concepts. Review existing literature to identify the gaps your concept paper aims to fill.

3. Outline Contents in the Introduction:

Introduce the concept paper with a brief overview of the problem or idea you’re addressing. Explain its significance. Identify the specific knowledge gaps your research aims to address and mention any contradictory theories related to your research question.

4. Define a Mission Statement:

The mission statement follows a clear problem statement that defines the problem or concept that need to be addressed. Write a concise mission statement that engages your research purpose and explains why gaining the reader’s approval will benefit your field.

5. Explain the Research Aim and Objectives:

Explain why your research is important and the specific questions you aim to answer through your research. State the specific goals and objectives your concept intends to achieve. Provide a detailed explanation of your concept. What is it, how does it work, and what makes it unique?

6. Detail the Methodology:

Discuss the research methods you plan to use, such as surveys, experiments, case studies, interviews, and observations. Mention any ethical concerns related to your research.

7. Outline Proposed Methods and Potential Impact:

Provide detailed information on how you will conduct your research, including any specialized equipment or collaborations. Discuss the expected results or impacts of implementing the concept. Highlight the potential benefits, whether social, economic, or otherwise.

8. Mention the Feasibility

Discuss the resources necessary for the concept’s execution. Mention the expected duration of the research and specific milestones. Outline a proposed timeline for implementing the concept.

9. Include a Support Section:

Include a section that breaks down the project’s budget, explaining the overall cost and individual expenses to demonstrate how the allocated funds will be used.

10. Provide a Conclusion:

Summarize the key points and restate the importance of the concept. If necessary, include a call to action or next steps.

Although the structure and elements of a concept paper may vary depending on the specific requirements, you can tailor your document based on the guidelines or instructions you’ve been given.

Here are some tips to write a concept paper:

Example of a Concept Paper

Here is an example of a concept paper. Please note, this is a generalized example. Your concept paper should align with the specific requirements, guidelines, and objectives you aim to achieve in your proposal. Tailor it accordingly to the needs and context of the initiative you are proposing.

 Download Now!

Importance of a Concept Paper

Concept papers serve various fields, influencing the direction and potential of research in science, social sciences, technology, and more. They contribute to the formulation of groundbreaking studies and novel ideas that can impact societal, economic, and academic spheres.

A concept paper serves several crucial purposes in various fields:

In summary, a well-crafted concept paper is essential in outlining a clear, concise, and structured framework for new ideas or proposals. It helps in assessing the feasibility, viability, and potential impact of the concept before investing significant resources into its implementation.

How well do you understand concept papers? Test your understanding now! 

Fill the Details to Check Your Score

Role of AI in Writing Concept Papers

The increasing use of AI, particularly generative models, has facilitated the writing process for concept papers. Responsible use involves leveraging AI to assist in ideation, organization, and language refinement while ensuring that the originality and ethical standards of research are maintained.

AI plays a significant role in aiding the creation and development of concept papers in several ways:

1. Idea Generation and Organization

AI tools can assist in brainstorming initial ideas for concept papers based on key concepts. They can help in organizing information, creating outlines, and structuring the content effectively.

2. Summarizing Research and Data Analysis

AI-powered tools can assist in conducting comprehensive literature reviews, helping writers to gather and synthesize relevant information. AI algorithms can process and analyze vast amounts of data, providing insights and statistics to support the concept presented in the paper.

3. Language and Style Enhancement

AI grammar checker tools can help writers by offering grammar, style, and tone suggestions, ensuring professionalism. It can also facilitate translation, in case a global collaboration.

4. Collaboration and Feedback

AI platforms offer collaborative features that enable multiple authors to work simultaneously on a concept paper, allowing for real-time contributions and edits.

5. Customization and Personalization

AI algorithms can provide personalized recommendations based on the specific requirements or context of the concept paper. They can assist in tailoring the concept paper according to the target audience or specific guidelines.

6. Automation and Efficiency

AI can automate certain tasks, such as citation formatting, bibliography creation, or reference checking, saving time for the writer.

7. Analytics and Prediction

AI models can predict potential outcomes or impacts based on the information provided, helping writers anticipate the possible consequences of the proposed concept.

8. Real-Time Assistance

AI-driven chat-bots can provide real-time support and answers to specific questions related to the concept paper writing process.

AI’s role in writing concept papers significantly streamlines the writing process, enhances the quality of the content, and provides valuable assistance in various stages of development, contributing to the overall effectiveness of the final document.

Concept papers serve as the stepping stone in the research journey, aiding in the crystallization of ideas and the formulation of robust research proposals. It the cornerstone for translating ideas into impactful realities. Their significance spans diverse domains, from academia to business, enabling stakeholders to evaluate, invest, and realize the potential of groundbreaking concepts.

Frequently Asked Questions

A concept paper can be defined as a concise document outlining the fundamental aspects of a grant proposal such as the initial ideas, objectives, and theoretical framework of a proposed research project.

A good concept paper should offer a clear and comprehensive overview of the proposed research. It should demonstrate a strong understanding of the subject matter and outline a structured plan for its execution.

Concept paper is important to develop and clarify ideas, develop and evaluate proposal, inviting collaboration and collecting feedback, presenting proposals for academic and research initiatives and allocating resources.

I got wonderful idea

It helps a lot for my concept paper.

Rate this article Cancel Reply

Your email address will not be published.

Enago Academy's Most Popular Articles

• Career Corner

Academic Webinars: Transforming knowledge dissemination in the digital age

Digitization has transformed several areas of our lives, including the teaching and learning process. During…

• Manuscripts & Grants
• Reporting Research

Mastering Research Grant Writing in 2024: Navigating new policies and funder demands

Entering the world of grants and government funding can leave you confused; especially when trying…

How to Create a Poster That Stands Out: Tips for a smooth poster presentation

It was the conference season. Judy was excited to present her first poster! She had…

Academic Essay Writing Made Simple: 4 types and tips

The pen is mightier than the sword, they say, and nowhere is this more evident…

Ensuring Academic Integrity and Transparency in Academic Research: A comprehensive checklist for researchers

Academic integrity is the foundation upon which the credibility and value of scientific findings are…

Sign-up to read more

Subscribe for free to get unrestricted access to all our resources on research writing and academic publishing including:

• 2000+ blog articles
• 50+ Webinars
• 10+ Expert podcasts
• 50+ Infographics
• 10+ Checklists
• Research Guides

We hate spam too. We promise to protect your privacy and never spam you.

• Industry News
• Publishing Research
• AI in Academia
• Promoting Research
• Diversity and Inclusion
• Infographics
• Expert Video Library
• Other Resources
• Enago Learn
• Upcoming & On-Demand Webinars
• Peer-Review Week 2023
• Open Access Week 2023
• Conference Videos
• Enago Report
• Journal Finder
• Enago Plagiarism & AI Grammar Check
• Editing Services
• Publication Support Services
• Research Impact
• Translation Services
• Publication solutions
• AI-Based Solutions
• Thought Leadership
• Call for Articles
• Call for Speakers
• Author Training
• Edit Profile

I am looking for Editing/ Proofreading services for my manuscript Tentative date of next journal submission:

In your opinion, what is the most effective way to improve integrity in the peer review process?

How To Write a Concept Paper for Academic Research: An Ultimate Guide

A concept paper is one of the first steps in helping you fully realize your research project. Because of this, some schools opt to teach students how to write concept papers as early as high school. In college, professors sometimes require their students to submit concept papers before suggesting their research projects to serve as the foundations for their theses.

If you’re reading this right now, you’ve probably been assigned by your teacher or professor to write a concept paper. To help you get started, we’ve prepared a comprehensive guide on how to write a proper concept paper.

Related: How to Write Significance of the Study (with Examples)

Table of Contents

What is the concept paper, 1. academic research concept papers, 2. advertising concept papers, 3. research grant concept papers, concept paper vs. research proposal, tips for finding your research topic, 2. think of research questions that you want to answer in your project, 3. formulate your research hypothesis, 4. plan out how you will achieve, analyze, and present your data, 2. introduction, 3. purpose of the study, 4. preliminary literature review, 5. objectives of the study, 6. research questions and hypotheses, 7. proposed methodology, 8. proposed research timeline, 9. references, sample concept paper for research proposal (pdf), tips for writing your concept paper.

Generally, a concept paper is a summary of everything related to your proposed project or topic. A concept paper indicates what the project is all about, why it’s important, and how and when you plan to conduct your project.

Different Types of the Concept Paper and Their Uses

This type of concept paper is the most common type and the one most people are familiar with. Concept papers for academic research are used by students to provide an outline for their prospective research topics.

These concept papers are used to help students flesh out all the information and ideas related to their topic so that they may arrive at a more specific research hypothesis.

Since this is the most common type of concept paper, it will be the main focus of this article.

Advertising concept papers are usually written by the creative and concept teams in advertising and marketing agencies.

Through a concept paper, the foundation or theme for an advertising campaign or strategy is formed. The concept paper can also serve as a bulletin board for ideas that the creative and concept teams can add to or develop. 

This type of concept paper usually discusses who the target audience of the campaign is, what approach of the campaign will be, how the campaign will be implemented, and the projected benefits and impact of the campaign to the company’s sales, consumer base, and other aspects of the company.

This type of concept paper is most common in the academe and business world. Alongside proving why your research project should be conducted, a research grant concept paper must also appeal to the company or funding agency on why they should be granted funds.

The paper should indicate a proposed timeline and budget for the entire project. It should also be able to persuade the company or funding agency on the benefits of your research project– whether it be an increase in sales or productivity or for the benefit of the general public.

It’s important to discuss the differences between the two because a lot of people often use these terms interchangeably.

A concept paper is one of the first steps in conducting a research project. It is during this process that ideas and relevant information to the research topic are gathered to produce the research hypothesis. Thus, a concept paper should always precede the research proposal. 

A research proposal is a more in-depth outline of a more fleshed-out research project. This is the final step before a researcher can conduct their research project. Although both have similar elements and structures, a research proposal is more specific when it comes to how the entire research project will be conducted.

Getting Started on Your Concept Paper

1. find a research topic you are interested in.

When choosing a research topic, make sure that it is something you are passionate about or want to learn more about. If you are writing one for school, make sure it is still relevant to the subject of your class. Choosing a topic you aren’t invested in may cause you to lose interest in your project later on, which may lower the quality of the research you’ll produce.

A research project may last for months and even years, so it’s important that you will never lose interest in your topic.

• Look for inspiration everywhere. Take a walk outside, read books, or go on your computer. Look around you and try to brainstorm ideas about everything you see. Try to remember any questions you might have asked yourself before like why something is the way it is or why can’t this be done instead of that . 
• Think big. If you’re having trouble thinking up a specific topic to base your research project on, choosing a broad topic and then working your way down should help.
• Is it achievable? A lot of students make the mistake of choosing a topic that is hard to achieve in terms of materials, data, and/or funding available. Before you decide on a research topic, make sure you consider these aspects. Doing so will save you time, money, and effort later on.
• Be as specific as can be. Another common mistake that students make is that they sometimes choose a research topic that is too broad. This results in extra effort and wasted time while conducting their research project. For example: Instead of “The Effects of Bananas on Hungry Monkeys” , you could specify it to “The Effects of Cavendish Bananas on Potassium-deficiency in Hungry Philippine Long-tailed Macaques in Palawan, Philippines”.

Now that you have a general idea of the topic of your research project, you now need to formulate research questions based on your project. These questions will serve as the basis for what your project aims to answer. Like your research topic, make sure these are specific and answerable.

Following the earlier example, possible research questions could be:

• Do Cavendish bananas produce more visible effects on K-deficiency than other bananas?
• How susceptible are Philippine long-tailed macaques to K-deficiency?
• What are the effects of K-deficiency in Philippine long-tailed macaques?

After formulating the research questions, you should also provide your hypothesis for each question. A research hypothesis is a tentative answer to the research problem. You must provide educated answers to the questions based on your existing knowledge of the topic before you conduct your research project.

After conducting research and collecting all of the data into the final research paper, you will then have to approve or disprove these hypotheses based on the outcome of the project.

Prepare a plan on how to acquire the data you will need for your research project. Take note of the different types of analysis you will need to perform on your data to get the desired results. Determine the nature of the relationship between different variables in your research.

Also, make sure that you are able to present your data in a clear and readable manner for those who will read your concept paper. You can achieve this by using tables, charts, graphs, and other visual aids.

Related: How to Make Conceptual Framework (with Examples and Templates)

Generalized Structure of a Concept Paper

Since concept papers are just summaries of your research project, they are usually short and  no longer than 5 pages. However, for big research projects, concept papers can reach up to more than 20 pages.

Your teacher or professor may give you a certain format for your concept papers. Generally, most concept papers are double-spaced and are less than 500 words in length. 

Even though there are different types of concept papers, we’ve provided you with a generalized structure that contains elements that can be found in any type of concept paper.

The title for your paper must be able to effectively summarize what your research is all about. Use simple words so that people who read the title of your research will know what it’s all about even without reading the entire paper. 

The introduction should give the reader a brief background of the research topic and state the main objective that your project aims to achieve. This section should also include a short overview of the benefits of the research project to persuade the reader to acknowledge the need for the project.

The Purpose of the Study should be written in a way that convinces the reader of the need to address the existing problem or gap in knowledge that the research project aims to resolve. In this section, you have to go into more detail about the benefits and value of your project for the target audience/s. 

This section features related studies and papers that will support your research topic. Use this section to analyze the results and methodologies of previous studies and address any gaps in knowledge or questions that your research project aims to answer. You may also use the data to assert the importance of conducting your research.

When choosing which papers and studies you should include in the Preliminary Literature Review, make sure to choose relevant and reliable sources. Reliable sources include academic journals, credible news outlets, government websites, and others. Also, take note of the authors for the papers as you will need to cite them in the References section.

Simply state the main objectives that your research is trying to achieve. The objectives should be able to indicate the direction of the study for both the reader and the researcher. As with other elements in the paper, the objectives should be specific and clearly defined.

Gather the research questions and equivalent research hypotheses you formulated in the earlier step and list them down in this section.

In this section, you should be able to guide the reader through the process of how you will conduct the research project. Make sure to state the purpose for each step of the process, as well as the type of data to be collected and the target population.

Depending on the nature of your research project, the length of the entire process can vary significantly. What’s important is that you are able to provide a reasonable and achievable timeline for your project.

Make sure the time you will allot for each component of your research won’t be too excessive or too insufficient so that the quality of your research won’t suffer.

Ensure that you will give credit to all the authors of the sources you used in your paper. Depending on your area of study or the instructions of your professor, you may need to use a certain style of citation.

There are three main citation styles: the American Psychological Association (APA), Modern Language Association (MLA), and the Chicago style.

The APA style is mostly used for papers related to education, psychology, and the sciences. The APA citation style usually follows this format:

The MLA citation style is the format used by papers and manuscripts in disciplines related to the arts and humanities. The MLA citation style follows this format:

The Chicago citation style is usually used for papers related to business, history, and the fine arts. It follows this citation format:

This is a concept paper sample provided by Dr. Bernard Lango from the Jomo Kenyatta University of Agriculture and Technology (modified for use in this article). Simply click the link above the download the PDF file.

• Use simple, concise language. Minimize the use of flowery language and always try to use simple and easy-to-understand language. Too many technical or difficult words in your paper may alienate your readers and make your paper hard to read. 
• Choose your sources wisely. When scouring the Internet for sources to use, you should always be wary and double-check the authenticity of your source. Doing this will increase the authenticity of your research project’s claims and ensure better data gathered during the process.
• Follow the specified format, if any. Make sure to follow any specified format when writing your concept paper. This is very important, especially if you’re writing your concept paper for class. Failure to follow the format will usually result in point deductions and delays because of multiple revisions needed.
• Proofread often. Make it a point to reread different sections of your concept paper after you write them. Another way you can do this is by taking a break for a few days and then coming back to proofread your writing. You may notice certain areas you’d like to revise or mistakes you’d like to fix. Make proofreading a habit to increase the quality of your paper.

