An Analysis of the Kinematics and Dynamics Performance of a New Type of Three-Pronged Sliding Universal Coupling

Round 1

Reviewer 1 Report

The paper presents the kinematic and dynamic modeling of a three-pronged sliding universal coupling, which was developed by the research team.  

The introduction should be extended. The drawbacks of the published research regarding the kinematics and dynamics of universal couplings should be stressed out.

The highlights of the paper should be presented versus previous results (including the authors’ own results, i.e. references 9-11, or Kinematics Simulation on the Centre of Sliding Universal Joints / De Gong Chang,  C. Wang, B. Zuo etc.).

Figures 2, 3 – the notations should be written above the line (i.e. angle beta, etc.). Figure 6 – the legend for X axis is missing.

The readability of the paper should be improved, the method should be detailed, many notations / symbols are missing from the text ( and omitting term , substituting C3 simplifies…, , is the same, the peak value of is much smaller than that of . Under .. , etc.) some notations are not explained at their first use, the authors use either w or omega for the same parameter etc.).

The impact of assumptions on the results should be discussed, too.

The authors should be consistent by using either moment or torque throughout the paper.

The passive forms are better in academic papers than the active use of "we”.

There are many typos and English  language problems  in the text (the relation curves of ϕ−′YR when the β angle is been different value .., Due to the transformation relationship between the fixed coordinate system and the moving coordinate system OXYZ. etc.)  that should be corrected.

Author Response

Dear Reviewers:

     Thank you for your letter and for the reviewers’ comments concerning our manuscript entitled Analysis of kinematics and dynamics performance of a new type of three-pronged sliding universal coupling .Those comments are all valuable and very helpful for revising and improving our paper, as well as the important guiding significance to our researches. We have studied comments carefully and have made correction which we hope meet with approval. Revised portion are marked in red in the paper.

Question 1: The introduction should be extended. The drawbacks of the published research regarding the kinematics and dynamics of universal couplings should be stressed out.

     Response：In response to this question, we have added the following to the introduction: Introduction: The study of the three-pronged slip universal coupling was mainly carried out in the field of synchronicity and motion law. This research is mainly to establish a kinematic model and dynamic model that can guide the development of a new type of constant angular velocity universal coupling structure, and analyze the kinematics and dynamic characteristics of the new structure, which is of great significance to guide the application of a new type of three-pronged universal coupling.

Question 2: The highlights of the paper should be presented versus previous results (including the authors’ own results, i.e. references 9-11, or Kinematics Simulation on the Centre of Sliding Universal Joints / De Gong Chang,  C. Wang, B. Zuo etc.).

      Response：We then add the introduction at the end of question 1: Most of the previous studies carried out by our group focused on the motion trajectory simulation of the components of the three-pronged sliding universal coupling (such as the center point slide bar, etc.), but this study is to establish a guiding model and systematically analyze the model.

Question 3: Figures 2, 3 – the notations should be written above the line (i.e. angle beta, etc.). Figure 6 – the legend for X axis is missing.

      Response：We have made changes to Figure 2, Figure 3, Figure 6.

Question 4: The readability of the paper should be improved, the method should be detailed, many notations / symbols are missing from the text ( and omitting term , substituting C3 simplifies…, , is the same, the peak value of is much smaller than that of . Under .. , etc.) some notations are not explained at their first use, the authors use either w or omega for the same parameter etc.).

       Response：In response to this problem, we have made changes to the T ₀ ,C₃ and other symbols by double-checking, as well as filling in the missing items. And changed  ω to 3ω.

Question 5: The impact of assumptions on the results should be discussed, too.

The authors should be consistent by using either moment or torque throughout the paper.

       Response：In order to solve this problem, we add to the conclusion: the analysis methods adopted in this paper, the directional cosine matrix method and the single force indicator pair method, are effective analysis methods, which play an important role in obtaining the correct analysis results. In addition, the consistency of torque and torque was maintained throughout the paper by means of checks.

       We sincerely thank you for reading it carefully. Based on your suggestion, in our resubmitted manuscript, we have expanded the introduction, revised the figures in the text, added the symbols and missing items in the text, and changed some detail issues, I am very sorry for our careless mistakes, thank you for the reminder.

