Kinematics and Statics of the Gough-Stewart Platform

Round 1

Reviewer 1 Report

By defining the velocity screw, the paper presents an analysis of the kinematics and statics of a Gough–Stewart platform. Although this paper is well written, it
could be improved in some aspects as follows:

1- The innovation and benefits of the paper should be explained more clearly.

2- The results of the article should be quantitatively compared with previous researches.

3-It seems that some items should be corrected in the formulas:

*- In first line of formulas 11 and 12, the index of the last variable must be modified (Change 1 to i).

*- Formulas13, the index of summation should be modified.

*- In second line of formula 14, it seems that the sign of the formula should be negative.

Author Response

Please see the attached response.

Author Response File: Author Response.docx

Reviewer 2 Report

Overall the manuscript is well-written and structured. The purpose is clearly stated. However, the kinematics and static problems of Gough–Stewart platforms have been handled previously by many researchers. I suggest the authors highlight the gap in the literature. For example, could you establish a comparison to demonstrate that the proposed method outperforms conventional ones in terms of eliminating the complex algebraic manipulation and allowing a direct calculation of the six constraint variables for all joints?

I suggest contrasting the results of the study to that of previous works. For example,

Gallardo-Alvarado, J. (2016). Kinematic analysis of parallel manipulators by algebraic screw theory (pp. 1-377). Switzerland: Springer International Publishing.

Wen, K., Du, F., & Zhang, X. (2016). Algorithm and experiments of six-dimensional force/torque dynamic measurements based on a Stewart platform. Chinese Journal of Aeronautics, 29(6), 1840-1851.

Author Response

Please see the attached response.

Author Response File: Author Response.docx

Reviewer 3 Report

The paper treats an algorithm for the kinematics and statics analysis of a Gough–Stew art platform.

I have the following remarks:

·        The paper is interesting and presents a relatively new method regarding the kinematic control of a Gough–Stew art platform.

·        The presented results can be used for a kinematic control of position? A kinematic control would be necessary.

·        Stability analysis in the context of the use of dynamic components would be useful.

·        The results are verified by simulation. I think that an experimental application would be necessary.

·        The conclusion should be improved. The new directions of investigations should be given by the authors.

Author Response

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Author Response File: Author Response.docx

Reviewer 4 Report

In the reviewed paper, the Authors propose a new algorithm for analyzing the kinematics and statics of the parallel mechanical platform, namely, the Gough–Stewart platform.
I like the overall concept of the study, and the obtained results seem reliable to me. I especially value a thorough theoretical section of the paper.
Besides, some points are to be clarified during the revision prior to publication. Please, find my questions and concerns below.

1. "a kinematic and static analysis methodology" - methodology is a complex term, which includes concepts, methods, and techniques. In my opinion, this statement can be softened because the paper certainly does not introduce a new methodology, but improves and generalizes existing approaches.
2. Some practical applications of the Gough–Stewart platform can be mentioned in the introduction to emphasize the contribution and practical value of the study. For example, can the proposed solutions be used to improve landing platforms, robots for artistic painting, 3D printers, etc.? What is the practical motivation of the study?

3. The comparison with existing methods is scarce. Why the proposed improvements are important? What benefits do they provide?

4. The experimental section should contain more information about the software, conditions, parameters, and solvers used for simulation to increase the reproducibility of the study. How numerical errors were taken into account in your research?

5. I recommend choosing a more complex movement than a circular one (given by eq. 32) for the simulation. For example, chaotic motion can be considered with a variable degree of chaos, which is closer to real mechanics which acts in uncertain conditions due to actuators' imperfectness.

6. The Authors claim that "This algorithm is easy to compute and program with high efficiency", but the complexity of the proposed algorithm is not properly evaluated, as well as the efficiency of algorithm-based software.

Nevertheless, I like this study and believe it can be accepted for publication after moderate revisions.

The language of the paper is generally fine. Only minor proofreading is needed.

Author Response

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Author Response File: Author Response.docx

Reviewer 5 Report

The article provides a variety of information related to the kinematics of composite robotics applications topic. At the same time, an algorithm for analyzing the kinematics and statics of the Gough-Stewart platform is proposed. It is worth noting that the paper is characterized by a remarkable visualization in the the description of the proposed techniques and the platform's kinematic diagram. The authors proposed a theoretical method that gives more convenience in solving problems of kinematics and statics of spatial mechanisms. However, the reviewer has a few comments and questions:

1. At the end of the Introduction section, there is no brief description of each Section of the paper.

2. Starting from the second section of the paper there are no references to the sources of the used formulas.

3. The majority of the used references, particularly in the introduction, are outdated. Although Stewart's platform and its applications are not novel, there are more relevant works currently available.

It is also worth highlighting the paper's relevance here, highlighting the Stewart's platform applications, e.g. in the medical field (for prosthesis stability testing).

4. There is no clear understanding in the article why the presented algorithm "is easy to compute". Compared to which algorithms the presented one performed better?

The article requires minor revision in terms of declared remarks with the same results obtained.

 Minor editing of English language required

Author Response

Please see the attached response.

Author Response File: Author Response.docx

Round 2

Reviewer 2 Report

The authors have undertaken substantial revisions of the manuscript, incorporating most of the changes that were highlighted during the initial round of review. However, I still have reservations regarding the paper's level of novelty.

Take, for instance, the following sentence: "While the conventional methods start with displacement, and then solve the velocities and accelerations through first- and second-order numerical interpolation, respectively, which leads to high computational costs." Given the conditional start with "While," I anticipated the introduction of a contrasting idea. However, the authors instead emphasized the high computational cost. To address this, I propose that the authors conduct a comparative analysis of the computational costs between the traditional approach based on screw theory and the proposed solution. It would be valuable to ascertain how the computational cost of Gallardo's paper compare to those of the proposed solution.

Furthermore, I strongly recommend that the authors explicitly outline the novelty of their manuscript in relation to the works of Gallardo-Alvarado (2016) and Wen, Du, & Zhang (2016). This will help elucidate the distinctive contributions of the present study.

In this revised version, the authors confined their comparisons to numerical outcomes, with minimal commentary on the practical applications of the algorithm or the requisite computational time. I suggest the authors to address this aspect, as readers would greatly benefit from insights into the algorithm's applications and the computational time it demands. This additional commentary would significantly enhance the manuscript's ability to emphasize its novelty.

Overall, by addressing these points, the authors can further underscore the originality and significance of their manuscript.

No particular comments in this regard.

Author Response

Please see the attached file of response.

Author Response File: Author Response.docx

Reviewer 4 Report

I am impressed by volume and quality of revisions made by Authors. I will recommend the revised paper for publication and wish the Authors all the success in their future studies.

The language was improved appropriately.

Author Response

Comment: I am impressed by volume and quality of revisions made by the Authors. I will recommend the revised paper for publication and wish the Authors all the success in their future studies.

Response: Thank you so much for your time and effort involved in reviewing our manuscript and your valuable comments. We wish you all the best in your future!