Written by Ruth Raganit

in Career and Education , Juander How

Ruth Raganit

Ruth Raganit obtained her Bachelor of Science degree in Geology from the University of the Philippines – Diliman. Her love affair with Earth sciences began when she saw a pretty rock and wondered how it came to be. She also likes playing video games, doing digital art, and reading manga.

Browse all articles written by Ruth Raganit

Copyright Notice

All materials contained on this site are protected by the Republic of the Philippines copyright law and may not be reproduced, distributed, transmitted, displayed, published, or broadcast without the prior written permission of filipiknow.net or in the case of third party materials, the owner of that content. You may not alter or remove any trademark, copyright, or other notice from copies of the content. Be warned that we have already reported and helped terminate several websites and YouTube channels for blatantly stealing our content. If you wish to use filipiknow.net content for commercial purposes, such as for content syndication, etc., please contact us at legal(at)filipiknow(dot)net

Community Blog

Keep up-to-date on postgraduate related issues with our quick reads written by students, postdocs, professors and industry leaders.

What is a Concept Paper and How do You Write One?

• By DiscoverPhDs
• August 26, 2020

What is a Concept Paper?

A concept paper is a short document written by a researcher before starting their research project, with the purpose of explaining what the study is about, why it is important and the methods that will be used.

The concept paper will include your proposed research title, a brief introduction to the subject, the aim of the study, the research questions you intend to answer, the type of data you will collect and how you will collect it. A concept paper can also be referred to as a research proposal.

What is the Purpose of a Concept Paper?

The primary aim of a research concept paper is to convince the reader that the proposed research project is worth doing. This means that the reader should first agree that the research study is novel and interesting. They should be convinced that there is a need for this research and that the research aims and questions are appropriate.

Finally, they should be satisfied that the methods for data collection proposed are feasible, are likely to work and can be performed within the specific time period allocated for this project.

The three main scenarios in which you may need to write a concept paper are if you are:

• A final year undergraduate or master’s student preparing to start a research project with a supervisor.
• A student submitting a research proposal to pursue a PhD project under the supervision of a professor.
• A principal investigator submitting a proposal to a funding body to secure financial support for a research project.

How Long is a Concept Paper?

The concept paper format is usually between 2 and 3 pages in length for students writing proposals for undergraduate, master’s or PhD projects. Concept papers written as part of funding applications may be over 20 pages in length.

How do you Write a Concept Paper?

There are 6 important aspects to consider when writing a concept paper or research proposal:

• 1. The wording of the title page, which is best presented as a question for this type of document. At this study concept stage, you can write the title a bit catchier, for example “Are 3D Printed Engine Parts Safe for Use in Aircraft?”.
• A brief introduction and review of relevant existing literature published within the subject area and identification of where the gaps in knowledge are. This last bit is particularly important as it guides you in defining the statement of the problem. The concept paper should provide a succinct summary of ‘the problem’, which is usually related to what is unknown or poorly understood about your research topic . By the end of the concept paper, the reader should be clear on how your research idea will provide a ‘solution’ to this problem.
• The overarching research aim of your proposed study and the objectives and/or questions you will address to achieve this aim. Align all of these with the problem statement; i.e. write each research question as a clear response to addressing the limitations and gaps identified from previous literature. Also give a clear description of your primary hypothesis.
• The specific data outputs that you plan to capture. For example, will this be qualitative or quantitative data? Do you plan to capture data at specific time points or at other defined intervals? Do you need to repeat data capture to asses any repeatability and reproducibility questions?
• The research methodology you will use to capture this data, including any specific measurement or analysis equipment and software you will use, and a consideration of statistical tests to help interpret the data. If your research requires the use of questionnaires, how will these be prepared and validated? In what sort of time frame would you plan to collect this data?
• Finally, include a statement of the significance of the study , explaining why your research is important and impactful. This can be in the form of a concluding paragraph that reiterate the statement of the problem, clarifies how your research will address this and explains who will benefit from your research and how.

You may need to include a short summary of the timeline for completing the research project. Defining milestones of the time points at which you intend to complete certain tasks can help to show that you’ve considered the practicalities of running this study. It also shows that what you have proposed is feasible in order to achieve your research goal.

If you’re pitching your proposed project to a funder, they may allocate a proportion of the money based on the satisfactory outcome of each milestone. These stakeholders may also be motivated by knowing that you intend to convert your dissertation into an article for journal publication; this level of dissemination is of high importance to them.

Additionally, you may be asked to provide a brief summary of the projected costs of running the study. For a PhD project this could be the bench fees associated with consumables and the cost of any travel if required.

Make sure to include references and cite all other literature and previous research that you discuss in your concept paper.

This guide gave you an overview of the key elements you need to know about when writing concept papers. The purpose of these are first to convey to the reader what your project’s purpose is and why your research topic is important; this is based on the development of a problem statement using evidence from your literature review.

Explain how it may positively impact your research field and if your proposed research design is appropriate and your planned research method achievable.

The scope and delimitations of a thesis, dissertation or paper define the topic and boundaries of a research problem – learn how to form them.

Stay up to date with current information being provided by the UK Government and Universities about the impact of the global pandemic on PhD research studies.

Learn more about using cloud storage effectively, video conferencing calling, good note-taking solutions and online calendar and task management options.

Join thousands of other students and stay up to date with the latest PhD programmes, funding opportunities and advice.

Browse PhDs Now

A science investigatory project is a science-based research project or study that is performed by school children in a classroom, exhibition or science fair.

Find out how you can use Scrivener for PhD Thesis & Dissertation writing to streamline your workflow and make academic writing fun again!

Michele is a first-year PhD candidate in a double degree program between the University of Girona (Spain) & Technical University Munich (Germany). His research has the aim of innovating water treatment technologies.

Christian is a PhD student at the University of Leeds. His research project investigatores the role of the molecular clock in sympathetic preganglionic neurons.

Join Thousands of Students

What exactly is a Concept Paper, and how do you write one?

Learn why a concept paper is important, what the main elements of a research concept paper are, and how to create an excellent one.

Prior to submitting a formal proposal (business proposal, product, or research proposal), many private organizations have historically asked for the submission of a concept paper for review. 

Recently, organizations have begun to advocate for the usage of concept papers as a way for applicants to obtain informal input on their ideas and projects before submitting a proposal. Several of these organizations now demand a concept paper as part of the official application process. 

Simply described, a concept paper is a preliminary document that explains the purpose of research, why it is being conducted, and how it will be performed. It examines a concept or idea and offers an outline of the topic that a researcher wants to pursue. Continue reading to learn more about concept papers and how to create a good one. 

What a concept paper is and its purpose

A concept paper is a brief paper that outlines the important components of a research or project before it is carried out. Its purpose is to offer an overview. Entrepreneurs working on a business idea or product, as well as students and researchers, frequently write concept papers .  

Researchers may be required to prepare a concept paper when submitting a project proposal to a funding authority to acquire the required grants.

As a consequence, the importance is based on the fact that it should help the examiner determine whether the research is relevant, practicable, and useful . 

If not, they may suggest looking into a different research area. It also allows the examiner to assess your comprehension of the research and, as a result, if you are likely to require assistance in completing the research.

Illustrate your Concept Paper with infographics 

Infographics are very useful to explain complex subjects in a very short time. Use Mind the Graph to create beautiful infographics for your Concept Paper with scientifically accurate illustrations, icons, arrows and many other design tools.

Concept paper’s elements for an academic research 

To produce an effective concept paper, you must first comprehend the essential elements of academic research:

• Title page: Mention the applicant’s name, institution, project title, and submission date.
• Background for the research: The second section should be the purpose section, which should be able to clear out what has already been stated about the subject, any gaps in information that need to be filled or problems to be solved, as well as the reason why you wish to examine the issue.
• Literature review: In this section, you should provide a theoretical basis and supporting material for your chosen subject.
• State the problem and your goals: Describe the overall problems, including the research questions and objectives. State your research’s unique and original aspects, concentrate on providing and clearly discussing your goals towards the problem.
• Methodology: Provide the data analysis system to be utilized, data collecting method, tools to be used, and research participants in this section.
• Timeline: Include a realistic timeline estimate that is defined in months and years.
• References: Add a list of all sources cited in your concept paper , such as books, journals, and other resources.

Tips on writing an effective concept paper

A concept paper is extremely crucial for a project or research, especially if it requires funding. Check out these simple tips to ensure your concept paper is successful and simple.

• Choose a research topic that truly piques your curiosity
• Create a list of research questions. The more, the merrier.
• When describing the project’s reasoning, use data and numbers. 
• Use no more than 5 single-spaced pages. 
• Tailor your speech to the appropriate audience.
• Make certain that the basic format elements, such as page numbers, are included. 
• Spend additional time on your timeline as this section is critical for funding.
• Give specific examples of how you plan to measure your progress toward your goals.
• Provide an initial budget when seeking funds. Sponsors will want to obtain an idea of how much funds are required.

Start creating infographics and scientific illustrations

Use the power of infographics and scientific illustrations to your advantage. Including graphic assets in your work may increase your authority and highlight all of the most valuable information, ensuring that your audience is engaged and completely comprehensive of the information you are providing.

Subscribe to our newsletter

Exclusive high quality content about effective visual communication in science.

Sign Up for Free

Try the best infographic maker and promote your research with scientifically-accurate beautiful figures

no credit card required

About Jessica Abbadia

Jessica Abbadia is a lawyer that has been working in Digital Marketing since 2020, improving organic performance for apps and websites in various regions through ASO and SEO. Currently developing scientific and intellectual knowledge for the community's benefit. Jessica is an animal rights activist who enjoys reading and drinking strong coffee.

Content tags

Research Concept Paper

What is a research concept paper.

The Concept Paper lays the foundation for the applied dissertation process, providing an introductory form of communication between the doctoral student and the doctoral committee. Essentially, the Concept Paper acts as a tentative proposal; it allows the doctoral student the opportunity to define a research focus and obtain early feedback on the research idea. A well-planned Concept Paper will capture the interest of the dissertation committee and establish a clear plan for the student’s dissertation.

When is the Research Concept Paper Written?

The Research Concept Paper is completed prior to the dissertation proposal and serves as a development tool and summary of the planned dissertation. The Concept paper is a brief document. Depending upon the requirements of the specific school or academic program, the Concept Paper may range from as few as 2-3 pages to as many as 10-20 pages. The essential point of the Concept Paper is to explain the importance of a particular research project.

The Concept Paper initiates the dissertation phase of a doctoral degree, which follows the completion of necessary coursework and training and represents a culmination of the student’s learning. The dissertation is a student’s final academic effort to synthesize course material by applying their learning to a research project. The project is expected to add new information to the field of study.  The Concept Paper acts as a summary of this project.

The Concept Paper, although highly abridged, is comprised of many of the same items found in a dissertation. The specific elements of the Concept Paper may vary depending upon the academic program and the chosen degree. Programs typically provide a grading rubric that serves as an outline for the required components, and students are encouraged to follow those rubrics closely in developing their Concept Paper.

What are the Main Elements of a Research Concept Paper?

Need help with your research.

Schedule a time to speak with an expert using the calendar below?

Title page  — provides a tentative title for the dissertation.  The title of the Concept Paper should be a stand-alone statement that can fully describe the project by summarizing the main idea of the manuscript.  The title should concisely identify the variables being investigated and the relationship among those variables (American Psychological Association , 2010).  Words should serve a useful purpose; avoid words that do not add substance or words that are misleading.  The title of the Concept Paper may become the title of the dissertation.

Statement of the Problem — provides the purpose for the research.  This section of the Concept Paper introduces the problem under investigation, addresses why the researcher wants to investigate this problem, and how the research findings may help address the problem.  Supporting documentation, including statistical data if available, should be used to emphasize the need for this research.  This section is one of the most important sections of the Concept Paper; it serves to gain the reader’s attention and support.  You care about the research, but the reader may need some convincing.  The first few sentences of the Concept Paper should intrigue the reader to pique his or her interest and encourage further reading.

As you begin to write the problem statement of your Concept Paper, consider your research.  First consider why the problem is important.  Consider how your study relates to previous work in the field, how you will link your hypotheses and objectives to theory, and how the hypotheses relate to the research design.  Finally, consider the theoretical and practical implications involved in your research project (APA, 2010).  A well-developed, concise, and clear problem statement will lay the foundation for a strong Concept Paper and the dissertation that follows. Preliminary Literature Review — provides identification of major literature that supports and validates the topic.  The literature review focuses on areas that offer support for new research and offers the student an opportunity to analyze and synthesize past research in the context of their present problem.  For the Concept Paper, the student should connect their research project to a theoretical model reported in the literature.  The most successful research projects have been based on the research of predecessors, and this section of the Concept Paper provides enough of a description of previous research to plant seeds in the mind of the reader suggesting more information is needed.  A strong Concept Paper is based on a wide-range literature review that is condensed into a summary of key points. Goal Statement — provides a broad or abstract intention, including the research goals and objectives.  This part of the Concept Paper tells the reader “who, what, and when” regarding the research goal.

Research Questions  — provides a preliminary view of the questions the student will investigate.  Questions are based on theory, past research, and need.  These questions will direct the research methodology; their inclusion in the Concept Paper links the research problem with the methodology.  For some, composing the research questions may be the most difficult part of the research project, or possibly the most difficult aspect of writing the Concept Paper.  The questions will direct everything that will be done; therefore, it is important that they are focused to the main research problem.  These research questions will specifically direct the research and the type of analyses conducted; as such, their compatibility is essential. An Abridged Methodology  — provides the student’s best idea on how to conduct the research and analyze the data. The goals identified in previous sections of the Concept Paper should relate to the research methods described in this section.  For the Concept Paper, the methodology is simplified or summarized, serving as a general outline of the methods that will be employed.

Timeline — provides a range of time for completion of the project, highlighting key elements for each stage of the project.  This element is unique to the Concept Paper and provides the student structure for managing sections of the project within a realistic time frame. References — provides references to the material cited in the literature review and elsewhere in the Concept Paper.

How to Write a PhD Concept Paper

A concept paper – or concept note – is one of the initial requirements of a PhD programme. It is normally written during the PhD application process as well as early on in the programme once a student has been admitted.

A concept paper is basically a shorter version of a research proposal – in most cases between 2,000 and 2,500 words – that expresses the research ideas of the potential PhD student.

Besides being short, it should be concise yet have adequate details to convince the Department the student is applying to that he/she is worth being admitted to the programme.

Example of a title with a sub-title

References/bibliography, why do phd programmes require applicants to submit a concept paper.

A concept paper serves four main purposes:

• It gives the Department the student is applying to an idea of the student’s research interests.
• Based on point one, it informs the Department whether the student will be a good fit to the Department or not. To be a good fit, the research interests of the applicant should match those of the Department’s faculty.
• Based on the two points above, it enables the Department to offer support to the student throughout his/her PhD studies in the form of supervision and mentorship.
• Because the concept paper is written – and must be accepted – before the full proposal, it saves the student time and effort that would otherwise be spent on topics that may end up being rejected by the Department. A concept paper is therefore the first step to writing the PhD thesis/dissertation (see the figure below).

Format of a PhD Concept Paper

The format of a concept paper might vary from one university to another. A PhD student should therefore read the guidelines provided by his/her University of interest before writing a concept paper.

In general, the following is a common format of a concept paper:

Title of proposed study

The title of the proposed study is the first element of a concept paper.

The title should describe what the study is about by highlighting the variables of the study and the relationship between the variables if applicable.