Author Response File: Author Response.pdf

Reviewer 2 Report

This paper presents a simple kinematic and dynamic characteristics study of a three-pronged sliding universal coupling which is already published with different studies. 

1. All the math letters inserted in the text should be rewritten in an adequate form.

 2. Figures 2, 3, 4 are not of good quality and should be remade.

3. Figures 10, 12, 13 should not be a screenshots, please provide good qualtiy ones.

4. The horizontal space between letter math letters in the equations is not respected and should be improved.

5. The vertical space between figures and text and between equations and text should be improved.

6. References should be revised, and some of them are not found.

7. kinematics and dynamics analysis isn't a sufficient study to be published in this journal, and another developed study should be added. 

Minor editing of English language required.

Author Response

Dear Reviewers:

       We are very grateful for your professional comments on our articles, and you are very grateful for your valuable comments. Based on your suggestion, we have made extensive corrections to the previous manuscript as follows:

Question 1: All the math letters inserted in the text should be rewritten in an adequate form.

       Response：We've rewritten the letters inserted in this article.

Question 2: Figures 2, 3, 4 are not of good quality and should be remade.

       Response：We have redone Figures 2, 3, and 4 in this article.

Question 3: Figures 10, 12, 13 should not be a screenshots, please provide good qualtiy ones.

       Response：We have redone the figures 10, 12, and 13 in this article.

Question 4: The horizontal space between letter math letters in the equations is not respected and should be improved.

       Response：We've rewritten the equation letter spacing and vertical spacing.

Question 5: The vertical space between figures and text and between equations and text should be improved.

       Response：We modified the vertical space between the graph and the text and between the equation and the text to 0.5 times the line spacing.

Question 6: References should be revised, and some of them are not found.

        Response：We revised the references and described the unfound references in detail.

Question 7: kinematics and dynamics analysis isn't a sufficient study to be published in this journal, and another developed study should be added.

       Response：We add a developed study to this article. Modifications are added to the end of the conclusion. Applying the dynamics and kinematics models established in this study, our group has developed a number of three-pronged equal-angular velocity universal couplings, which have different new structures, but the kinematic principles and kinematic characteristics reflect the guiding significance of this research result.

        Thank you for your suggestion, we have revised the pictures, equations, and references in the article, adjusted the position appropriately, and modified the mathematical letters in the text, and marked them in red. Thank you for taking the time out of your busy schedule to critique our paper.

Author Response File: Author Response.pdf

Reviewer 3 Report

The manuscript appears to present an original contribution; however, the novelty and utility of the proposed coupling mechanism warrant scrutiny. Several suggestions are offered to enhance the clarity of the paper:

1. The unique features of the proposed coupling in comparison to conventional Hooke joints remain ambiguous. It is implied that the novel coupling allows for variable output shaft speeds within certain bounds. However, it is widely acknowledged that two interconnected Hooke joints establish a homokinetic transmission, wherein the output velocity precisely mirrors the input velocity. Therefore, the authors should articulate distinct advantages of the proposed coupling over the utilization of two Hooke joints.

2. Furthermore, the paper solely resides in the realm of theoretical discourse. It is noted that the concept of these new joints was introduced in 2003, as referenced by [11]. However, the referenced source cannot be located in any extant database. The title of the purported reference bears resemblance to the current research. It would be pertinent for the authors to accurately cite reference [11] or provide a means to access the referenced work.

3. In order to augment the scholarly merit and reader confidence in the theoretical findings presented, experimental validation is deemed imperative. Even by referencing previously published experimental results, the credibility and applicability of the theoretical outcomes can be substantiated.

The English is clear, only minor editing being necessary.

Author Response

Dear reviewers:

Thank you very much for your interest in our article and for pointing out the flaws in the analytical manuscript. We've addressed your question point by point below, and we hope you'll find the revised content acceptable for publication.

