PONE-D-25-26746 Monolithic scalable compliant mechanisms PLOS ONE

Dear Dr. Parkinson,

Thank you for submitting your manuscript to PLOS ONE. After careful consideration, we feel that it has merit but does not fully meet PLOS ONE’s publication criteria as it currently stands. Therefore, we invite you to submit a revised version of the manuscript that addresses the points raised during the review process.

Based on the reviewers' comments and our evaluation of the paper, we recommend a major revision.

We kindly ask the authors to make detailed revisions in line with the reviewers' suggestions.

Please submit your revised manuscript by Aug 25 2025 11:59PM. If you will need more time than this to complete your revisions, please reply to this message or contact the journal office at plosone@plos.org. When you're ready to submit your revision, log on to https://www.editorialmanager.com/pone/ and select the 'Submissions Needing Revision' folder to locate your manuscript file.

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We look forward to receiving your revised manuscript.

Kind regards,

Geng Wang, PhD

Academic Editor

PLOS ONE

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[This work was supported through funds awarded to BDJ by Castle Grayskull, LLC, owned by Mark Rober. Mark Rober did not participate in data collection and analysis. He did participate in study design, the decision to publish, and preparation of the manuscript.].

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[I have read the journal's policy and the authors of this manuscript have the following competing interests: This work was supported through funds awarded to BYU by Castle Grayskull, LLC, owned by Mark Rober. A patent application is pending on the planar spring that is integral to the blaster case study. A patent has been issued on the LET joints that are part of the chair case study.].

We note that one or more of the authors are employed by a commercial company: name of commercial company.

1.        Please provide an amended Funding Statement declaring this commercial affiliation, as well as a statement regarding the Role of Funders in your study. If the funding organization did not play a role in the study design, data collection and analysis, decision to publish, or preparation of the manuscript and only provided financial support in the form of authors' salaries and/or research materials, please review your statements relating to the author contributions, and ensure you have specifically and accurately indicated the role(s) that these authors had in your study. You can update author roles in the Author Contributions section of the online submission form.

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8. If the reviewer comments include a recommendation to cite specific previously published works, please review and evaluate these publications to determine whether they are relevant and should be cited. There is no requirement to cite these works unless the editor has indicated otherwise.

Additional Editor Comments:

Based on the reviewers' comments and the evaluation of this paper, it is recommended that the paper needs major revision.

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Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Author

1. Is the manuscript technically sound, and do the data support the conclusions?

The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented.

Reviewer #1: Yes

Reviewer #2: Yes

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2. Has the statistical analysis been performed appropriately and rigorously?

Reviewer #1: N/A

Reviewer #2: N/A

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3. Have the authors made all data underlying the findings in their manuscript fully available?

The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.

Reviewer #1: Yes

Reviewer #2: Yes

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4. Is the manuscript presented in an intelligible fashion and written in standard English?

PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.

Reviewer #1: Yes

Reviewer #2: Yes

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5. Review Comments to the Author

Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)

Reviewer #1: The manuscript presents an investigation into the scalability of displacement-driven compliant mechanisms, addressing an important aspect of compliant mechanism design that has significant implications for multi-scale applications. The authors demonstrate, through experimental validation and detailed case studies, that the strain remains constant across geometric scales while force scales linearly with width, confirming the theoretical foundations proposed.

The discussion appropriately highlights the counterintuitive nature of displacement-driven compliant mechanisms compared to conventional force-driven systems, and, in general, it insightfully points to potential future applications.

Overall, the topic fits the interest of the journal.

Language and writing, under the syntactic and grammar aspects, results in being sufficiently fluent and clean.

The following specific remarks are provided:

1) The manuscript could benefit from a more detailed exploration of potential manufacturing challenges and material limitations that might arise at extreme scales, as well as a clearer explanation of how these scaling principles might integrate with existing design optimization frameworks.

2) The explanation of the theoretical background, while generally sound, lacks sufficient depth and rigor in some parts; for example, the assumptions behind the scaling laws are not always clearly stated or justified, which may leave readers questioning the generality of the results.