The title should be short and specific: it is best to have a title that is not more than 15 words’ long.

Example of a title:

Use of Mobile Phone Applications for Weight Management in the United States

In order to add more specificity to the title, you can add a subtitle to the main title. The title and subtitle should be separated by a full colon.

Use of Mobile Phone Applications for Weight Management in the United States:

A Behavioural Economics’ Analysis

Background to the study

The background to the study contains the following elements:

• The history of the topic, both globally and in the proposed location of your study.
• What other researchers have found out from their own studies.
• What the gaps in the existing literature are, that is, what the other researchers have not addressed.
• What your study will contribute towards filling the identified gaps.

The implication of the above is that one must have conducted some literature review prior to writing the background to the study.

Statement of the problem

The statement of the problem is a clear description of the issue that the study will address, the relevance of the issue, the importance (benefits) of addressing the issue, and the method the researcher will use to address the issue.

Goal and objectives of the study

Once you have identified the problem of your study, the next step is to write the goal and objectives of the study. There is a difference between these two:

The goal of the study is a broad statement of what the researcher hopes to accomplish at the end of the study. The goal should also be related to the problem statement.

Any given project should have one goal because having many goals would lead to confusion. However, that one goal can have multiple elements in it, which would be accomplished through the project’s objectives.

The objectives of the study, on the other hand, are specific and detailed statements of how the researcher will go about accomplishing the stated goal.

The objectives should:

• Support the accomplishment of the goal.
• Follow a sequence, that is, like a step-by-step order. This will help you frame the activities needed to be undertaken in a logical manner so that the goal is achieved.
• Be stated using action verbs, for instance, “to identify”, “to create”, “to establish”, “to measure”, etc.
• Be about 3-4: having too few of objectives will limit the scope of your PhD dissertation, while having too many objectives may complicate the dissertation.
• Be SMART, that is, Specific, Measurable, Achievable, Realistic, and Time-bound.

The video below clearly explains how to set SMART goals and objectives:

https://www.youtube.com/watch?v=MAhs-m6cNzY

Important tip 1: depending on your PhD programme, you may be required to have at least 3 journal papers to qualify for graduation. Each of your objectives can be converted into a separate journal paper on its own.

Research questions and hypotheses

Every PhD dissertation needs research questions. Research questions will help the student stay focused on his/her research.

The aim of the research is to provide answers to the research questions. The answers to the questions will form the thesis statement.

Examples of research questions:

In the title example given earlier about use of mobile phone applications for weight management in the United States, a student may be interested in the following questions:

• To what extent do adults in the United States use mobile phone applications to manage their weight?
• Is there any gender disparity in the use of mobile phone apps for weight management in the United States?
• How effective are mobile apps for weight management in the United States?

Good research questions are those that can be explored deeply and widely as well as defended using evidence. Questions with ‘yes” or “no” responses are not academic-worthy.

When developing research questions, you also need to think about the data that will be required to answer the questions. Do you have access to that data? If no, will your time and financial resources allow you to collect that data?

Important tip 2: Your PhD study is time-limited therefore data requirement issues need to be thought through at the initial stages of your concept paper writing so that you don’t waste too much time either collecting the data in the future or trying to access the data if it already exists elsewhere.

Preliminary literature review

At the concept paper stage, a preliminary literature review serves three main purposes:

• It shows whether you have knowledge of the current state of debate about your chosen topic.
• It shows whether you are familiar with the experts in your chosen topic.
• It also helps you identify the research gaps.

Proposed research design, methods and procedures

This sections provides a brief overview of the research methodology that you will adopt in your study. Some issues to consider include:

• Will your study use quantitative, qualitative or mixed-methods approach?
• Will you use secondary or primary data?
• What will be the sources of your data? Will you need any ethical clearance from your university before collecting data?
• Will the data sources be readily accessible?
• Will you use external assistance for data collection? Or will you do all the data collection yourself?
• How will the data be analysed? Which softwares will you use? Are you competent in those softwares?

While the above issues are important to think through, please note that the research design and methods will be informed by your research objectives and research questions. As an illustration:

A research question that aims to measure the effect of one (or more) variable(s) on another variable will definitely require quantitative research methods.

On the other hand, a research question that aims to explain the existence of a phenomenon will render itself to the use of qualitative research methods.

Contribution to knowledge

This is perhaps the most important aspect of a PhD dissertation. Your concept note needs to briefly highlight how your project will add value to knowledge.

Making significant contribution to knowledge at the PhD level does not mean a Nobel prize standard of knowledge (this you can do after your PhD when you’ll have all the time in the world to do so). You can achieve this in various ways:

• New applications of existing ideas.
• New interpretations of previous ideas.
• Investigating an existing issue in a new location.
• Development of a new theory.
• Coming up with a new technique, among others.

The last section of the concept paper is the reference list or bibliography. This is the section that lists the literatures that you have reviewed and cited in your paper.

There is a slight difference between a reference list and a bibliography:

A reference list includes all those studies that have been directly cited in the paper.

A bibliography, on the other hand, includes all those studies that have been directly cited in the paper as well as those that were reviewed and consulted but not cited in the paper.

When creating the reference list/bibliography, one should be mindful of the referencing style that is required by their PhD department (that is, whether APA, MLA, Chicago, Havard, etc).

Final Thoughts on Writing a PhD Concept Paper

The concept paper is the first step to writing the PhD dissertation. Once accepted, the student will proceed to writing the proposal, which will then be defended before proceeding with writing the full dissertation.

The concept paper is a mini-proposal and has most of the components expected in the proposal.

However, the concept paper should be short and precise while at the same time have adequate information to enable the PhD Committee of the PhD Programme the student is applying to judge if the student will be a good fit to the programme or not.

Related posts

How To Choose a Research Topic For Your PhD Thesis (7 Key Factors to Consider)

Comprehensive Guidelines for Writing a PhD Thesis Proposal (+ free checklist for PhD Students)

Grace Njeri-Otieno

Grace Njeri-Otieno is a Kenyan, a wife, a mom, and currently a PhD student, among many other balls she juggles. She holds a Bachelors' and Masters' degrees in Economics and has more than 7 years' experience with an INGO. She was inspired to start this site so as to share the lessons learned throughout her PhD journey with other PhD students. Her vision for this site is "to become a go-to resource center for PhD students in all their spheres of learning."

Recent Content

SPSS Tutorial #12: Partial Correlation Analysis in SPSS

Partial correlation is almost similar to Pearson product-moment correlation only that it accounts for the influence of another variable, which is thought to be correlated with the two variables of...

SPSS Tutorial #11: Correlation Analysis in SPSS

In this post, I discuss what correlation is, the two most common types of correlation statistics used (Pearson and Spearman), and how to conduct correlation analysis in SPSS. What is correlation...

• Translation

Concept Paper vs. Research Proposal – and when to use each

By charlesworth author services.

• Charlesworth Author Services
• 08 March, 2022

On the surface, concept papers sound like they do the same job as a research proposal – and essentially, they do. Both are designed to communicate the rationale, methodology and outcomes of a proposed piece of work. The difference between the two lies mostly in the level of detail and the potential audience, based on which your approach towards writing each will vary. In this article, we dig deeper into these and recommend when to use which.

Concept paper: Putting your idea to paper

• What : A concept paper verbalises an idea and puts it to paper for the first time. Here, an overall rationale is presented, with a focus on the essential idea and potential impact of the expected outcome(s). However, what you would not include here is much in-depth detail.
• When : Writing a concept paper is most useful when an initial expression of interest is made to either a collaborator or funder – provided the funder has mechanisms for you to do this, like an open call.
• Why : The aim of your concept paper will be to win your audience over with your idea and its potential ramifications. 

(For more on concept papers, read: Understanding and developing a concept paper )

Research proposal: Showing how things will get done

Let’s say that through your concept paper, you find funding and collaborators for your proposed research project. You will now get into the nitty gritty of the project with a research proposal, while still keeping it “consumable” enough for a broader audience.

• What : A research proposal builds on a concept paper by now including aspects like key deliverables, milestones and specific outcomes, as well as how you plan to achieve these. 
• When : You will typically send a research proposal to sources of funding of an open nature, i.e. those that do not require a standardised form to be filled in, as is often the case with institutional internal funding or private investors.
• Why : It is not necessary for you to first send someone a concept paper and follow it up with a proposal. However, you may often need to follow this sequence in order to provide only ‘need to know’ material depending on the stage of your relationship with potential partners.

( For more on research proposals, read: Writing a successful research proposal )

When both are needed, a concept paper precedes a research proposal

Deciding between a concept paper and a research proposal

Whether you send someone a concept paper or a research proposal depends entirely on two things: 

• Your existing relationship with whomever you are reaching out to
• What you are trying to achieve

If you are emailing an organisation or individual for the first time, you are more likely to receive a response by attaching a brief, snappy concept paper that is easily read by a multitude of people. On the other hand, some larger organisations, such as pharmaceutical companies, are very used to seeing full-fledged research proposals and may have a portal on their website where you would need to upload one, enabling them to skip the preliminary step of vetting your work through a concept paper.

Our recommendation : Given how pressed many people are for time these days, it would be prudent to send concept papers more frequently than research proposals. If more information is required, you will be asked for it.

Concept papers and research proposals do very similar things, but set out and achieve very different aims. They are often sent in sequence – the concept paper first, followed by the research proposal. The need for a research proposal arises when the concept paper has achieved its mark – when, for example, more information is required for a funding decision to be reached, or due diligence is to be performed, as a result of your concept paper gaining preliminary acceptance. Following up with a research proposal fills in the gaps and will aid in answering questions arising from the concept paper.

Read previous (second) in series: Writing a successful Research Proposal

Maximise your publication success with Charlesworth Author Services.

Charlesworth Author Services, a trusted brand supporting the world’s leading academic publishers, institutions and authors since 1928. 

To know more about our services, visit: Our Services

Share with your colleagues

Scientific Editing Services

Sign up – stay updated.

We use cookies to offer you a personalized experience. By continuing to use this website, you consent to the use of cookies in accordance with our Cookie Policy.

+1 888 701 5192

What Is a Concept Paper: Definition, Format, and Example

• Concept Paper Definition
• Concept Paper Format
• How to Write a Concept Paper
• 2. Introduction to the concept
• 3. Background research
• 4. Objectives
• 5. Need for the study
• 6. Research methodology
• 7. References
• Conceptual Paper Example
• Introduction
• Background Research
• Aim and Need for the Study
• Research Methodology
• Concept Paper Writing Services

Research papers and dissertations are common and important writing tasks for undergraduates and post-graduate students. Researchers and other professionals from academic and scientific institutions also write research papers. These research and studies are often lengthy and time-consuming. A research study can last for one to two years, it can even exceed this time depending on the field and complexity of the research study. However, before they can write these lengthy documents, they will first need to create a concept paper for dissertation and research.

The concept paper will act as a proposal paper for dissertation and research papers. Writing this document will be the first step in proceeding with the research. Students and professionals will need to choose the best outline and format for their concept paper to gain the approval of the reader. This document is essential not only for students but also for researchers that are looking for individuals to fund their study. In this article, readers can learn how to write a concept paper and read a conceptual paper example to act as a guide in writing.

Before starting to write the document, individuals should learn what is a concept paper. This document is a summary of a research study that students and professionals will undertake. The concept paper should provide the study’s purpose, background, and research questions. The goal of this document is to capture the reader’s interest and provide information that shows the research’s merit. The researchers should view a concept paper as a proposal and write it to make the readers support the study.

Need a concept paper? I can help!

A standard concept paper format will be around two to three pages long. Undergraduates and post-graduate students typically write in this type of concept paper format. For researchers in specific fields that are looking for funding, their proposal document can be over 20 pages long. Since the definition of a concept paper states that it is a summary of a research study, most documents will need to provide complete information that will lengthen the page count. The documents that take 20 pages long often give multiple background information of related studies to emphasize the importance of the researcher’s endeavors. Papers for dissertation and research papers tend to be shorter since they are not asking for monetary funding and their topics are less complex. Individuals should look at sample papers to find the perfect format for their papers.

How to Write a Concept Paper

Individuals should consider looking at concept paper examples to better understand the document’s outline. This will make writing a concept paper an easier task. For a standard outline, individuals can follow the list below when writing the document. 

After learning the definition and correct format of a concept paper, individuals can now begin to write the document. The first task in writing a concept paper is choosing a title. This is important for every document since its readers will know and remember a research study based on its title. Researchers should write short titles that are direct to the point. The best titles for this type of document are in question format. A question statement directly tells the readers what questions and problems the researchers are going to answer. Consider looking at research document examples to get an idea of how most researchers format their titles.

Once the researchers establish a working title, they can then proceed with writing an introduction. The introduction of the concept paper should provide background information about the study. The introduction should also briefly tell the readers why the study is important and how it can benefit others. For researchers that are looking for monetary funding, they should state how an organization or institution will benefit from the study. A research study about  video games as storytellers can spark the interest of an education-focused institution which will increase the chance of a researcher to receive funding. 

Researchers should also consider the introduction as the first impression of the concept paper and the study. They should state the main objective and problem they are trying to solve. Try expounding on the title of the concept paper. Researchers can use the title as a guide when creating their thesis statement, in most research, the title is the thesis statement. Consider looking at sample thesis statements to get an idea of how to structure the sentence. Citing this in the introduction will help readers understand the purpose of the study.

The next section of the concept paper will be the background research section. Here, researchers should indicate the related studies that others have made. They should include studies that are closely related to their thesis statement or title. Citing these studies will show the readers that the topic has gained the attention of other experts. The researchers should also cite the limitations of these studies and that the researcher’s work will try to answer some of those limitations. 

An extensive version of this section is mostly found in longer concept papers. Individuals who are trying to make a case for their research and gain funding will need to make an extensive version of this section to provide more information to possible sponsors. They will need to fill this section with a large number of background studies that are relevant to their work. For documents that are only two to three pages long, researchers can cite some studies and state which limitation they are trying to solve.

While the introduction will state the main objective of the study, the objective section will provide all the specific objectives of the research. Researchers should use consistent phrasing when stating the objectives in a concept paper. Use the word “To” at the beginning of each objective statement. Avoid using statements that are in question format. Before the researchers state the objectives, they should restate the thesis statement in a paragraph before the lists of objectives. Most concept paper examples will show a list type objective section. It will be easier for the reader to recognize the objective in this format.

The next step in writing a concept paper is citing the aim and need for the study. After stating the thesis statement in the introduction, the researchers should explain their objectives further in this section. Students can use a method where they address the problems they stated in the previous sections. If the previous sections state that future researchers will need to create video games solely for educational purposes, researchers can write a response in the “aim and need” section of the concept paper. They can state how the researchers will develop a game to measure student’s recall capacity.

The need for the paper simply refers to the importance of the research. While the “aim“ talks about the purpose of the researchers, the need should state the effects of the research on a targeted group or society. Individuals should provide evidence to the claims they will be stating. This will help show their’s and the concept paper’s credibility. They should consider referring to previous researchers that have done an extensive study about the topic.

The research methodology section of the concept paper will include the instruments and measuring devices that the researchers will use. This includes laboratory equipment, computer software, questionnaires, types of tests, and other means of gathering and interpreting data. The researchers should state how they will prepare the tools and how they will authenticate the information. This section should also include the target population, type of data, and the timeline for the research. Researchers should provide all the information of their methodology. Try asking the questions who, what, where, when, and how to write a complete research methodology for the concept paper. Some concept paper outlines can also include a research timeline. This is basically a timeline of how long the research will last.

