Ultra-Compact Orthoplanar Spring via Euler-Spiral Flexures

Round 1

Reviewer 1 Report

n this paper, orthoplanar spring and Euler-spiral concepts are synthesized to create a single-component spring mechanism that lies flat under a load. The stiffness property of the orthoplanar Euler-spiral spring is examined. A use case where the Euler-spiral orthoplanar spring is utilized as a deployment mechanism for an antenna is presented. However, there are some problems with this paper. Please consider the following comments:

1.     An Euler spiral is useful for areas that need smooth transitions. What performance does this characteristic mainly improve for flexible mechanisms? What are the advantages of Euler-spiral orthoplanar springs compared to compliant orthoplanar springs?

2.     This paper lists 5 major methods for manufacturing springs, and the advantages, disadvantages, and applicable situations of these methods need to be explained. Why choose FDM 3D printing for validation?

3.     In the sample applications, the importance of Euler-spiral orthoplanar spring is not explained, and it seems that compliant orthoplanar springs can also achieve the required functions. Can you provide other examples where Euler-spiral orthoplanar springs have unique advantages？

Author Response

1. An Euler spiral is useful for areas that need smooth transitions. What performance does this characteristic mainly improve for flexible mechanisms? What are the advantages of Euler-spiral orthoplanar springs compared to compliant orthoplanar springs?

Thank you for this feedback. To further clarify the advantages of using Euler-spiral orthoplanar springs in particular situations, we have added a sentence to the abstract on line 6-7 as well as a sentence to the introductions on lines 19-21.

2. This paper lists 5 major methods for manufacturing springs, and the advantages, disadvantages, and applicable situations of these methods need to be explained. Why choose FDM 3D printing for validation?

Thank you for this suggestion.  This is an area that we intend to explore in more depth in future work.  An explanation for why FDM 3D printing was chosen for validation was added on line 171.

3. In the sample applications, the importance of Euler-spiral orthoplanar spring is not explained, and it seems that compliant orthoplanar springs can also achieve the required functions. Can you provide other examples where Euler-spiral orthoplanar springs have unique advantages？

To better explain the importance of Euler-spiral orthoplanar springs we have added text in section 5 on line 211.

Reviewer 2 Report

In this article, the creativity to provide a hybrid geometry, useful for various applications is observed. 

It is only requested that the following comments be addressed:

1. In the text, it is recommended to mention that equations (8) - (10) are well-known for bending in a beam, as indicated in the conclusions.

2. In Figure 5b, indicate the meaning of BVP.

3. In Figure 6, it is desirable to indicate the shape(s) of the supports used, so that they can be easily removed.

Author Response

Thank you for your careful review. We have made the changes in response to the comments as outlined below:

1. In the text, it is recommended to mention that equations (8) - (10) are well-known for bending in a beam, as indicated in the conclusions.

We have added a sentence on line 134 to address this.

2. In Figure 5b, indicate the meaning of BVP.

This feedback has been addressed on line 146, and by the addition of a sentence to the caption for Figure 5.

3. In Figure 6, it is desirable to indicate the shape(s) of the supports used, so that they can be easily removed.

The caption for figure 6 has been edited to be clearer about the 3D printed prototype in the figure. It explains the different components of the print including the supports.

Reviewer 3 Report

The manuscript introduces Euler-spiral orthoplanar springs obtained from the combination of orthoplanar springs and deployable Euler-spiral connectors. An analytical model of the proposed orthoplanar springs is developed to optimise the main design variables. Possible, alternative manufacturing techniques are discussed and an example is shown of a 3D printed prototype. Lastly, an application is proposed for a deployable antenna.

The study conducted is innovative and in line with the scope of the journal. The manuscript is well organised and clearly written. Therefore, it can be accepted for publication in present form.

As a very minor correction, I would suggest to add the definitions of acronyms PLA and BVP in the main text.

Author Response

1. As a very minor correction, I would suggest to add the definitions of acronyms PLA and BVP in the main text.

This feedback has been addressed on line 146. Thank you for your review.