Transmission Angle Analysis of a Type of Parallel Manipulators
Round 1
Reviewer 1 Report
the title seems good for presentations. but, in my opinion, there is many problem should be addressed as follows:
1- the main contributions of paper are not clear for me.
2- the refs should be updated and covered all type of closed kinematic chain and parallel ones. for example the follows:
10.1109/ICRoM.2017.8466214
10.1109/ICRoM48714.2019.9071871
3- the numerical analysis needed to be added to abstract and conclusion sections
4- the flowcharts for implementing the process are needed.
5- the simulation results should be checked and validated precisely as well as verified with the external data.
6- the formulations are too massive and needed to summarized by the use of appendixes.
Author Response
- the main contributions of paper are not clear for me.
Reply: Thank you for your valuable comments. The main contributions of the paper are that two types of transmission angles are defined to evaluate the kinematic performance of parallel manipulators, with which the direct and indirect singularities can be identified in a straightforward manner. At present, many research works related to the kinematic performance are mainly focused on a conditioning index obtained from the Jacobian matrix, such as the conditioning number, determinant and singular valued, etc. However, some problems still exist when they are taken as performance indices: (a) for the studied out-parallel manipulator, it is inappropriate to utilize the condition number as the distance measure for the singularity. The study work in [16] indicates that the singular configuration of a 2-DOF out-parallel robot still can be obtained even though the condition number of Jacobian matrixes equals one. As a consequence, a comprehensive index is adopted combining both the area of workspace and condition number of Jacobian matrixes to carry out the optimal design, employing minimum transmission angle as the extra constraint. (b) It seems that the conditioning indices own no exact physical meaning. As a result, it is difficult to define the reasonable limited value of the conditioning indices as design criterion.
As a result, this paper presents a novel common approach that transmission angle analysis for a type of parallel manipulators to solve this problem, and in this way the motion transmission performance in a mechanism can be evaluate during the course of design
- the refs should be updated and covered all type of closed kinematic chain and parallel ones. for example the follows:
10.1109/ICRoM.2017.8466214
10.1109/ICRoM48714.2019.9071871
Reply: Thank you for your valuable comments. Because there are so many related to all types of closed kinematic chains and parallel ones, we have updated some important ones. Such as:
Korayem, M. H., and Dehkordi, S. F. Derivation of motion equation for mobile manipulator with viscoelastic links and revolute-prismatic flexible joints via recursive Gibbs-Appell formulations. Robotics & Autonomous Systems, 2018, 103, 175-198.
Hajiabadi, S., Dehkordi ,S. F. A New Method of Dynamic Modelling and Optimal Energy Distribution for Cooperative Closed Chain Manipulators. 2019 7th International Conference on Robotics and Mechatronics (ICRoM), 2019.
Salunkhe, D. H.; Michel, G.; Kumar, S.; et al. An efficient combined local and global search strategy for optimization of parallel kinematic mechanisms with joint limits and collision constraints. Mechanism and Machine Theory, 2022, 173, 104796-104830.
- the numerical analysis needed to be added to abstract and conclusion sections
Reply: Thank you for your valuable comments. We add the numerical analysis to abstract and conclusion sections.
4、the flowcharts for implementing the process are needed.
Reply: Thank you for your valuable comments. The process flow is as follows: First, we analyzed one type of the parallel manipulators that composed of one rigidity platform with only translation motion in space, together with kinematic chains formed by three joints and two moving links. Second, build the Jacobian Matrix to obtain the linear speed of the moving platform and angular speed of the link. And then, the angle α and β related to the singularities can be regarded as the inner transmission angle (ITA) and cross transmission angle (CTA) for the kinematic chain, respectively. The redundancy feature can improve the performance of avoiding the kinematic singularities. Finally, in order to investigate the influence of transmission angles on the kinematic performance of this type of parallel manipulators, the Diamond robot and Delta robot are adopted here for the analysis. The flowcharts for implementing the process is as follows:
5、the simulation results should be checked and validated precisely as well as verified with the external data.
Reply: Thank you for your valuable comments. We provide detailed simulation results and analysis. The comparative effects of condition number and the transmission angle on the kinematic performance of the Diamond robot and Delta can be obtained from the figure. And in the figure, we give the detailed numerical change results.
6、the formulations are too massive and needed to summarized by the use of appendixes.
Reply: Thank you for your valuable comments. For each step, we elaborate our analysis method through formula derivation and graphics as much as possible. Therefore, there are too massive formulations, so that readers can understand how each step comes. Because many formulas are analyzed together with the graphics, if put in the appendix, they may not be very clear for readers.
Author Response File: 
Author Response.docx
Reviewer 2 Report
Manuscript Number: applsci-1866912
Full TitleTransmission Angle Analysis in a Type of Parallel Manipulators
The authors proposed to define a transmission/pressure angle for a type of parallel manipulators to achieve the translations in space with the same topological struc tures applied in such Delta and Diamond robot in this paper. My reviews and suggestions about their publications are listed;
Why did you do such a study? What is your motivation? What is the contribution of such a study to the literature? In general, these are not given in detail in the paper. So, to attract the reader's attention, you should present the article from a different perspective.