Similar to other academic documents, a concept paper should include a reference list. The researchers should cite the sources that they used while writing the document. Individuals can also use in-text citations in the aim and need section and background section. When writing the reference list, make sure to use a consistent format. Individuals can look at sample papers to find reference list formats. For students, they should ask their professors which referencing format to use. The common formats are APA, MLA, Chicago, and Harvard styles.

“Using Video Games as Educational Tools to Help High School Students Write Better Essays”

Most high school students dread essay writing homework. Writing assignments often include reading thick books that authors have filled with blocks of text. They will need to do research and reading the blocks of texts can feel exhausting to most students. On the contrary, video games tend to hold a person’s attention longer than any other medium. Despite the debate over the advantages and disadvantages of video games , there have been games that people developed to teach nursing and business students practical skills. There also have been some games that are made using real-life history that teachers can use to teach a class. However, there is a lack of research regarding the correlation between video games and writing abilities. This study will help in understanding the capacity of games to inform students and how they can help in essay writing. The study will help educators create an effective lesson plan in using video games as educational tools to help high school students write better essays.

There have been studies that promote video games as effective educational tools for all education levels. However, there are still many aspects of video games and education that researchers have yet to analyze. The research of Utoyo, Arsa on video games as tools for education concludes that using video games provides an opportunity to improve education due to realistic simulations that only the medium can offer. (Widitiarsa, 2018). The researcher stated that the next step is to design educational video games to create the standards for effective educational games. However, this study does not mention video games as good teaching tools for writing essays or any type of written works.

There have also been reports of educators using video games to teach writing to students. Students were able to write game reviews, autobiographical pieces, and other writing works. The teacher used character images, famous video game quotes, and great writing lines to inspire students to think of essay topics (Jones, 2018). The students that are interested in games were able to freely discuss topics and ideas. They use articles from game journalists to back up their claims during open discussions. This report shows that some educators are already recognizing the ability of video games to act as a teaching tool for writing essays and other written works.

The researchers aim to achieve their objective of using video games as educational tools to help high school students write better essays by answering the following specific objectives:

To analyze the influence of critical thinking in using video games as educational tools to help high school students write better essays.

To assess the influence of student’s writing skills in using video games as educational tools to help high school students write better essays.

To assess the influence of video game genres in using video games as educational tools to help high school students write better essays.

Most high school students often have difficulty with writing assignments. They dread the process of researching and writing down notes. Most students will carry this behavior up until college which can result in having difficulty writing their research papers and dissertation. Some teachers have already addressed this issue by using video game topics to help spark student interests. However, the researchers believe that targeted research is necessary to create an effective lesson plan in using video games as educational tools to help high school students write better essays.

The researchers aim to analyze the influence of critical thinking in using video games as educational tools to help high school students write better essays. The study will test how video games help in the development of critical thinking skills and how they can transfer to better essay writing. This will help educators understand how video games affect a student’s brain and thinking skills. The study also aims to assess the influence of student’s writing skills in using video games as educational tools to help high school students write better essays. The study will take into account the existing writing skills of high school students and observe how video games can help improve the existing skills. This will provide teachers and researchers quantitative data on the extent of how video games can act as writing education tools. Lastly, the study aims to assess the influence of video game genres in using video games as educational tools to help high school students write better essays. The researchers will use different games from different genres to assess how the different genres affect high school student’s writing skills. This will help to understand what type of games teachers should use to help students write better essays.

The researchers will use three different video games from the following genres: The Elder Scrolls IV: Oblivion from the Role-playing genre, The Sims 4 from the Simulation genre, and Firewatch from the Adventure genre to assess using video games as educational tools to help high school students write better essays. 

The researchers will conduct the study on 400 WXY high school students out of a population of 600 high school students. The researchers will take note of the students’ most recent English subject grades. This is to gather data on how existing writing skills can affect using video games as educational tools to help high schools student write better essays. The researchers will divide the students into three groups corresponding to the three video game genres state above. The students will play the games for an hour for a three-week period. After each week, the students will take critical thinking exams that will measure their critical thinking skills.

The researcher will collect primary data from the activities and secondary data from related literature. The researcher will analyze the quantitative data using descriptive and inferential statistics. The quantitative data will be from the assessment of how the different genres influence video games as tools to help high school students write better essays. The researchers will triangulate the qualitative data and report comparisons between the gathered data and existing data. 

Jones, Sarah. (2018, April 2018). Teaching Writing Through Video Games, Part I. Moving Writers. https://movingwriters.org/2018/04/18/teaching-writing-through-video-games-part-i/

Widitiarsa, Arsa (2018). Video Games as Tools for Education.  https://zenodo.org/record/2669725#.YW2VqBxn0uU

Deadline Approaching?

We work 24/7 and we are affordable (from $13.95/page). Our writers, managers and support agents all have been involved in academic ghostwriting for years. We can assist even with the most difficult writing assignment under time constraints.

Writing a concept paper is the foundation of any research study. The document will dictate whether a panelist will approve or decline a research study. This is why individuals should ensure that their concept paper effectively emphasizes the importance of their study. For individuals who feel that they don’t have the writing capabilities to create a concept paper, the writing services from CustomEssayMeister can help. The website offers a variety of services to help students and professionals with their writing tasks. They can find sample papers and how-to guides in essay writing. Students who are stuck in their thesis writing will find these services extremely helpful. Our experienced writers can write concept papers that will spark the interest of a panelist and perhaps get their approval.

more in Writing Guides / Research Paper

• Contents of a Good Research Paper Mar 11, 2019
• How to Write a Research Paper Without Plagiarizing Apr 3, 2019
• Why Citations and Citation Styles Are Important Jun 6, 2019
• What Happened in Tiananmen Square Jun 4, 2019

Let’s get your assignment done!

PADM 885 Research Concept

• Course Description

The course is designed to develop research skills, culminating in the development and approval of a research concept. The research concept approval process is under the direct supervision of the student’s dissertation chair or capstone advisor. The research concept must be written and approved prior to enrollment in dissertation or capstone courses.

For information regarding prerequisites for this course, please refer to the  Academic Course Catalog .

Course Guide

View this course’s outcomes, policies, schedule, and more.*

Requires a student login to access.

*The information contained in our Course Guides is provided as a sample. Specific course curriculum and requirements for each course are provided by individual instructors each semester. Students should not use Course Guides to find and complete assignments, class prerequisites, or order books.

This course requires students to complete a research concept paper, consisting of a problem statement,  literature review, research question, and research design.   This   is designed to lay the foundation for the  student’s  dissertation.  

Course Assignment

Readings, video presentations, and narrated powerpoint presentations.

No details available.

Course Requirements Checklist

After reading the Course Syllabus and  Student Expectations  the  student will complete the related checklist found in  the Course Overview .  

Dissertation Abstract Assignment

The student will write a  one-paragraph dissertation abstract in  current APA form at that  offers a clear and concise summary of his/her planned research project.

The student will complete the official Collaborative Institutional Training Initiative (CITI) training certification. The student will upload a pdf of his/her completion certificate.

Concept Paper: Problem Statement Assignment

The student will write a one- or two-paragraph problem statement in  current APA format that introduces the general topic of his/her research, defining the problem to be addressed, summarizing existing research, exp laining shortcomings of existing research, and concluding with  a focused statement about the contribution the student’s research will make to this problem .

Concept Paper: Annotated Bibliography Assignment

The student will  prepar e  an annotated bibliography in current APA format consisting of at least 30 peer-reviewed academic sources relevant to his/her proposed dissertation research .

Concept Paper: Literature Review Assignment

The student will write a  14-16 page literature review  in  current APA format , based on the literature included in his/her annotated bibliography,  that  explores existing literature rel ated  to the student’s proposed research topic, identif ying the central insights, themes, and/or gaps that support the student’s research proposal .

Concept Paper: Research Question Assignment

The student will write a one-  or two- paragraph  research question  in  current APA format that defines  a clear , feasible, significant, and ethical   research proposal .

Concept Paper: Research Design Assignment

The student will write  a 5-8 page paper in current APA format explaining his/her research design , including  an  explanation  and theoretical justification for his/her selected research method.

Concept Paper: Data Collection and Interpretation Assignment

The student will write a 3 -5 page paper in current APA format explaining the data on which his/her research will be based, including issues related to the method, manner, and feasibility of  data collection ; the population(s), data set(s) or other location(s) from which the data will be collected; and the  coding of data and/or definitions of key terms.

Concept Paper: Final Paper Assignment

The student will  prepare a research concept paper in current APA format that consists of a compilation of revised versions of their: 1) Problem Statement  Assignment ; 2) Literature Review   Assignment ; 3)  Research Question   Assignment ; 4) Research Design   Assignment; 5) Data Collection and Interpretation Assignment. The final research concept paper should incorporate  feedback given to  the  student in all previous assignments and should blend each  of the components of paper into an intellectually coherent whole.   The completed research concept paper should be approximately 30-33 pages.  

The student will give an oral presentation of his or her Concept Paper: Final Assignment. The Oral Presentation must be between 15-20 minutes long and cover all major points of the Concept Paper: Final Assignment.

The student will complete a quiz affirming that he or she has access to the HSOG Doctoral Community Canvas page, and that he or she agrees to be bound to all policies contained therein.

The student will upload screenshots of his or her official correspondence, securing a Chair and Reader for his or her thesis/dissertation. 

Have questions about this course or a program?

Speak to one of our admissions specialists.

Inner Navigation

• Assignments

Have questions?

Are you ready to change your future?

Apply FREE This Week*

Request Information

*Some restrictions may occur for this promotion to apply. This promotion also excludes active faculty and staff, military, non-degree-seeking, DGIA, Continuing Education, WSB, and certificate students.

Request Information About a Program

Request info about liberty university online, what program are you interested in, choose a program level.

Choose a program level

Bachelor’s

Master’s

Certificate

Select a Field of Study

Select a field of study

Select a Program

Select a program

Next: Contact Info

Legal first name.

Enter legal first name

Legal Last Name

Enter legal last name

Enter an email address

Enter a phone number

Full Address

Enter an address

Apt., P.O. Box, or can’t find your address? Enter it manually instead .

Select a Country

Street Address

Enter Street Address

Enter State

ZIP/Postal Code

Enter Zip Code

Back to automated address search

Start my application now for FREE

• Vehicle Technologies Office
• About the Vehicle Technologies Office
• Technology Areas
• Technology Integration
• Reports and Publications

Office: Vehicle Technologies Office FOA number: DE-FOA-0003383 Link to apply:  Apply on EERE Exchange FOA Amount: $42,950,000

The U.S. Department of Energy (DOE) announced $43 million in funding for projects that will advance research, development, demonstration, and deployment (RDD&D) in several areas critical to the future of advanced batteries. The funding will drive innovations in low-cost electric vehicle (EV) battery electrode, cell, or pack manufacturing; improve battery safety and reduce cascading failures; and strengthen the domestic supply chain of inexpensive and abundant battery materials. This funding is aligned with strategies detailed in the U.S. National Blueprint for Transportation Decarbonization , which is a landmark interagency framework of strategies and actions to remove all emissions from the transportation sector by 2050, by advancing battery technologies that can power safe and efficient zero-emission EVs. 

DOE’s Vehicle Technologies Office (VTO) will supply the funding and build on the Office of Energy Efficiency and Renewable Energy’s leadership in RDD&D of new technologies leading to efficient, clean, and affordable mobility options. Topic areas in VTO’s Fiscal Year 2024 Batteries funding opportunity include:

• Improving 12V lead-acid battery service life and performance requirements to meet critical safety features while reducing cost. 
• Developing cell, module, pack, vehicle, or structural strategies that reduce cascading effects of thermal issues that could lead to EV fires. 
• Conducting research and development that would reduce the manufacturing cost at the electrode, cell, or pack level by at least 30% compared to the state of the art, and increasing throughput by at least 50% compared to the state of the art.
• Researching, fabricating, and testing silicon-based lithium battery cells that meet EV battery performance requirements.
• Developing high energy density cathodes containing metal chalcogenide, oxide, or halide materials that surpass the energy density of state-of-the art nickel cathodes. 

As part of this approach, VTO encourages the participation of underserved communities and underrepresented groups. Applicants are highly encouraged to include individuals from groups historically underrepresented in STEM on their project teams.

Learn more about this funding opportunity and other funding opportunities within DOE’s Office of Energy Efficiency and Renewable Energy .

Topic Areas

This FOA has five topic areas:

Topic 1 Improved 12 Volt Lead Acid Batteries for Safety-Critical Electric Vehicle Applications,  focused on improving the service life and performance requirements to meet critical safety features while reducing cost ($10 million).

Topic 2 Develop Vehicle or Structural Level Strategies to Reduce the Likelihood of the Cascading Effects of Electric Vehicle Fires, focused on university-led teams conducting research at the cell, pack, and vehicle level ($3.9 million).

Topic 3 Battery Electrode, Cell, and Pack Manufacturing Cost Reduction, focused on developing improved manufacturing technologies for EV battery electrodes, cells, and packs ($12.5 million). 

Topic 4 Silicon-Based Anodes for Lithium-Ion Batteries, focused on researching, fabricating, and testing lithium battery cells implementing silicon electrodes with a commercially available cathode technology to achieve cell and cost performance targets (more than 350 Wh/kg of usable energy with a cell cost target of less than $70/kWh) ($12.5 million). 

Topic 5 High Energy Density Conversion Cathodes,  focused on developing high energy density battery cells containing metal chalcogenide, oxide, or halide cathodes by solving key challenges for the cathode, electrolyte, electrode integrity, or safety ($4.05 million). 

Additional Information

• Download the full funding opportunity  on the EERE Exchange website.
• For FOA-specific support, contact  [email protected] .
• Sign up for the Office of Energy Efficiency and Renewable Energy (EERE) email list  to get notified of new EERE funding opportunities. Also sign up for the VTO GO! newsletter to stay current with the latest VTO news.

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

• View all journals
• Explore content
• About the journal
• Publish with us
• Sign up for alerts
• Open access
• Published: 26 July 2024

Adaptive hierarchical origami-based metastructures

• Yanbin Li   ORCID: orcid.org/0000-0003-0870-4507 1   na1 ,
• Antonio Di Lallo 1   na1 ,
• Junxi Zhu 1 ,
• Yinding Chi 1 ,
• Hao Su   ORCID: orcid.org/0000-0003-3299-7418 1 , 2 , 3 &
• Jie Yin   ORCID: orcid.org/0000-0002-6297-1262 1  

Nature Communications volume  15 , Article number:  6247 ( 2024 ) Cite this article

2611 Accesses

198 Altmetric

Metrics details

• Applied mathematics
• Mechanical engineering

Shape-morphing capabilities are crucial for enabling multifunctionality in both biological and artificial systems. Various strategies for shape morphing have been proposed for applications in metamaterials and robotics. However, few of these approaches have achieved the ability to seamlessly transform into a multitude of volumetric shapes post-fabrication using a relatively simple actuation and control mechanism. Taking inspiration from thick origami and hierarchies in nature, we present a hierarchical construction method based on polyhedrons to create an extensive library of compact origami metastructures. We show that a single hierarchical origami structure can autonomously adapt to over 10 3 versatile architectural configurations, achieved with the utilization of fewer than 3 actuation degrees of freedom and employing simple transition kinematics. We uncover the fundamental principles governing theses shape transformation through theoretical models. Furthermore, we also demonstrate the wide-ranging potential applications of these transformable hierarchical structures. These include their uses as untethered and autonomous robotic transformers capable of various gait-shifting and multidirectional locomotion, as well as rapidly self-deployable and self-reconfigurable architecture, exemplifying its scalability up to the meter scale. Lastly, we introduce the concept of multitask reconfigurable and deployable space robots and habitats, showcasing the adaptability and versatility of these metastructures.