3) The discussion section touches on promising applications but tends to be somewhat speculative without clear pathways for practical implementation or addressing potential limitations in manufacturing and material behavior at extreme scales.

4) Furthermore, the paper would benefit from a more critical treatment of challenges related to scaling, such as non-ideal material properties, fabrication tolerances, and environmental factors.

5) The paper also overlooks the possible impact of stress concentrations responses when scaling compliant mechanisms, which could lead to unexpected failure modes (or early failure) during the application of cycles loads.

6) How does fatigue behavior modify when dimensions change? Please, add a discussion on this point in the manuscript.

7) Authors may consider discussing the following reference: in this recent paper on cross-axis flexure hinges (a) https://doi.org/10.1016/j.mechmachtheory.2024.105894, the authors demonstrate that second-order kinematic invariants (specifically the polodes and the inflection circle) scale linearly with the length of the flexure hinge.This finding offers an interesting perspective that could enrich your discussion by highlighting that certain elasto-kinematic properties of compliant mechanisms also exhibit scaling relationships useful for the design.

Downstream of these points, the Reviewer proposes a major revision and defer the publication decision pending the authors' response and modifications according to these remarks.

Reviewer #2: This work shows that for displacement-driven compliant mechanisms, mechanical stress is uniquely invariant with scale. This effect is described theoretically, verified through computer models and physical testing, and is demonstrated in three examples: a parallel-guiding mechanism, a projectile launcher, and a chair.

The work is useful and emphasized scalability challenges and how to overcome them.

Here are comments to improve the work:

- the motivation can be improved on why scalability matters and how to approach it. In the case of compliant mechanisms how scalability can be beneficial for monolithic design

- discuss the actuation of complaint mechanisms as well as the power needed in the context of scalability

- the conclusions need improvement: clearly state the contributions of the work as well as how to interpret the main findings for design

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Reviewer #1: No

Reviewer #2: No

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PONE-D-25-26746R1 Monolithic scalable compliant mechanisms

PLOS ONE

Dear Dr. Parkinson,

Thank you for submitting your manuscript to PLOS ONE. After careful consideration, we feel that it has merit but does not fully meet PLOS ONE’s publication criteria as it currently stands. Therefore, we invite you to submit a revised version of the manuscript that addresses the points raised during the review process.

After evaluation, please revise the manuscript thoroughly in accordance with the reviewers' comments. Note that the references recommended by the reviewers are not mandatory, unless they are necessary and truly relevant.

Please submit your revised manuscript by Nov 30 2025 11:59PM. If you will need more time than this to complete your revisions, please reply to this message or contact the journal office at plosone@plos.org. When you're ready to submit your revision, log on to https://www.editorialmanager.com/pone/ and select the 'Submissions Needing Revision' folder to locate your manuscript file.

Please include the following items when submitting your revised manuscript:

• A rebuttal letter that responds to each point raised by the academic editor and reviewer(s). You should upload this letter as a separate file labeled 'Response to Reviewers'.
• A marked-up copy of your manuscript that highlights changes made to the original version. You should upload this as a separate file labeled 'Revised Manuscript with Track Changes'.
• An unmarked version of your revised paper without tracked changes. You should upload this as a separate file labeled 'Manuscript'.

If you would like to make changes to your financial disclosure, please include your updated statement in your cover letter. Guidelines for resubmitting your figure files are available below the reviewer comments at the end of this letter.

If applicable, we recommend that you deposit your laboratory protocols in protocols.io to enhance the reproducibility of your results. Protocols.io assigns your protocol its own identifier (DOI) so that it can be cited independently in the future. For instructions see: https://journals.plos.org/plosone/s/submission-guidelines#loc-laboratory-protocols. Additionally, PLOS ONE offers an option for publishing peer-reviewed Lab Protocol articles, which describe protocols hosted on protocols.io. Read more information on sharing protocols at https://plos.org/protocols?utm_medium=editorial-email&utm_source=authorletters&utm_campaign=protocols.