You should also pay attention to the following topics.
1) The abstract should include the context or background information for your research; the general topic under study; the specific topic of your research; why is it important to address these questions; the significance or implications of your findings or arguments. It must also contain more numeric values. Please highlight your contribution. Reorganize the abstract to conclude:
(a) The overall purpose of the study and the research problems you investigated.
(b) The basic design of the study.
(c) Major findings or trends found as a result of the study.
(d) A brief summary of your interpretations and conclusions.
2)The introduction should be extended to the more detailed background that would be supported by some literatüre. The contributions of the article should be presented in more detail in this section. The introduction needs to clarify the (1) motivation, (2) challenges, (3) contribution, (4) objectives, and (5) significance/implication.
3) Add more recent reference to enhance literature survey section. Discuss the state-of-art techniques with their merits and issues. The literature should be developed and, if possible, presented in more papers published in 2021 and 2022. Literature Review section can be further strengthened by discussing various recent related article. Discuss the research gaps and relate how the proposed work has improved them. Literature Review section can be further strengthened by discussing various recent related article. Discuss the research gaps and relate how the proposed work has improved them.
4) You should submit more experimental study results for your work. Experimental studies are insufficient. You should also provide comparisons with similar studies (In particular, studies in recent years).
5) What solution you propose to make the system more robust. What is your difference from similar studies?
6) the Conclusions section, the contribution of the study should be supported by numerical values. In other words, the author should discuss the future works related to proposed method and its drawbacks. Rewrite the conclusion with following comment:
(a) Highlight your analysis and reflect only the important points for the whole paper.
(b) Mention the implication in the last of this section. Please, carefully review the manuscript to resolve these issues.
(c) This section should be supported with numerical values.
There are some typos and grammar errors in the manuscript. The authors should polish the manuscript to improve its writing. The quality of the article should be increased.
I think a similar study was done in 2013. You should do a better literature search.
Mei, J. P., & Hu, L. H. (2013). Parallel Manipulators' Analysis by Transmission Angle. In Applied Mechanics and Materials (Vol. 401, pp. 226-230). Trans Tech Publications Ltd.
The authors really spent a lot of time preparing the article. However, the contribution of the article to the literature is very low. There are some typos and grammar errors in the manuscript. The authors should polish the manuscript to improve its writing. The quality of the article should be increased. The contribution of the article to the literature is low and lack of novelty. Authors should examine the subject in more different to contribute to the literature. In particular, there is no comparison with similar studies in the article. It must be given as a table or paragraph. The overall quality is very poor, also the English must be strongly revised to make the paper even readable.
Author Response
1、Why did you do such a study? What is your motivation? What is the contribution of such a study to the literature? In general, these are not given in detail in the paper. So, to attract the reader's attention, you should present the article from a different perspective.
You should also pay attention to the following topics.
1) The abstract should include the context or background information for your research; the general topic under study; the specific topic of your research; why is it important to address these questions; the significance or implications of your findings or arguments. It must also contain more numeric values. Please highlight your contribution. Reorganize the abstract to conclude:
(a) The overall purpose of the study and the research problems you investigated.
(b) The basic design of the study.
(c) Major findings or trends found as a result of the study.
(d) A brief summary of your interpretations and conclusions.
Reply: Thank you for your valuable comments. The motivation of the paper is to define a transmission/pressure angle for a type of parallel manipulators to achieve the translations in space with the same topological structures applied in such Delta and Diamond robot. Though transmission angle analysis for the parallel mechanisms, the kinematic performance can be accurately ensured. The main contributions of the paper are that two types of transmission angles are defined to evaluate the kinematic performance of parallel manipulators, with which the direct and indirect singularities can be identified in a straightforward manner. At present, many research works related to the kinematic performance are mainly focused on a conditioning index obtained from the Jacobian matrix, such as the conditioning number, determinant and singular valued, etc. However, some problems still exist when they are taken as performance indices: (a) for the studied out-parallel manipulator, it is inappropriate to utilize the condition number as the distance measure for the singularity. The study work in [19] indicates that the singular configuration of a 2-DOF out-parallel robot still can be obtained even though the condition number of Jacobian matrixes equals one. As a consequence, a comprehensive index is adopted combining both the area of workspace and condition number of Jacobian matrixes to carry out the optimal design, employing minimum transmission angle as the extra constraint. (b) It seems that the conditioning indices own no exact physical meaning. As a result, it is difficult to define the reasonable limited value of the conditioning indices as design criterion.
As a result, this paper presents a novel common approach that transmission angle analysis for a type of parallel manipulators to solve this problem, and in this way the motion transmission performance in a mechanism can be evaluate during the course of design
In addition, we have revised the abstract according to your suggestion, as follows:
2、The introduction should be extended to the more detailed background that would be supported by some literature. The contributions of the article should be presented in more detail in this section. The introduction needs to clarify the (1) motivation, (2) challenges, (3) contribution, (4) objectives, and (5) significance/implication.