Similar content being viewed by others

Large-scale modular and uniformly thick origami-inspired adaptable and load-carrying structures

Rigidly flat-foldable class of lockable origami-inspired metamaterials with topological stiff states

Jigsaw puzzle design of pluripotent origami

Introduction.

Versatile shape-morphing capability is crucial for enabling multifunctionality in both biological and artificial systems, allowing them to adapt to diverse environments and applications 1 , 2 , 3 . For example, the mimic octopus can rapidly transform into up to 13 distinct volumetric shapes, mimicking various marine species 1 . In the realm of artificial systems, there has been a range of strategies proposed to create shape-morphing structures, including continuous forms of beams, plates, and shells 4 , 5 , 6 , bar-linkage networks or mechanical kinematic mechanisms 7 , 8 , 9 , 10 , 11 , 12 , 13 , folding or cutting-based origami/kirigami structures 12 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , and reconfigurable robotic structures composed of assembled magnetic or jointed modules 23 , 24 , 25 , 26 , 27 , 28 . These structures have found broad applications in transformable architecture 21 , 29 , reconfigurable robotics 25 , 30 , biomedical devices 8 , 31 , flexible spacecraft 32 , 33 , multifunctional architected materials 20 , 34 , reprogrammable shape-morphing matter 6 , 35 , 36 , as well as deployable structures that can undergo dramatic volume change for convenient storage and transport 15 , 29 , 32 , 33 , 37 , 38 , 39 .

However, despite these advancements, artificial shape-morphing structures have yet to rival their biological counterparts in terms of the diversity of attainable volumetric shapes, as well as the efficiency and autonomy with which such versatile shape morphing can be achieved through simple actuation and control 6 , 23 , 24 , 26 , 27 , 35 , 36 . One of the primary challenges resides in the tradeoff between theoretically allowable versatility of shape-morphing, which encompasses the quantity and diversity/type of reconfigured shapes, and practical controllability in terms of actuation. For instance, while previously reported structures 11 , 23 , 24 , 26 , 27 , 28 , 36 have demonstrated the ability to change into a vast number of distinct shapes, they often require exceedingly complex actuation and control systems. This complexity can render the shape morphing process tedious, time-consuming, and energy-inefficient. On the other hand, certain structures may exhibit simpler reconfiguration kinematics 3 , 5 , 6 , 7 , 15 , 31 , 40 , 41 , 42 , enabling them to feasibly attain desired shapes. However, their specified structural forms may largely limit the achievable reconfigured shapes within few specific categories. These challenges, along with others such as complex reconfiguration kinematics, poor re-programmability, lack of inverse design capability, and limited functionality of the reconfigured shapes, as summarized in Supplementary Table  1 , could considerably impede the broad applications of shape-morphing structures in areas such as reconfigurable architecture, metamaterials, and robotics (see more details in Supplementary Note  1 ). The versatility of shape morphing is intricately linked to a structure’s mobility, i.e., the number of degrees of freedom (DOF). Theoretically, structures with a higher number of DOFs tend to exhibit greater versatility in shape morphing 11 , 23 , 24 , 25 , 26 , 27 , 35 , 36 . However, this very versatility in theory often makes it exceedingly difficult to actuate structures with higher DOFs, considering the potential need for distributed actuation of each DOF 25 .

Conventional rigid mechanism-based origami structures, constrained by their folding interconnections, are limited to morphing between their original and compact states due to one single DOF. This limitation simplifies actuation and deployment but sacrifices the potential for achieving a variety of shapes 12 , 13 , 16 , 18 , 22 , 38 , 40 , 43 . To address this limitation, recent advances have introduced modular origami metastructures composed of assembled polyhedron-shaped modules 26 , 36 , 39 , such as cubes and tetrahedrons, etc. These structures offer more than four mobilities. For example, recent studies demonstrated that a single unit cell consisting of six extruded cubes could transform into four different configurations using four distributed pneumatic actuators to control folding angles 39 . However, when scaling up to a 4 × 4 × 4 periodic meta-structures to achieve similar transformations, it requires a staggering 96 distributed actuators for each DOF 39 , resulting in low actuation efficiency. More recently, we proposed shape-morphing planar kinematic origami/kirigami modules composed of a closed-loop connection of eight cubes 36 . These modules can be manually transformed into over five different configurations via kinematic bifurcation. When assembled into a 5 × 5 array, they theoretically offer over 10,000 mobilities through bifurcation 36 . However, practically, they pose grand challenges in terms of actuation and control. Similarly, discrete kinematic cube-based modules are often assembled into lattice, chain, or hybrid architectures and used in robotic structures with higher DOFs for multifunctional modular reconfigurable robots 25 . Although these modular origami and robotic structures offer enhanced shape-morphing capabilities, they typically require control and actuation systems for each module. This complexity results in lengthy and intricate reconfiguration steps, as well as complex and time-consuming actuation, morphing kinematics, and reconfiguration paths, primarily due to their redundant DOFs 11 , 25 , 26 , 27 , 35 , 36 (Supplementary Table  1 and related discussions in Supplementary Note  1 ).

Drawing inspiration from planar thick-panel origami 12 , 18 , 22 , 36 and hierarchical materials/structures 44 , 45 , 46 , 47 in nature and engineering, here, we propose leveraging hierarchical architecture of spatial closed-loop mechanisms interconnected both within (locally) and across (globally) each hierarchical level to address the versatility-actuation tradeoff in an example system of highly reconfigurable hierarchical origami metastructures. As illustrated in Fig.  1 a, a base or level-1 structure is a spatial closed-loop mechanism consisting of n rigid linkages and n rotational hinges, an n R looped mechanism. Simply replacing each rigid linkage in a k R looped mechanism with the level-1 structure creates a level-2 “ k R” spatial looped flexible mechanism (Fig.  1b ), since each linkage becomes an n R looped mechanism, with k being the number of rotational hinges at level 2 (note that k is not necessarily equal to n ). The rotary hinges can employ origami line folds and the rigid links can take variously shaped structural elements, such as thick plates and polyhedrons (e.g., cubes, triangular or hexagonal prisms) (Fig.  1c ). The polyhedrons can be combinatorically connected at their edges using rotary hinges at each hierarchical level, offering extensive design space for diverse reconfigurable hierarchical metastructures (Fig.  1d – f and Supplementary Note  2 ).

Schematic illustrations of a level-1 metastructure composed of an n R spatial looped mechanism with n rotary hinges and n rigid linkages ( a ) and a level-2 metastructure composed of a “ k R” spatial looped mechanism at level 2 and n R looped mechanisms at level 1 ( b ). c The designs of rotary hinges and rigid linkages in the forms of respective origami line fold and different polyhedrons. d Illustration of two types of reconfigurable metastructures using planar and spatial tessellation of thin plates and prims, respectively. Examples of 3D-printed prototypes of self-reconfigurable level-1 ( e ) and level-2 ( f ) origami-based robotic metastructures actuated by electrical servomotors. Scale bar: 3 cm. The level-1 and level-2 metastructures are composed of closed-loop connections of 8 and 32 cubes, respectively. g Demonstration of the advantages of hierarchical looped mechanism in creating self-reconfigurable metastructures with versatile shape morphing under fewer reconfiguration DOFs (actuated servomotors) than 3.

We demonstrate the unprecedented properties of the metastructures arising from their hierarchical architecture of spatial closed-loop mechanisms. We find that hierarchical closed-loop mechanisms naturally introduce intricate geometric constraints that dramatically reduce the number of active DOFs required for shape morphing, even when involving a large number of structural elements (Fig.  1f, g ). Benefiting from this hierarchical coupling of closed-loop mechanisms, we show that these hierarchical origami metastructures can be efficiently actuated and controlled while achieving a wealth of versatile morphed shapes (over 10 3 ) through simple reconfiguration kinematics with low actuation DOF (≤3) (Fig.  1g ). The proposed construction strategy unlocks a vast design space by orchestrating combinatorial folding both within and across each hierarchical level, relying on spatial closed-loop bar-linkage mechanisms. It effectively overcomes the intrinsic limitations in our previous ad-hoc shape-morphing designs with similar structural elements 36 , including geometric frustrations, large number of DOF, and a lack of generalizability due to the use of units with specific shapes 13 (see Supplementary Note  1.2 for detailed comparison). Compared to the state-of-the-art shape-morphing systems 7 , 8 , 9 , 10 , 11 , 14 , 16 , 18 , 22 , 24 , 25 , 26 , 27 , 28 , 29 , 30 , 32 , 36 , 37 , 39 , 40 , 43 , 48 , our combinatorial and hierarchical origami-inspired design shows superior multi-capabilities, including high reconfiguration and actuation efficiency (requiring less time and fewer transition steps and actuations), simple kinematics and control, high (re)-programmability, a large number of achievable shapes, and potential multi-functionalities (see Supplementary Note  1.1 and Supplementary Table  1 for detailed comparison). We explore the underlying science of versatile shape morphing and actuation in the hierarchical origami metastructures, as well as their applications in self-reconfigurable robotics, rapidly self-deployable and transformable buildings, and multi-task reconfigurable space robots and infrastructure.

Hierarchical origami-based shape-morphing structures with combinatorial design capability

Figure  2a–c and Supplementary Figs.  1 – 3 illustrate the hierarchical approach employed to construct a category of planar thick-panel origami-based shape-morphing structures. In Fig.  2a , the level-1 structure represents an over-constrained rigid spatial bar-linkage looped mechanism, characterized by the number of linkages being equal to or greater than the connected bars. This structure consists of n (where n  = 4, 6, 8) rigid cubes (Fig.  2a , i) serving as linkages interconnected by n hinge joints (i.e., line folds) at cube edges functioning as rotatable bars (see details in Fig.  2a , ii) 36 . These hinges are highlighted by yellow lines in Fig.  2a , iii. An example of a level-1 structure with n  = 8 is shown in Fig.  2a , ii and iii, while additional examples with n  = 4 and 6 are depicted in Supplementary Fig.  1a–c .

a–c Schematics of constructing level-1 ( a ), level-2 ( b ), and level-3 ( c ) reconfigurable and deployable structures using hierarchical closed-loop rigid bar (line hinges)-linkage (cubes) mechanisms (column ii) as different-leveled structural motifs (column iii). The representative morphed architectures with internal structural loops (ISLs) are shown in column iv. d Schematics of selected combinatorial designs by either combinatorically hinging two adjacent cubes at one of the four cube edge pairs at level 1 (i) and level 2 (ii) or flipping any level-1 structure with asymmetric hinge locations on top and bottom surfaces (ii) or combined. e Comparison of the maximum initial structural DOFs of different hierarchical structures composed of 4, 6, and 8 cubes at level 1. f Comparison of the combinatorically designed four categories of level-2 structures in ( b ) (insets and Supplementary Fig.  6 ) on the number of combinatorial level-2 hinge connections, reconfiguration modes, and morphed configurations with ISLs.

The connectivity between the cubes, namely the placement of the joints, dictates the spatial folding patterns of the structure (Supplementary Figs.  1 and 2 ). Broadly, the deployment follows four fundamental structural motifs, defined here as the mechanism-based connecting systems used to construct each leveled structure: one 2R chain-like mechanism and three 4R, 6R 10 , 18 , 22 , or 8R closed-loop mechanisms 41 , where n R denotes mechanisms with n rotational links and n rotatable (R) joints (see Supplementary Fig.  3 , and detailed definitions in Supplementary Note  3 ). For two adjacent cube faces, four potential edge locations exist to accommodate hinge joints (Fig.  2d , i). Consequently, a structure with n cubes theoretically allows for 4 n combinatorial sets of connections, offering an extensive design space for level-1 structures (Supplementary Fig.  4 ). Specially, we define this multiple design possibility by the placement of hinge joints in all leveled structures as their combinatorial design capability. As illustrated later, the combinatorial design capability of our proposed systems can be considerably expanded given the structural asymmetries and the multiple choices of structural motifs. Depending on the chosen connectivity, level-1 structures composed of n cubes exhibit an initial maximum number of 2 ( n  = 4), 3 ( n  = 6) and 5 ( n  = 8) DOFs (Fig.  2e ), which can be utilized for morphing into a diverse array of distinct 3D architected structures (as exemplified in Fig.  2a , iv, and further elaborated in Supplementary Fig.  1 and Supplementary Movie  1 ).

By substituting the higher-level linkages with the lower-level basic or hierarchical structures (e.g., Fig.  2a–c , i–iii and Supplementary Fig.  3a, b ) in the four fundamental structural motifs (2R, 4R, 6R, and 8R), we can create a class of flexible spatial hierarchical mechanism-based origami structures by combinatorically choosing any type of the n R linkages as different-level structural motifs (Supplementary Fig.  3c ). Notably, the term “flexible spatial mechanism” refers to mechanical mechanisms with bars and linkages arranged in 3D space, where the length of linkages is not fixed and varies during reconfiguration. For example, Fig.  2c , ii illustrates a level-3 structure comprising 8R linkages at level 1, 4R linkages at level 2, and 2R linkages at level 3, denoted as <8R, 4R, 2R>. The sequence from left to right corresponds to the structural motifs used from lower-level structure to higher-level structure.

The associated level-2 structure is depicted in Fig.  2b and denoted as <8R, 4R>. Additional examples of hierarchical origami structures with varying numbers of cubes at level 1 are presented in Supplementary Figs.  2 , 5 and 6 . Upon deployment, these structures can continuously transform into a multitude of intricate architected forms featuring internal structural loops (ISLs): internal voids within reconfigured architected structures enclosed by boundary structural components (as illustrated in Fig.  2a–c , iv, Supplementary Figs.  5c and  6 ). These ISLs efficiently facilitate different-level kinematic bifurcations, where a singular configuration state triggers a sudden increase in structural DOFs, leading to additional subsequent reconfiguration branches. This is in sharp contrast to the counterparts composed of four cubes at level 1, which are primarily limited to simple chain-like configurations (Supplementary Fig.  2a ) despite having a greater number of initial DOFs in the hierarchical structures of <4R, 4R> and <4R, 4R, 4R> (Fig.  2e ).

Moreover, the design space of hierarchical structures can be considerably expanded by combinatorically (1) adjusting the connectivity at higher-level bars (Fig.  2d , ii) and (2) manipulating structural asymmetries at the lower-level linkages given the asymmetric patterned joints on the top and bottom surfaces across the thickness, e.g., simple upside-down flipping (see Fig.  2d , ii for an example of level 2 structure). As an illustration, the insets in Fig.  2f and Supplementary Fig.  5 show four selected categories of combinatorial <8R, 4R> level-2 structures created by flipping the level-1 8R linkages and modifying the connections at the level-2 joints. By employing combinatorial design strategies involving mechanism hierarchy, spatial fold patterning across multiple levels of bars, and folding asymmetries in the linkages, we can generate an extraordinary vast design space encompassing millions of configurations, even within a simple level-2 structure (see analysis in Supplementary Note  2 ).

Compared to state-of-the-art 2D 14 , 16 , 40 , 48 and 3D origami designs 12 , 18 , 22 , 36 , 42 including our previous ad-hoc design of specific tessellated closed-loop mechanism of cubes 36 , this hierarchical approach offers several advantages: Firstly, it largely broadens the range of designs by allowing combinatorial connections within and across each hierarchical mechanism, which are either disabled or severely limited in previous studies 12 , 18 , 22 , 36 , 42 . Secondly, it effectively avoids geometric frustration in our previous ad-hoc designs 36 , which refers to structural constraints arising from deformation incompatibility during deployment 44 , 45 . This avoidance is made possible by the compatible reconfigurations of differently leveled spatially looped mechanisms (Fig.  2a–c , ii). Thirdly, this fundamental design principle establishes a versatile structural platform that can be applied to various shaped building blocks, overcoming the limitations in our previous ad-hoc designs 36 and other studies associated with specific structural elements 22 , 26 , 36 , 38 , 39 , 42 . Fourthly, it possesses the intrinsic benefit of structural hierarchy 46 , 47 , 49 , favoring higher-level structures with greater diversity and quantity of actuated reconfigured shapes under simple control and actuation.