We look forward to receiving your revised manuscript.

Kind regards,

Geng Wang, PhD

Academic Editor

PLOS ONE

Journal Requirements:

If the reviewer comments include a recommendation to cite specific previously published works, please review and evaluate these publications to determine whether they are relevant and should be cited. There is no requirement to cite these works unless the editor has indicated otherwise.

Additional Editor Comments:

After evaluation, please revise the manuscript thoroughly in accordance with the comments. Note that the references recommended by the reviewers are not mandatory, unless they are necessary and truly relevant.

[Note: HTML markup is below. Please do not edit.]

Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Author

1. If the authors have adequately addressed your comments raised in a previous round of review and you feel that this manuscript is now acceptable for publication, you may indicate that here to bypass the “Comments to the Author” section, enter your conflict of interest statement in the “Confidential to Editor” section, and submit your "Accept" recommendation.

Reviewer #3: All comments have been addressed

Reviewer #4: All comments have been addressed

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2. Is the manuscript technically sound, and do the data support the conclusions?

The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented.

Reviewer #3: Yes

Reviewer #4: Yes

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3. Has the statistical analysis been performed appropriately and rigorously?

Reviewer #3: Yes

Reviewer #4: N/A

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4. Have the authors made all data underlying the findings in their manuscript fully available?

The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.

Reviewer #3: Yes

Reviewer #4: Yes

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5. Is the manuscript presented in an intelligible fashion and written in standard English?

PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.

Reviewer #3: Yes

Reviewer #4: Yes

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6. Review Comments to the Author

Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)

Reviewer #3: All my indications and/or suggestions have been correctly implemented. The paper is well written and well structured, and the results have been described in a thorough and comprehensive manner. I believe that the paper is ready for publication.

Reviewer #4: This manuscript explores the scalability of displacement-driven compliant mechanisms, demonstrating that mechanical stress remains invariant under geometric scaling. The work combines analytical derivation, finite element analysis, and physical testing across three illustrative case studies: a parallel-guiding mechanism, a projectile launcher, and a deployable chair. The authors argue that this property simplifies design transferability across scales and opens new opportunities in areas such as MEMS, medical devices, and deployable structures.

The revised manuscript addresses most of the issues raised in earlier review rounds, improving clarity, rigor, and relevance. Overall, it represents a valuable and well-supported contribution to the field of compliant mechanism design. The following comments need to be addressed.

1. Add scale bar in Fig. 1, Fig. 3. Also Fig. 1 a, a and c and be laid in single column.

2. Figure 2 sub figures should be labeled as a, b, c and d to improve readability

3. Figure 3 and 4 can be merged to single figure as they are similar and this will make the manuscript more readable.

4. Did author check the projectile launch for all scales? What the distance that the launcher can travel as illustrated in Figure 9. Is MEMS launcher functional as beans are deformed. Can it store the force, it should be supported with video or tracking the displacement.

5. Figure 6 and 7 should be merged as they don’t add more information. How were the sensors on Figure 7 calibrated?

6. A supporting video on formation of chair should be included in the supporting information along with projectile launch.

7. Add scale bar for Figure 10. What weight of the person that the chair can bear without deformation or break.

8. The following statement should be supported by experimental results: ‘A Keyence VHX microscope was used in conjunction with a micromanipulator probe to view and actuate the CICNT devices’

9. Recent work on compliant mechanisms with multi degrees of freedom (DOF) should be included in discussion section. Some examples includes.

i. Yang, H., Patel, D.K., Johnson, T. et al. A compliant metastructure design with reconfigurability up to six degrees of freedom. Nat Commun 16, 719 (2025). https://doi.org/10.1038/s41467-024-55591-2

ii. Humphrey Yang, et al. 2022. ReCompFig: Designing Dynamically Reconfigurable Kinematic Devices Using Compliant Mechanisms and Tensioning Cables. In Proceedings of the 2022 CHI Conference on Human Factors in Computing Systems (CHI '22). Association for Computing Machinery, New York, NY, USA, Article 170, 1–14. https://doi.org/10.1145/3491102.3502065

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7. PLOS authors have the option to publish the peer review history of their article (what does this mean?). If published, this will include your full peer review and any attached files.