Question 1: The unique features of the proposed coupling in comparison to conventional Hooke joints remain ambiguous. It is implied that the novel coupling allows for variable output shaft speeds within certain bounds. However, it is widely acknowledged that two interconnected Hooke joints establish a homokinetic transmission, wherein the output velocity precisely mirrors the input velocity. Therefore, the authors should articulate distinct advantages of the proposed coupling over the utilization of two Hooke joints.

       Response：The traditional Hooke universal joint has the advantages of simple structure and strong transmission capacity. However, the angular velocity of the input shaft and the output shaft is instantaneously unequal when single-linked, resulting in a moment of inertia, which causes effects such as vibration. This is especially noticeable at high speeds. Under the proper arrangement conditions, although the input shaft and the output shaft can rotate at equal angular speeds, the movement of the intermediate shaft will still produce a vibration effect. The new cardan coupling achieves accurate angular velocity transmission, whether single or double, with almost no moment of inertia effect. Vibration is reduced and the transmission is smooth, especially at high speeds.

Question 2: Furthermore, the paper solely resides in the realm of theoretical discourse. It is noted that the concept of these new joints was introduced in 2003, as referenced by [11]. However, the referenced source cannot be located in any extant database. The title of the purported reference bears resemblance to the current research. It would be pertinent for the authors to accurately cite reference [11] or provide a means to access the referenced work.

        Response：For this issue, we have revised ref. 11.

Question 3: In order to augment the scholarly merit and reader confidence in the theoretical findings presented, experimental validation is deemed imperative. Even by referencing previously published experimental results, the credibility and applicability of the theoretical outcomes can be substantiated.

       Response：We added in the introduction part: the three-pronged sliding universal coupling was tested for synchronization experiments under different rotation angles in the early stage, and the experimental results proved that the universal coupling can achieve the effect of accurate angular velocity rotation, in the case of small  corner, the error is extremely small, and does not affect the engineering application, and can be used in the occasion that requires the use of equal angular velocity transmission universal coupling. The error law of the experiment has an important reference role for the analysis of mechanical properties in this paper.

        Thank you again for reviewing and guiding our papers, and for your valuable comments.

Author Response File: Author Response.pdf

Reviewer 4 Report

The study investigates the kinematic and dynamic characteristics of a novel three-pronged sliding universal coupling using directional cosine matrices and simplified geometric models. Findings suggest the coupling demonstrates quasi-constant angular velocity and optimal mechanical performance within a specific operating angle range. Before publication, the authors should consider the following concerns.

1) The aim of the study should be given. For example, “This study aims to.” In this regard, please consider adding a line or two at the beginning of the abstract, providing background context to the study. Then, highlight the gap to be filled and the purpose of the paper. Why is it necessary to study the kinematic and dynamic characteristics of the novel system? This is the first study on it.
2) What are the implications of the proposed system? Please consider adding a line or two at the end of the abstract, commenting on the broader application of the study.
3) Figure 2–4 should be improved. Some of the angles are difficult to read and understand.
4) It would be interesting to compare the dynamic response of the novel solution to traditional ones so that interested readers could consider implementing the novel solution.
5) The concluding section is a summary of the results. Thus, this section requires substantial changes. The conclusion should be clearly stated that the objectives of the study have been met, comment on the limitation, potential future work and the broader implication of the results.

Author Response

Dear Reviewers:

       We thank you for your professional review work, constructive comments and valuable suggestions for our manuscripts. We do your job very much. In response to your comments, we have the following responses:

Question 1: The aim of the study should be given. For example, “This study aims to.” In this regard, please consider adding a line or two at the beginning of the abstract, providing background context to the study. Then, highlight the gap to be filled and the purpose of the paper. Why is it necessary to study the kinematic and dynamic characteristics of the novel system? This is the first study on it.

       Response：In response to this question, we add after the first sentence of the summary: The purpose of this study is to demonstrate that compared with the traditional unequal angular velocity universal coupling (such as Hooke universal coupling), the universal coupling has the superior characteristics of constant angular speed transmission, simple structure and strong transmission capacity by performing kinematic and dynamic analysis of the new three-pronged sliding constant angular velocity universal coupling. It provides a broad prospect for applications in automotive and other fields.

Question 2: What are the implications of the proposed system? Please consider adding a line or two at the end of the abstract, commenting on the broader application of the study.