Within this extensive design space, designs of particular interest are those that exhibit high reconfiguration capabilities via collision-free kinematic paths involving only a few active structural DOF during shape-changing processes. Such designs enable rich shape-morphing capability with simple and reliable control. After comparison (Supplementary Note  2 ), we identified an optimal category composed of four identical <8R> type of level-1 structures (see Category 1 in Fig.  2f and Supplementary Fig.  5b , with detailed definitions provided in Supplementary Notes  2 and 3 ) to showcase their extensive shape-morphing behavior under few active DOF. These designs boast the highest structural symmetries and the largest number of ISLs, facilitating bifurcation and shape diversity (Fig.  2f ).

Continuously evolving versatile shape morphing

Figure  3a provides a comprehensive view of the shape-morphing configurations diagram of one exemplary optimal <8R, 4R> level-2 structure selected from Category 1 in Fig.  2b (see Fig.  3a , i for its hierarchical design details). These structures were fabricated by assembling the 3D-printed rigid square facets (in white) into hollow cubes via interlocking mechanisms and flexible printed line hinges made of rubber-like materials (in black) (Supplementary Fig.  7a , see “Methods” and Supplementary Movie  2 for details). This design not only facilitates straightforward assembly but also allows for easy disassembly and reassembly of facets into hierarchical structure (Supplementary Fig.  7b–d ). For clarity, configurations with folding angles that are multiples of 90° are displayed since these angles correspond to kinematic bifurcations, as discussed later.

a Shape-morphing configurations diagram in the 3D-printed prototype exhibiting hierarchical transition tree-like features. The branches in the transition tree of represent the bifurcated configurations. Scale bar: 3 cm. b The variation of flexible level-2 link length with the opening angle of hinges during the shape transition from node M D to M E , and node M E to M F in reconfiguration loop 1 in ( a ). Inset shows the eigenvalues v kk as a function of the rotating angle in both level-1 and level-2 structures. c The relationship between the number of reconfiguration paths and the number of kinematic bifurcation configuration states for the combinatorically designed category I–III level-2 systems. d One selected combinatorial design of the shape-morphing level-2 structures by rearranging the level-1 hinges (i), and some of its representative reconfigured shapes (ii–v). Scale bar: 3 cm. e Comparison among the total number of hinges, the number of rotated joints, and the number of reconfiguration DOFs during the reconfiguration loop from node M A to M F and back to M A in ( a ).

With the inherent capacity for versatile shape changes provided by the level-1 linkage structure (Supplementary Fig.  7b ), the level-2 structure can continuously evolve, adopting various representative complex architectures along multiple reconfiguration paths (indicated by different colored lines in Fig.  3a ). Notably, these shapes bear a striking resemblance to trucks, trophies, tunnels, shelters, and various architectural structures (see more details in Supplementary Fig.  8 and representative reconfiguration processes in Supplementary Movie  3 ).

To systematically represent all reconfigured shapes and their corresponding shape transitions in Fig.  3a (ii), we employ a data-tree-like diagram (Supplementary Fig.  9 ), inspired by graph theory used in computer science to elucidate logical relationships among adjacent data nodes 50 (Supplementary Note 4 ). In this diagram, both nodes and line branches are assigned specific physical meanings, signifying individual reconfigured shapes and the relative shape-morphing kinematic pathways connecting them. As shown in Fig.  3a and Supplementary Fig.  9 , starting from a compact state (node M A ), the analyzed level-2 structure can traverse a closed-loop shape-morphing path (termed reconfiguration loop 1, RL-1, or a parent loop). Along this path, it transitions from simple chain-like structures (e.g., node M A  → M B  → M C  → M D ) to intricate architectures featuring ISLs (e.g., node M D  → M E  → M F ). Subsequently, starting from node M E with ISLs, it can further transform into nodes M F , M 5 , M 6 , or return to M D ). Theoretically, this continuous evolution in shape arise from the varying link lengths of the flexible level-2 linkage as line folds exhibit changing folding angles (Fig.  3b and Supplementary Fig.  11 , see the analysis in Supplementary Notes  5 – 7.1 , which examines length variations in level-2 links during two representative shape-morphing processes from node M D to M E and from node M E to M F ).

Benefitting from both chain-like and closed-loop mechanisms embedded in the morphed structural configurations, the parent loop gives rise to several subtrees (e.g., at node M A , M B or M 2 , M E , and M F ). These subtrees, in turn, branch into more paths through kinematic bifurcations (e.g., at node M 11 , M 15 , and M 17 ), as depicted in the inset of Fig.  3b . These bifurcations can be accurately predicted based on the number of null eigenvalues v kk in the kinematics model (see Supplementary Note  7.2 for detailed theoretical analysis). Importantly, node M 6 and node M 10 , located in different subtrees, are interconnected to form another reconfiguration loop (i.e., RL-2). This allows for direct transformation between two configurations or nodes that traverse different subtrees efficiently, without the need to return to the initial configuration and repeat redundant transforming steps, as required in previous reconfigurable structures 11 , 14 , 16 , 23 , 24 , 25 , 26 , 28 , 36 . Comparable hierarchical transition tree structures featuring bifurcated branches and interconnected nodes are observed in most of the four categories of other combinatorial <8R, 4R> level-2 structures (Supplementary Fig.  11 ). These structures are obtained by rearranging multilevel joint locations on top or bottom surfaces or by flipping the level-1 linkage (as seen in the level-2 representative in Fig.  3d and Supplementary Fig.  7d , e ). Consequently, a multitude of versatile and distinct morphed configurations are generated (Supplementary Figs.  12 and 13 ) based on differing hinge connectivity.

Additionally, for all combinatorial designs (Supplementary Fig.  5b ), we observed that the number of reconfiguration paths increases approximately linearly with the number of bifurcated nodes or configurations (Fig.  3c ). Notably, starting from a defined fold pattern, the same level-2 structure can generate nearly 10 3 reconfiguration paths with approximately 100 bifurcation nodes, thereby bestowing extensive shape-morphing capabilities (see analysis in Supplementary Note  8 ). In comparison to previous designs 12 , 16 , 18 , 22 , 26 , 29 , 31 , 38 , 39 , 40 , 43 , 48 that offer only a few shape-morphing paths from a defined fold pattern, our hierarchical design strategy enables a high number ( N  ~ 10–10 3 ) of kinematic transitions, demonstrating substantial versatility in generating numerous shapes and architectures.

Given that each reconfigured shape in Fig.  3a is defined by internal fold rotation angles that are multiples of 90°, we can accurately represent each shape by collecting spatial vectors v of the body center coordinates of all structural elements into a shape matrix M (see “Methods” for details). This matrix takes the explicit form M  = ( v 1 , v 2 , v 3 , …, v n ) (with n  = 32 for the level-2 structures shown in Fig.  3 and Supplementary Fig.  5 , see “Methods” and Supplementary Note  4 for details). Consequently, we can systematically annotate all reconfigured shapes in Fig.  3a using their corresponding shape matrices M k (with k as the shape index, see inset in Fig.  3a and Supplementary Fig.  9 ). Once the initial shape matrix M A is known, we can theoretically determine all the reconfigured shapes of the level-2 structure in Fig.  3a accordingly (see “Methods” for details). Importantly, this annotation approach is generalizable and can be applied to all other hierarchical origami metastructures presented in this work.

Remarkably, despite the level-2 structure’s total of 36 joints, only a small number of them are needed to drive the shape-morphing process, referred to as active reconfiguration DOF (Fig.  3e ). For example, when considering the multistep shape-morphing process from node M D to node M A , i.e., M D  → M E  → M F  → M A in Fig.  3a , it exhibits only 2, 2 and 1 DOF, respectively, even though it involves the rotation of 16, 8, and 24 joints (Fig.  3e and more details in Supplementary Figs.  14 and 15 ). This is in contrast to our previous ad-hoc design of cube-based reconfigurable metastructures 36 . Despite the presence of multiple closed-chain loops, they often function as independent units that barely couple with each other during shape morphing due to the specific architecture design of these metastructures, which results in high mobilities over 10,000 36 , making it impossible for control and actuation. In contrast, the reduction in active joints in this work is due to the specific interconnectivity of the looped level-1 and level-2 structures as geometric constraints, which dramatically reduces the number of active joints required while enabling high reconfigurability. Additionally, the multilevel closed-loop interconnectivity simplifies the control of shape-morphing paths in terms of simple transition kinematics, as demonstrated below.

Simple transition kinematics during shape morphing

The transition kinematics describes the quantitative relationship among the folding angles during the shape morphing of hierarchical structures. In Fig.  4a , we utilize the transformation matrix T (d, γ) to describe the relative spatial relationship of the four links, where d is the shortest distance between adjacent joints, and γ is the opening angle between adjacent cube-based links, as shown in Fig.  4b, c and Supplementary Fig.  16 . For a looped mechanism, it holds that \({\sum }_{i=1}^{m}{{{{\bf{T}}}}}_{i}={{{\bf{I}}}}\) , where m  = 8 and m  = 4 for the level-1 and level-2 links, respectively, and I is the identity matrix (see Supplementary Note  6 for details). With such simple equations, we can readily derive the relationship among the joint angles for all the transition paths using the local Cartesian coordinate systems presented in Fig.  4c (see Supplementary Note  7.1 for details).

a Schematics of level-2 structures with labeled hinge connections on top and bottom surface. b Schematics of the opening angles γ kj ( k , j are integers with 1 ≤  k  ≤ 4 and 1  ≤  j  ≤ 8 denote the link and hinges opening angles, respectively) between adjacent cubes in level-1 structure. c Construction of eight local coordinate systems for the 8 hinges of level-1 structure. d The reconfiguration kinematics from node M 7 (i) to node M 13 (iii) in Fig.  3a, b : the involved shape-changing details of level-1 link #1 and #3 (ii) and variations of the rotating angles for all folds (iv). Scale bar: 3 cm. e The reconfiguration kinematics from node M 15 (i) to node M 21 (v) by bypassing node M 25 (iii) in Fig.  3a, b : the involved shape-changing links #1 and #2 for the process from node M 15 to M 25 (ii) and links #2 and #4 for the process from node M 25 to M 21 (iv) and variations of all folds during these two processes (vi). Scale bar: 3 cm. f Low reconfiguration DOFs for the reconfiguration process in ( d ) (1 DOF) and ( e ) (1 or 2 DOF(s)).

To illustrate the simplicity of transition kinematics, we select two representative reconfiguration paths (node M 7  → node M 13 and node M 15  → node M 21 in Fig.  3a ) that transform from simple chain-like structures to complex architectures with ISLs (“Methods”). Figure  4d, e shows their detailed transition kinematics for these paths. It is observed that both shape-morphing paths involve only local and stepwise transition kinematics. For example, when transitioning from node M 7 to M 13 (Fig.  4d , i and iii), only the joints in link #2 and #4 (Fig.  4d , i) are engaged in sequential rotations (Fig.  4d , ii), while the remaining joints in link #1, link #3, and level-2 joints remain stationary (Fig.  4d , iv) (see “Methods” for details). Similarly, the reconfiguration kinematics from node M 15 to M 21 , bypassing node M 25 , follows a straightforward linear angle relationship, as shown in Fig.  4e , i–vi. Despite these two reconfiguration processes representing the most complex shape morphing (see more details in Supplementary Figs.  17 and 18 ), they can be achieved using simple kinematics-based control. Moreover, Fig.  4f shows that the number of active DOFs for each step remains below 3 during these two reconfiguration processes, thanks to the specific looped interconnectivity of hierarchical structures. This is superior to previous designs, which either featured condensed 11 , 12 , 14 , 16 , 18 , 22 , 26 or completely discrete internal connections 25 , 27 .

Given the unveiled simple transition kinematics of hierarchical structure and the low number of active DOFs during shape morphing, next, we explore and demonstrate their potential applications such as autonomous robotic transformers with adaptive locomotion, rapidly deployable self-reconfigurable architectures, and multifunctional space robots.

Autonomous multigait robotic transformer

To achieve autonomous shape morphing in the hierarchical origami structure, we utilize servomotors to actuate the active joints, while passive joints are secured using metal pins (Fig.  5a , i). These servomotors are powered by onboard rechargeable batteries and controlled through a customized circuit board equipped with a Bluetooth signal receiver (Fig.  5a , ii, see more details in “Methods” and Supplementary Note  9 ). This setup enables untethered shape morphing via a developed remote control system (Fig.  5a , iii, see more details in Supplementary Figs.  19 – 21 and Supplementary Movies  4 and  8 ).

a Schematics of untethered actuation design details for the level 1 eight-cube-based structure: 5 electrically powered servomotors for active hinge rotation (i), onboard power system and Bluetooth wireless receiver to conduct reconfiguration order (ii) from customized remote control software (iii). b Demonstrated untethered shape morphing in the level-1 structure through looped mechanisms. c – e Shape transformation in level-1 structure for multigait locomotion. Scale bar: 3 cm. c Forward (i) and sideway locomotion (ii). d Locomotion gait switch from reconfiguration to legged walking; e Legged walking with carried payload on flat surface (i) and 10°-sloped surface (ii). f Demonstration of the specific positions of 22 active servomotors and the rolling locomotion of level-2 structure. Scale bar: 3 cm. g Locomotion speeds of both level-1 and level-2 structures in ( c – f ).

Thanks to the specific kinematics, even though there are a total number of 8 joints in a level-1 structure and 32 joints in a level-2 structure, only 5 (Fig.  5a ) and 22 (Fig.  5f ) servomotors are needed to accomplish all the reconfiguration paths in these structures (Fig.  5b–e in level 1, and Figs.  5 f and 6a–c in level 2, respectively, see details in Supplementary Fig.  22 ). Importantly, the number of active servomotors involved in the reconfiguration paths does not exceed 3 (Fig.  6d ). For the level-1 structure, it can rapidly and continuously transform from the compact planar state to 6R and 8R-looped linkage configurations via looped mechanisms within a few seconds (Fig.  5b and Supplementary Movie  4 ). Additionally, it can assume simple 2R chain-like configurations via chain-like mechanisms (Fig.  5c ).

Self-deployment into bridge and/or shelter-frame-like ( a ) and fully open 4-story building-like structures ( b ) with high loading capacity of over 10 kg ( c ). Scale bar: 3 cm. d Comparison among the total number of hinges, the total number of servomotors, the rotated hinges, and the actively actuated servomotors during the shape transformation shown in ( b ).

Next, we delve into harnessing active shape morphing for autonomous robotic multigait (Fig.  5c–e ) and rolling (Fig.  5f ) locomotion. By following the chain-like reconfiguration loop path (Supplementary Fig.  7b ), the level-1 structure can repeatedly transform its body shape to achieve impressive multigait robotic locomotion. For instance, it can perform forward or backward locomotion (one cycle is shown in Fig.  5c , i) at a rapid speed of approximately 1000 mm/min (3.07 body length/min) (Fig.  5g ). Alternatively, it can change its movement direction from forward motion to sideway motion (Fig.  5c , ii) or switch its reconfiguration locomotion mode to a bipedal crawling mode (Fig.  5d and see more details in Supplementary Fig.  19c ). Moreover, it is capable of carrying some payload (around 1 kg, equivalent to its self-weight) and climbing sloped surfaces (10°, Fig.  5e ) at reduced speeds of approximately 225 mm/min and 190 mm/min (Fig.  5g ), respectively. Furthermore, a similar chain-like reconfiguration allows us to demonstrate rolling-based mobility in the level-2 structure (Fig.  5f and Supplementary Movie  5 ) at a speed of about 600 mm/min (Fig.  5g ).