If you choose “no”, your identity will remain anonymous but your review may still be made public.

Do you want your identity to be public for this peer review? For information about this choice, including consent withdrawal, please see our Privacy Policy.

Reviewer #3: No

Reviewer #4: No

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[NOTE: If reviewer comments were submitted as an attachment file, they will be attached to this email and accessible via the submission site. Please log into your account, locate the manuscript record, and check for the action link "View Attachments". If this link does not appear, there are no attachment files.]

While revising your submission, please upload your figure files to the Preflight Analysis and Conversion Engine (PACE) digital diagnostic tool, https://pacev2.apexcovantage.com/. PACE helps ensure that figures meet PLOS requirements. To use PACE, you must first register as a user. Registration is free. Then, login and navigate to the UPLOAD tab, where you will find detailed instructions on how to use the tool. If you encounter any issues or have any questions when using PACE, please email PLOS at figures@plos.org. Please note that Supporting Information files do not need this step.

Monolithic scalable compliant mechanisms

PONE-D-25-26746R2

Dear Dr. Parkinson,

We’re pleased to inform you that your manuscript has been judged scientifically suitable for publication and will be formally accepted for publication once it meets all outstanding technical requirements.

Within one week, you’ll receive an e-mail detailing the required amendments. When these have been addressed, you’ll receive a formal acceptance letter and your manuscript will be scheduled for publication.

An invoice will be generated when your article is formally accepted. Please note, if your institution has a publishing partnership with PLOS and your article meets the relevant criteria, all or part of your publication costs will be covered. Please make sure your user information is up-to-date by logging into Editorial Manager at Editorial Manager® and clicking the ‘Update My Information' link at the top of the page. For questions related to billing, please contact billing support.

If your institution or institutions have a press office, please notify them about your upcoming paper to help maximize its impact. If they’ll be preparing press materials, please inform our press team as soon as possible -- no later than 48 hours after receiving the formal acceptance. Your manuscript will remain under strict press embargo until 2 pm Eastern Time on the date of publication. For more information, please contact onepress@plos.org.

Kind regards,

Geng Wang, PhD

Academic Editor

PLOS One

Additional Editor Comments (optional):

Both reviewers and the editor have no further comments on the revised manuscript and recommend its acceptance.

Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Author

1. If the authors have adequately addressed your comments raised in a previous round of review and you feel that this manuscript is now acceptable for publication, you may indicate that here to bypass the “Comments to the Author” section, enter your conflict of interest statement in the “Confidential to Editor” section, and submit your "Accept" recommendation.

Reviewer #2: All comments have been addressed

Reviewer #4: All comments have been addressed

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2. Is the manuscript technically sound, and do the data support the conclusions?

The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented.

Reviewer #2: Yes

Reviewer #4: Yes

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3. Has the statistical analysis been performed appropriately and rigorously?

Reviewer #2: Yes

Reviewer #4: Yes

**********

4. Have the authors made all data underlying the findings in their manuscript fully available?

The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.

Reviewer #2: Yes

Reviewer #4: Yes

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5. Is the manuscript presented in an intelligible fashion and written in standard English?

PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.

Reviewer #2: Yes

Reviewer #4: Yes

**********

6. Review Comments to the Author

Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)

Reviewer #2: comments have been addressed and the authors have improved the manuscript. The manuscript is in good condition.

Reviewer #4: Authors have addressed the comments and incorp[orated in the revised manuscript. Best wishes to the authors.

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7. PLOS authors have the option to publish the peer review history of their article (what does this mean?). If published, this will include your full peer review and any attached files.

If you choose “no”, your identity will remain anonymous but your review may still be made public.

Do you want your identity to be public for this peer review? For information about this choice, including consent withdrawal, please see our Privacy Policy.

Reviewer #2: No

Reviewer #4: No

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