        Response：We added at the end of the summary: It can be widely used in the automobile industry, tie steel industry and other occasions that require angular transmission. It is especially used in high-speed operation and large transmission capacity.

Question 3: Figure 2–4 should be improved. Some of the angles are difficult to read and understand.

        Response：We have made changes to Figure 2-4.

Question 4: It would be interesting to compare the dynamic response of the novel solution to traditional ones so that interested readers could consider implementing the novel solution.

         Response：To address the above issues, we add to the conclusion: The new three-pronged sliding universal coupling as a new solution has significant advantages compared with the traditional solution. Especially in the application environment of high speed and heavy load, it reflects unique advantages, and is expected to replace traditional solutions and widely enter the application field.

Question 5: The concluding section is a summary of the results. Thus, this section requires substantial changes. The conclusion should be clearly stated that the objectives of the study have been met, comment on the limitation, potential future work and the broader implication of the results.

       Response：To address the above issues, we add to the conclusion: The study, kinematics, dynamics analysis has achieved the research objectives. The research results are mainly applied to the three-pronged universal coupling with constant angular velocity transmission. It is of guiding significance for the development of new structures and analytical mechanical properties in the future, and will be committed to systematic research in the future to reflect a wider range of application value.

      We did our best to improve the manuscript and made some changes in red in the revised paper, but it did not affect the content and framework of the paper. We would like to express our sincere gratitude to the editors and reviewers for their enthusiastic work and hope that the revisions will be recognized. Thank you again for your comments and suggestions.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

The authors answered to my comments and revised the paper accordingly.

My suggestion is to accept the paper in the present form.

Author Response

Dear reviewers:

       I am glad that you have accepted our article. Thank you very much for your guiding comments on our article. I wish you a happy life.

Reviewer 2 Report

Accept after minor revision. Conclusion is too long.

Minor editing of English language required.

Author Response

 Dear reviewers:

      Thank you very much for once again suggesting our article and pointing out the flaws in the analytical manuscript. We've made changes to your question and hope that you will find the revised content acceptable for publication.

Question：The conclusion is too long.

       Response：We have made modifications to address the issue of excessively long conclusions. We have made modifications to the parts of the conclusion numbered (1) and (3), and the modified parts are highlighted in red in the article.

       Thank you again for reviewing and guiding our papers, and for your valuable comments.

Author Response File: Author Response.pdf

Reviewer 3 Report

The authors answered all my questions and took my suggestions into consideration. I recommend publication of the paper in its present form.

The paper is written very well. Just minor correction is requested.

Author Response

Dear reviewers:

       I am glad that you have accepted our article. Thank you very much for your guiding comments on our article. I wish you a happy life.

Reviewer 4 Report

I appreciate that the authors have considered most of my concerns. However, I still believe that Concern 4 has not been properly tackled. That is, it would be interesting to compare the dynamic response of the novel solution to
traditional ones so that interested readers could consider implementing the novel solution.
The authors claim that "The new three-pronged
sliding universal coupling as a new solution has significant advantages over the traditional
solution. Especially in the application environment of high speed and heavy load, it reflects unique advantages and is expected to replace traditional solutions and widely enter the application field." However, there is no supporting evidence in the results section in this regard. Thus, the author should improve this aspect before publication.

No particular examples.

Author Response

Dear reviewers:

       We are very grateful for your professional comments on our articles, and you are very grateful for your valuable comments. Based on your suggestion, we have made extensive corrections to the previous manuscript as follows:

         In response to this question, we have added some content after the introduction. Specifically, after many experimental verifications, it is proved that the three-pronged sliding cardan shaft has the characteristics of stable transmission capacity in a straight line in the range of commonly used corner 25⁰ . The transmission capacity of the traditional coupling decreases in a curved state, and the decreasing speed is significantly accelerated, resulting in a significant decrease in the transmission capacity. When the rotation angle is less than 25⁰ , the three-pronged sliding universal coupling has the advantage of improving the transmission capacity and thus improving the transmission efficiency, which has become an important advantage in the promotion and application.

Author Response File: Author Response.pdf