Rapidly deployable and scalable self-reconfigurable architectures

Moreover, the compact level-2 structure can effectively self-transform and rapidly deploy into architectural forms resembling bridges, tunnels, and shelters (Fig.  6a, b and Supplementary Movie  6 ), both with and without internal looped structures. This transformation occurs within 2 min, a notable advance compared to previous studies that required several hours and complex algorithms 11 , 23 , 24 , 25 , 26 . Additionally, it can rapidly self-deploy into a fully open multi-story building-like structure, expanding its occupied volume fourfold (Fig.  6b , v). It can also quickly revert to a compact large cube (Fig.  6b , iv and Supplementary Movie  6 ). Due to its specific structural features (Supplementary Fig.  23 , see more details in Supplementary Note  10 ), the reconfigured level-2 structure can bear substantial loads without collapsing, such as approximately 13 kg (over 3.5 times its self-weight) for the bridge- or tunnel-like structures and about 10 kg (over 2.5 times its self-weight) for the multi-story structure (Fig.  6c ).

Notably, during the self-deployment from a compact planar structure to a complex multi-story open structure in Fig.  6b , the number of active motors remains low, never exceeding 3, despite the total number of 36 joints and 22 motors (Fig.  6d ). For example, during the reconfiguration from the compact cube to the fully open structure (Fig.  6b , iv–v), only 2 active servomotors drive the rotation of 16 joints (Fig.  6d ), demonstrating high reconfiguration efficiency.

As proof of concept, we demonstrate that these spatial hierarchical mechanism designs can be up-scaled to meter-sized buildings by assembling heavy-duty cardboard packing boxes (box side length 0.6 m). Starting from flat-packed cardboards with minimal space requirements, they can be rapidly assembled for easy deployment and reconfiguration into various structurally stable meter-scale tunnels, shelters, and multi-story open structures (Fig.  7a and Supplementary Movie  7 ). Remarkably, the total volume occupied by the deployed multi-story open architecture is 200 times larger than the initial volume of the flat-packed cardboards (Supplementary Fig.  24 ). Collectively, these properties make the proposed design promising for potential applications as temporary emergency shelters and other autonomously rapidly deployable and reconfigurable temporary buildings.

a Meter-scale demonstration of deployable, shape-morphing architectures using cubic packaging boxes (side length of 60 cm). Scale bar: 30 cm. b Schematics of potential conceptual applications in versatile reconfigurable space robots and habitats.

The hierarchical and combinatorial designs in both the links and joints at multiple levels of hierarchical structures provide an extensive design space for creating various spatial looped folding patterns and architected origami-inspired structures capable of shape morphing. It creates hierarchical origami-based metamaterials with (1) fewer active reconfiguration mobilities, (2) simple reconfiguration kinematics to facilitate practical control and actuation, and (3) rich shape-morphing capability adaptable to various applications. The hierarchical architecture couples the closed-loop mechanisms within and across each hierarchical level. Despite the large number of joints involved, the hierarchical looped mechanisms inherently impose geometric constraints that dramatically reduce the number of active DOFs required for shape morphing. This reduction greatly simplifies both actuation and control without sacrificing rich shape-morphing capability, which previously required the actuation of each DOF individually in reconfigurable origami metamaterials and robots. It also enables the feasibility of inverse designs, allowing for imitating target shapes and structures (Supplementary Figs.  20 ,  25 and  26 , see theoretical details in Supplementary Note  11 ).

Our design strategy combines structural hierarchy with over-constrained looped kinematic mechanism without considering elastic deformation in the hinges and cubes. Practically, the elastic deformation or slack, especially in the hinges, could cause the system to be floppy or potentially deviate from the desired non-bifurcated and/or bifurcated kinematic paths. As demonstrated in the multimaterial 3D-printed level-2 structure in Fig.  3a , the soft hinges are printed thin with little stiffness to ensure almost free rotation. Thus, in addition to bending for rotation motion, the hinges also undergo certain twisting deformation, potentially causing the structure to deviate from their ideal kinematic paths. However, deviations occur only during the complex reconfiguration processes, e.g., from configuration M 7 to M 13 in Fig.  3a . Such deviations are suppressed when the reconfiguring structure exhibits structural symmetries, e.g., from configuration M D to Configuration M E in Fig.  3a preserving x - y and z - y plane symmetries. The slack can be avoided by fabricating hinges with a low ratio of bending stiffness to twisting stiffness. This will help to suppress its twisting deformation to follow the kinematic paths without making the structure overly floppy. For systems fabricated with high-precision rigid links and hinges, slack or elastic deformation can be minimized or eliminated, as demonstrated in the prototype of both level-1 and level-2 structures with 3D-printed rigid cubes and rigidly rotatable hinges in Fig.  5a . Similar to studied 2D rigidly foldable origami structures, the reconfiguration kinematics of the system becomes energy scale independent. Thus, the system can rigorously follow its bifurcated reconfiguration kinematic path via fewer number of actuation hinges to smoothly reconfigure into all desired configurations without any locking issues as demonstrated in Figs.  5 and 6 .

We note that there are several limitations of this work. First, the load bearing capacity of some reconfigured 3D architectures is still limited, which could hinder their practical engineering and structural applications, especially at meter scales. The load bearing capacity is dependent of not only the transformed architectures (see the free body diagrams of force analysis for example in Supplementary Fig.  23 ), but also the bending stiffness of both cubes and hinges and the structural designs of the hinges. The hinges are imitated with 3D-printed soft rubber-like materials or tapes with low bending rigidity that facilitate the bending and rotation motion but sacrifice the load-carrying capabilities. The load bearing capacity could be improved by using stronger materials with high bending rigidity or locking hinges or devices at either 90° or 180° folded angles. Second, the shape-morphing capability for robotic applications is limited to multi-gait motion demonstrated in this work. How to leverage the rich shape-morphing capability for diverse and adaptive robotic locomotion in unstructured environments remains to be uncovered. Third, the demonstration of self-deployment and self-reconfiguration is limited to centimeter-scale prototypes while the meter-scale demo is done manually due to the limitation of both power and servomotors. At large scales, the heavier self-weight of cubes cannot be neglected, which requires high-torque servomotors and high-power batteries to generate sufficient torque output to counter the gravity and drive the folding.

Moving forward, these limitations also open new opportunities for future researches in morphing matter. First, this work explores only a small region of the tremendous design space in morphing matter to showcase its potential. The vast combinatorial folding patterns arise from the combinatorial connections in the base units, as well as within and across each hierarchical mechanism (Supplementary Fig.  3 ). These combinatorial hierarchical mechanisms are generalizable and can be applied to construct similar reconfigurable hierarchical metastructures composed of any shape-morphing spatial closed-loop mechanism for easy actuation and control yet rich shape morphing. For example, the cube units can be replaced by other composed geometrical shapes, such as thick plates with substantially reduced thickness dimension, tetrahedrons, and triangular-shaped prisms, or extended to genuine volumetric 3D structures (examples are provided in Supplementary Figs.  27 and 28 , with more details in Supplementary Note  12 ).

Second, this work focuses on exploring the reconfiguration kinematics of the hierarchical origami systems by modeling the system as idealized hierarchical rigid mechanisms and neglecting the deformation in both the cubes and hinges. However, in scenarios when such elastic deformation are non-negligible, similar to the non-rigidly deformable origami metamaterials in origami engineering, the over-constrained looped kinematic mechanisms become energy scale dependent, considering the potentially involved complex deformation in the cubes, hinges, and architectures during reconfiguration such as bending, stretching, twisting, and shearing or combined. Consequently, it will transform the rigid mechanisms into both reconfigurable and deformable architected materials and structures, which couples kinematics with mechanics. Such coupling will enrich new kinematics, mechanics, transformed configurations, reconfiguration paths, and reprogrammable mechanical behaviors such as multistability and stiffness anisotropy. Specially, how the energy scale affects the kinematic bifurcated paths and how the coupled kinematic bifurcation and elasticity change both the reconfigurations and mechanical responses of bifurcated mechanical metamaterials remain to be uncovered. We envision such studies could also find broad applications in reprogrammable mechanical computing, mechanical memory, and mechanical metamaterials.

Third, considering these multi-capabilities in conjunction with scalability, modularity, and disassemblability, we envision diverse applications in robotics, architecture, and even in space. Figure  7b conceptually illustrates potential applications in multitask adaptive shape-morphing space robots and habitat (Supplementary Movie  8 ). The hierarchical origami architectures could be deployed with largely increased exposed surface areas for enhanced solar energy harvesting, and reconfigured to avoid debris collision or accommodate more docking stations. It could also serve as reconfigurable space habitat or be des-assembled into modular robots for multitask exploration. For large-sized structures, the feasibility of actuation in a space environment is considerably higher, primarily due to the absence of gravity and the absence of ground-based collisions that can impede complex shape-morphing processes on Earth.

Sample fabrication of cube-based origami structures

To demonstrate the shape morphing in cube-based origami structures, we used two ways to fabricate and assemble the hollow cubes. One is for quick shape-morphing demonstration by directly 3D printing individual cubes with cube size of 2 cm (Stratasys Connex Objet-260 with stiff materials of Vero PureWhite) and connecting them with adhesive plastic tapes (Scotch Magic Tape, 6122) as free-rotation hinges (Supplementary Figs.  5 ,  8 and  11 – 13 ). The other is for easy assembly and disassembly demonstration by 3D printing Lego-like pieces of thin rigid plates (Fig.  3 ). Two types of thin plates were printed (Supplementary Fig.  7a ): one is a thin rigid plate with interlocking teeth (Vero PureWhite) for assembling into a hollow cube, the other is a connection piece composed of two connected thin rigid plates with soft hinges made of rubber-like materials (Agilus-black) through 3D multimaterial printing. The connection piece is used to connect two neighboring cubes at any selected hinge locations with the soft hinges facilitating the free rotation of cubes. The cube size is 3 cm.

Fabrication of autonomous robotic transformers

The cubes were 3D-printed with ABS printing materials (QIDI Tech X-Max 3D printer) with cube size of 81.5 mm and mass of 40 g. To ensure the compact contacts between the 3D-printed cube components, we created open areas at the joints positions and use the U-shaped bracket to hold electronic elements (Fig.  5a , i). Each motor (DSservo RDS3225) was powered by a 3.7 V LiPo battery and controlled via its specific control board (Adafruit ItsyBitsy nRF52840 Express). Additional chips were incorporated for accommodating the JST connector for the battery (Adafruit Pro Trinket LiIon/LiPoly Backpack Add-On) and for adaption of the supply voltage (SparkFun Logic Level Converter—Bi-Directional). The control boards were identified by a numeric ID and communicated with each other via Bluetooth by following a serial framework, where each controller receives the information from the previous one and sends them to the next one. More details can be found in Section S10 of Supplementary Information.

Fabrication of meter-scale samples

The cubes used in the meter-scale shape-morphing architectures in Fig.  7a were heavy-duty cardboard packing boxes (Recycled Shipping Box, Kraft) with dimensions of 0.6 m × 0.6 m × 0.6 m. Boxes were connected using the fiber-reinforced ultra-adhesive tape (BOMEI PACK Transparent Bi-Directional Filament Strapping Tape).

Fundamental principles governing the shape transformation

Given the mechanical kinematic mechanism’s structural features, the core of the shape transformations in these structures involves changes in the spatial positions of specific structural elements resulting from the directional rotations of internal hinges and their interconnections. Technically 10 , 22 , 51 , this operation can be mathematically modeled using a rotation matrix t (see details in Supplementary Note  4.2 ). Thus, the shape transformations of any leveled structures can be denoted as:

where M ′ represents the transformed shape from shape M , with both M and M ′ reflected in Fig.  3a and Supplementary Fig.  9 as M k , and t represents the mathematical operations between them. In our analysis, we initially build a fixed global Cartesian coordinate system at the bottom center of the original shape (see the inset at the initial shape in Fig.  3a , ii). Subsequently, we construct a local coordinate system at each fold to derive the body center coordinates of the rotated cube structural components (Supplementary Fig.  10a, b ) in each shape-morphing process. Mathematically, we can thus determine the new positions of the rotated cubes as follows:

where v n_local and v n_new represent the body center vectors of cube # n before and after shape morphing, respectively, in the local and fixed global coordinate systems. t n is a general functional form including all directional rotations of cube # n (Supplementary Fig.  10b–e ), see the systematic analytical details in Supplementary Note  4.2 . d n is the translational vector between the fixed global coordinate system and the local coordinate system of cube # n . Note that all shape matrices of the initial and reconfigured shapes are described in the fixed global coordinate systems.

We validate the theoretical framework by modeling the shape-morphing process of reconfiguration loop 1, i.e., from the initial shape M A to shape M F , passing through shapes M B , M C , M D and M E . The shape matrix of the initial shape is determined first in the fixed global coordinate system. Based on Eqs. ( 1 ) and ( 2 ), we rationally derive the new positions of the rotated cubes in new shapes accordingly. Specifically, we analyze the process from morphing from shape M D to shape M E , where a total of 24 cubes are involved. To provide a representative example, we select cube #20 and theoretically derive its new spatial positions. Subsequently, we compare these derived solutions with experimental results to validate our proposed theoretical framework.

Starting from the initial shape M A , we derive the shape matrix of M D , as expressed in Eq. ( 3 ). Consequently, in the fixed global coordinate system, we obtain the explicit spatial vector for cube #20 \({{{{\boldsymbol{v}}}}}_{20}^{{{{{\bf{M}}}}}_{D}}\) with \({{{{\boldsymbol{v}}}}}_{20}^{{{{{\bf{M}}}}}_{D}}={(1,3,1)}^{T}\) . During the shape-morphing process, cube #20 undergoes rotation along the x- axis within the locally built coordinate systems (Supplementary Fig.  10a , iv). To derive its new positions, we first calculate its spatial vector in the local coordinate systems, represented by \({{{{\boldsymbol{v}}}}}_{20\_local}^{{{{{\bf{M}}}}}_{D}}={(1,1,1)}^{T}\) . Utilizing a 90° x -directional rotation, we then derive its new coordinates in the global coordinate systems using Eq. ( 2 ) with explicit derivation details as:

Within the built fixed global coordinate systems, we extract the experimental result pertaining to the spatial position of cube #20 in the global coordinate system, denoted as \({{{{\boldsymbol{v}}}}}_{30}^{{{{{\bf{M}}}}}_{E}}={(1,3,-1)}^{T}\) . The theoretical model is in excellent agreement with the experimental result. In order to derive the shape matrices of shapes M D and M E in reconfiguration loop 1, we need firstly determine the shape matrix of the initial shape M A , which is presented with explicit components as:

Then, combining Eqs. ( 1 )–( 4 ), we can finally obtain the shape M D and shape M E as:

Reconfiguration kinematics in Fig.  4

The following gives the reconfiguration kinematic details for the morphing process shown in Fig.  4 d, e . Specially, we label the opening angles of four level-1 link structure as γ km ( k and m are integers with 1 ≤  k  ≤ 4 as the k th link while 1 ≤  m  ≤ 8 as the m th rotating folds between two adjacent cubes m and m  + 1 ( m  + 1 → 1 when m  = 8), see details in Fig.  4a, b ), and the level-2 folds angles separately as γ B11 , γ B11’ , γ T21 and γ Τ21’ (Fig.  4a, b and B and T represent the bottom and top surfaces, respectively).

The selected two reconfiguration processes exhibit only local and stepwise transition kinematics. From shape M 7 to M 13 (Fig.  4d , i and iii), only the folds of links #2 and #4 (Fig.  4d , i) are involved with sequential rotations (Fig.  4d , ii) and the remaining folds of link #1, link #3 and the level-2 keep unchanged (Fig.  4d , iv). For kinematic details of the reconfigured links #2 and #4 shown in Fig.  4d , iv, during the initial process ①  →  ② , we only need to linearly change the folds angle γ m4,6 ( m  = 2 or 4) from 180° to γ 0 (Here we set γ 0 as 150° while it ranges from 90° to 180°; see more details in Supplementary Fig.  17 ) and meanwhile linearly increase γ m2,8 from 0° to γ 0 . Then, in the following process ② → ③ , we can maintain folds angles γ m2,4,6,8 as γ 0 while both linearly decreasing γ m1,5 from 180° to sin -1 [(sin γ 0 ) 2 /(1 + (cos γ 0 ) 2 ] (≈ 109.5° for γ 0  = 150°) and augmenting γ m3,7 from 0° to 180°−sin −1 [(sin γ 0 ) 2 /(1 + (cos γ 0 ) 2 ] (≈ 70.5° for γ 0  = 150°). Lastly, for ③ → ④ → ⑤ , we can simultaneously transfigure links #2 and #4 as 8R-looped rigid linkage with kinematics as γ m1,5  = sin −1 [(sin γ m2 ) 2 /(1 + (cos γ m2 ) 2 ], γ m3,7  = 180°−sin −1 [(sin γ m2 ) 2 /(1 + (cos γ m2 ) 2 ] (γ m2 reducing from γ 0 to 90°) while γ m2  = γ m4  = γ m6  = γ m8 (see Supplementary Note  6 ) to reach shape M 13 . Moreover, as illustrated in Fig.  4e , vi that displays sequential and local kinematic features, we note that the reconfiguration kinematics from shape M 15 to M 21 by bypassing shape M 25 (Fig.  4e , i–v) are much simpler with only linear angle relationships.

Inverse design to imitate target shapes

Inverse design to imitate target shapes for special application scenarios can also be accessible for our hierarchical structures. However, the imitating process of our inverse design is different from previous designs by presetting material/structural patterns to purposely retain the target shapes. Our inverse design method is based on the selection algorithm from the reconfigured shape library by following several steps.

First is to build a database for the configuration library. Each cube can be treated as a spatial voxelated pixel with its geometrical center represented by a vector. Then, we can use a matrix to characterize a morphed shape, where the spatial positions of composed cubes are described by their corresponding vectors. For example, for all the combinatorically designed level-2 structures shown in Supplementary Fig.  5 , for one special design k , all its reconfigured shapes can be summarized into:

where M kn represent the mathematically expressed forms of the n th reconfigured shapes in the transition tree for the k th combinatorically designed level-2 structures.

Second is to compose all the combinatorically designed level-2 structures into the database matrix D in the form of:

where z stands for the maximum number of reconfigured shapes by the k th level-2 structure.

Third is to discretize the target shape into cube-shaped voxelated pixels and mathematically convert it into a mathematical matrix T .

Last is to find the shapes in the database that match for the target shape by comparing the matrix T with the components of database matrix, i.e., D ij . There are two criterions to find out the optimal imitated shape: (1) find the smallest value of the error function Errf defined as:

wherein || || represent the mode of matrix and usually \({\Vert {{{\bf{T}}}}-{{{{\bf{D}}}}}_{ij}\Vert }_{\max }\) is determined as \(\Vert {{{\bf{T}}}}\Vert+{\Vert {{{{\bf{D}}}}}_{ij}\Vert }_{\max }\) for simplicity. (2) The conditions that guarantee the imitated shapes whose cube pixels are with approximately the same absolute spatial positions with the target shape, i.e.:

Finally, we can obtain the most approximately imitated shape M km from the database. The inverse design method is briefly summarized in Supplementary Fig.  25 .

Simulation by customized software

A model has been developed for simulation in ROS-Gazebo (Supplementary Figs.  20 and 21 and Supplementary Movies  5 and  8 ). For simplicity, a single design composed of the four lateral faces of a cube is used to model every module of the robot. The connections between the modules are modeled as revolute joints (either passive or actuated). Additional blocks are used to replicate the positions and masses of the motors in the real system. Kinematic constraints are implemented to model the robot as a closed kinematic chain.

Data availability

The authors declare that the data supporting the findings of this study are available within the article and its Supplementary Information files.  Source data are provided with this paper.

Code availability

The code used for the analyses is deposited via Zenodo at https://doi.org/10.5281/zenodo.12690922 .

Hanlon, R. T., Conroy, L.-A. & Forsythe, J. W. Mimicry and foraging behaviour of two tropical sand-flat octopus species off North Sulawesi, Indonesia. Biol. J. Linn. Soc. 93 , 23–38 (2008).

Article   Google Scholar  

Wells, M. J. Octopus: Physiology and Behaviour of an Advanced Invertebrate (Springer Science & Business Media, 2013).

Hwang, D. et al. Shape morphing mechanical metamaterials through reversible plasticity. Sci. Robot. 7 , eabg2171 (2022).

Article   ADS   PubMed   Google Scholar  

Chi, Y. et al. Bistable and multistable actuators for soft robots: structures, materials, and functionalities. Adv. Mater. 34 , 2110384 (2022).

Article   CAS   Google Scholar  

Ford, M. J. et al. A multifunctional shape-morphing elastomer with liquid metal inclusions. Proc. Natl Acad. Sci. USA 116 , 21438–21444 (2019).

Article   ADS   CAS   PubMed   PubMed Central   Google Scholar  

Liu, K., Hacker, F. & Daraio, C. Robotic surfaces with reversible, spatiotemporal control for shape morphing and object manipulation. Sci. Robot. 6 , eabf5116 (2021).

Article   PubMed   Google Scholar  

You, Z. & Pellegrino, S. Foldable bar structures. Int. J. Solids Struct. 34 , 1825–1847 (1997).

Leveziel, M., Haouas, W., Laurent, G. J., Gauthier, M. & Dahmouche, R. MiGriBot: a miniature parallel robot with integrated gripping for high-throughput micromanipulation. Sci. Robot. 7 , eabn4292 (2022).

You, Z. & Chen, Y. Motion Structures: Deployable Structural Assemblies of Mechanisms (Taylor & Francis, 2012).

Chen, Y., You, Z. & Tarnai, T. Threefold-symmetric Bricard linkages for deployable structures. Int. J. Solids Struct. 42 , 2287–2301 (2005).

Félix, D., Branco, J. M. & Feio, A. Temporary housing after disasters: a state of the art survey. Habitat Int. 40 , 136–141 (2013).

Lang, R. J., Tolman, K. A., Crampton, E. B., Magleby, S. P. & Howell, L. L. A review of thickness-accommodation techniques in origami-inspired engineering. Appl. Mech. Rev . 70 , 010805 (2018).

Gao, W., Huo, K., Seehra, J. S., Ramani, K. & Cipra, R. J. in 2014 IEEE/RSJ International Conference on Intelligent Robots and Systems 4598–4604 (IEEE, 2014).

Callens, S. J. & Zadpoor, A. A. From flat sheets to curved geometries: origami and kirigami approaches. Mater. Today 21 , 241–264 (2018).

Filipov, E. T., Tachi, T. & Paulino, G. H. Origami tubes assembled into stiff, yet reconfigurable structures and metamaterials. Proc. Natl Acad. Sci. USA 112 , 12321–12326 (2015).

Dudte, L. H., Vouga, E., Tachi, T. & Mahadevan, L. Programming curvature using origami tessellations. Nat. Mater. 15 , 583–588 (2016).

Article   ADS   CAS   PubMed   Google Scholar  

Meloni, M. et al. Engineering origami: a comprehensive review of recent applications, design methods, and tools. Adv. Sci. 8 , 2000636 (2021).

Tachi, T. Rigid-foldable thick origami. Origami 5 , 253–264 (2011).

Tao, J., Khosravi, H., Deshpande, V. & Li, S. Engineering by cuts: how kirigami principle enables unique mechanical properties and functionalities. Adv. Sci. 10 , 2204733 (2023).

Bertoldi, K., Vitelli, V., Christensen, J. & Van Hecke, M. Flexible mechanical metamaterials. Nat. Rev. Mater. 2 , 1–11 (2017).

Reis, P. M., López Jiménez, F. & Marthelot, J. Transforming architectures inspired by origami. Proc. Natl Acad. Sci. USA 112 , 12234–12235 (2015).

Chen, Y., Peng, R. & You, Z. Origami of thick panels. Science 349 , 396–400 (2015).

Rus, D. & Vona, M. Crystalline robots: self-reconfiguration with compressible unit modules. Auton. Robots 10 , 107–124 (2001).

Murata, S. et al. M-TRAN: self-reconfigurable modular robotic system. IEEE/ASME Trans. Mechatron. 7 , 431–441 (2002).

Seo, J., Paik, J. & Yim, M. Modular reconfigurable robotics. Annu. Rev. Control Robot. Auton. Syst. 2 , 63–88 (2019).

Belke, C. H. & Paik, J. Mori: a modular origami robot. IEEE/ASME Trans. Mechatron. 22 , 2153–2164 (2017).

Zykov, V., Mytilinaios, E., Adams, B. & Lipson, H. Self-reproducing machines. Nature 435 , 163–164 (2005).

Li, S. et al. Particle robotics based on statistical mechanics of loosely coupled components. Nature 567 , 361–365 (2019).

Melancon, D., Gorissen, B., García-Mora, C. J., Hoberman, C. & Bertoldi, K. Multistable inflatable origami structures at the metre scale. Nature 592 , 545–550 (2021).

Rus, D. & Tolley, M. T. Design, fabrication and control of origami robots. Nat. Rev. Mater. 3 , 101–112 (2018).

Article   ADS   Google Scholar  

Suzuki, H. & Wood, R. J. Origami-inspired miniature manipulator for teleoperated microsurgery. Nat. Mach. Intell. 2 , 437–446 (2020).

Pellegrino, S. Large retractable appendages in spacecraft. J. Spacecr. Rockets 32 , 1006–1014 (1995).

Puig, L., Barton, A. & Rando, N. A review on large deployable structures for astrophysics missions. Acta Astronaut. 67 , 12–26 (2010).

Xia, X., Spadaccini, C. M. & Greer, J. R. Responsive materials architected in space and time. Nat. Rev. Mater. 7 , 683–701 (2022).

Article   ADS   PubMed   PubMed Central   Google Scholar  

Bai, Y. et al. A dynamically reprogrammable surface with self-evolving shape morphing. Nature 609 , 701–708 (2022).

Li, Y. & Yin, J. Metamorphosis of three-dimensional kirigami-inspired reconfigurable and reprogrammable architected matter. Mater. Today Phys. 21 , 100511 (2021).

Pellegrino, S. in Deployable Structures 1–35 (Springer, 2001).

Overvelde, J. T., Weaver, J. C., Hoberman, C. & Bertoldi, K. Rational design of reconfigurable prismatic architected materials. Nature 541 , 347–352 (2017).

Overvelde, J. T. et al. A three-dimensional actuated origami-inspired transformable metamaterial with multiple degrees of freedom. Nat. Commun. 7 , 1–8 (2016).

Felton, S., Tolley, M., Demaine, E., Rus, D. & Wood, R. A method for building self-folding machines. Science 345 , 644–646 (2014).

Wang, R., Song, Y. & Dai, J. S. Reconfigurability of the origami-inspired integrated 8R kinematotropic metamorphic mechanism and its evolved 6R and 4R mechanisms. Mech. Mach. Theory 161 , 104245 (2021).

Yang, Y., Zhang, X., Maiolino, P., Chen, Y. & You, Z. Linkage-based three-dimensional kinematic metamaterials with programmable constant Poisson’s ratio. Mater. Des. 233 , 112249 (2023).

Lee, D.-Y., Kim, J.-K., Sohn, C.-Y., Heo, J.-M. & Cho, K.-J. High-load capacity origami transformable wheel. Sci. Robot. 6 , eabe0201 (2021).

Cho, Y. et al. Engineering the shape and structure of materials by fractal cut. Proc. Natl Acad. Sci. USA 111 , 17390–17395 (2014).

Coulais, C., Sabbadini, A., Vink, F. & van Hecke, M. Multi-step self-guided pathways for shape-changing metamaterials. Nature 561 , 512–515 (2018).

Meza, L. R. et al. Resilient 3D hierarchical architected metamaterials. Proc. Natl Acad. Sci. USA 112 , 11502–11507 (2015).

Aizenberg, J. et al. Skeleton of Euplectella sp.: structural hierarchy from the nanoscale to the macroscale. Science 309 , 275–278 (2005).

Miyashita, S., Guitron, S., Li, S. & Rus, D. Robotic metamorphosis by origami exoskeletons. Sci. Robot. 2 , eaao4369 (2017).

Coulais, C., Teomy, E., de Reus, K., Shokef, Y. & van Hecke, M. Combinatorial design of textured mechanical metamaterials. Nature 535 , 529–532 (2016).

Whitley, D. A genetic algorithm tutorial. Stat. Comput. 4 , 65–85 (1994).

Howell, L. L. in 21st Century Kinematics: The 2012 NSF Workshop 189–216 (Springer, 2013).

Download references

Acknowledgements

J.Y. acknowledges the funding support from NSF (CMMI-2005374 and CMMI-2126072). H.S. acknowledges the funding support from NSF 2231419. The authors acknowledge the helpful discussions with Dr. K. Bertoldi and Dr. M. Yim.

Author information

These authors contributed equally: Yanbin Li, Antonio Di Lallo.

Authors and Affiliations

Department of Mechanical and Aerospace Engineering, North Carolina State University, Raleigh, NC, 27606, USA

Yanbin Li, Antonio Di Lallo, Junxi Zhu, Yinding Chi, Hao Su & Jie Yin

Lab of Biomechatronics and Intelligent Robotics, Joint NCSU/UNC Department of Biomedical Engineering, North Carolina State University, Raleigh, NC, USA

University of North Carolina at Chapel Hill, Chapel Hill, NC, USA

You can also search for this author in PubMed   Google Scholar

Contributions

Y.L. and J.Y. proposed the idea. Y.L. conducted theoretical and numerical calculations. Y.L. and Y.C. designed and performed experiments on shape-morphing prototypes. A.D. and J.Z. designed and performed experiments on untethered actuation of shape-morphing prototypes. Y.L., A.D., H.S. and J.Y. wrote the paper. H.S. and J.Y. supervised the research. All the authors contributed to the discussion, data analysis, and editing of the manuscript.

Corresponding authors

Correspondence to Yanbin Li , Hao Su or Jie Yin .

Ethics declarations

Competing interests.

The authors declare no competing interests.

Peer review

Peer review information.

Nature Communications thanks Evgueni Filipov and Damiano Pasini for their contribution to the peer review of this work. A peer review file is available.

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Supplementary information, peer review file, description of additional supplementary files, supplementary movie 1, supplementary movie 2, supplementary movie 3, supplementary movie 4, supplementary movie 5, supplementary movie 6, supplementary movie 7, supplementary movie 8, source data, source data, rights and permissions.

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ .

Reprints and permissions

About this article

Cite this article.

Li, Y., Di Lallo, A., Zhu, J. et al. Adaptive hierarchical origami-based metastructures. Nat Commun 15 , 6247 (2024). https://doi.org/10.1038/s41467-024-50497-5

Download citation

Received : 28 November 2023

Accepted : 12 July 2024

Published : 26 July 2024

DOI : https://doi.org/10.1038/s41467-024-50497-5

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

By submitting a comment you agree to abide by our Terms and Community Guidelines . If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.

Quick links

• Explore articles by subject
• Guide to authors
• Editorial policies

Sign up for the Nature Briefing: AI and Robotics newsletter — what matters in AI and robotics research, free to your inbox weekly.