Reply: Thank you for your valuable comments. We modified and extended the introduction. In the first and second paragraphs of the introduction, we introduced the paper’s background in detail, including two types of parallel manipulators that Diamond robots and Delta robots. In the third paragraph of the introduction, the challenges and the contribution are Summarized. In the fifth paragraph of the introduction, the purpose of this paper is to define a transmission/pressure angle for a type of parallel manipulators to achieve the translations in space with the same topological structures applied in such Delta and Diamond robot. In the sixth paragraph of the introduction, the significance/implication of the research work is demonstrated in the kinematic performance of one type of the parallel manipulators.
3、Add more recent reference to enhance literature survey section. Discuss the state-of-art techniques with their merits and issues. The literature should be developed and, if possible, presented in more papers published in 2021 and 2022. Literature Review section can be further strengthened by discussing various recent related article. Discuss the research gaps and relate how the proposed work has improved them. Literature Review section can be further strengthened by discussing various recent related article. Discuss the research gaps and relate how the proposed work has improved them.
Reply: Thank you for your valuable comments. We added several recent references, such as [2-4][14-16], etc. We discuss the methods of these references, summarize the advantages and disadvantages of the methods, and put forward some ideas for improvement. For example, transmission/pressure angle seems to be a way to solve this problem, and in this way the motion transmission performance in a mechanism can be evaluate during the course of design [20]. Though angle analysis has been extensively studied in planar mechanisms, little work has been conducted focusing on the parallel mechanisms. A method for dynamic dimensional synthesis in [21] is proposed for Delta robot, in which the kinematic performance can be partly ensured via introducing the constraint condition of transmission angle. Notably, the number of limbs may exceed the needed numbers for actuating the moving platform since it has only 3-DOF translations at most in space, which can make the manipulator to be actuation redundancy. Therefore, the approaches are also applicable to implement the kinematic design of redundant Delta-like robot mentioned in [22].
4、You should submit more experimental study results for your work. Experimental studies are insufficient. You should also provide comparisons with similar studies (In particular, studies in recent years).
Reply: Thank you for your valuable comments. In Section 4, we conducted comparison analysis of condition number and ITA/CTA taking Delta and Diamond robots. The relationship between the Jacobian's angle and the condition number is studied to demonstrate the validity of the angle in ensuring the motion performance for the parallel manipulator. The simulation works are conducted to prove the effectiveness of two kinds of transmission angle for the evaluating kinematic performance of parallel manipulators by using the Diamond and Delta robot. It indicates that the defined angles have the nearly the same features as the condition number of Jacobian matrixes in evaluating kinematic performance of the parallel manipulator and determining the workspace.
5、What solution you propose to make the system more robust. What is your difference from similar studies?
Reply: Thank you for your valuable comments. By analyzing the kinematic singularity of the translational parallel manipulator, two kinds of angles are proposed to evaluate the kinematic performance of parallel manipulator. The condition number cannot thoroughly depict the distance from singularity of parallel robots. Therefore, it may not be very suitable for merely taking the condition number or its modified versions as a performance index of parallel robots for performance evaluation or optimal design. Then, it is necessary to introduce the ITA and CTA into the optimal design of parallel robots. Figure 8 and Figure 9 exactly justify the above analysis and prove that all of these characteristic parameters nearly play the same role in determining a better-conditioned workspace.
6、In the conclusions section, the contribution of the study should be supported by numerical values. In other words, the author should discuss the future works related to proposed method and its drawbacks. Rewrite the conclusion with following comment:
(a) Highlight your analysis and reflect only the important points for the whole paper.
(b) Mention the implication in the last of this section. Please, carefully review the manuscript to resolve these issues.
(c) This section should be supported with numerical values.
Reply: Thank you for your valuable comments. The conclusions part has been revised according to your suggestions, as follows: This paper investigates two transmission angles for the parallel manipulator. By analyzing the kinematic singularity of the translational parallel manipulator, two kinds of angles are proposed to evaluate the kinematic performance of parallel manipulator. Taking both the Diamond and Delta parallel manipulators as an example, the relationships are investigated between the angles and condition number of Jacobian which is a vital performance index for parallel manipulators throughout the workspace. Then, the simulation works of the evaluating kinematic performance of the two kinds of parallel manipulators are conducted to verify the effectiveness of the proposed transmission angle. It indicates that the defined angles have the nearly the same features as the condition number of Jacobian matrixes in evaluating kinematic performance of the parallel manipulator and determining the workspace.
Author Response File: Author Response.docx
Round 2
Reviewer 1 Report
The revisions have been done properly.
Author Response
Thank you for your valuable comments!
Reviewer 2 Report
I have reviewed the revised manuscript title "Transmission Angle Analysis in a Type of Parallel Manipulators". After revising my initial comments and comparing the changes, done by the authors, with them. I found that the authors did not respond to some comments.
Authors should emphasize contribution and novelty in the abstract. Also Authors should provide more numerical values in the abstract and conclusions sections.
The authors really spent a lot of time preparing the article for both the previous version and the revised version. However, I think that the contribution of the article to the literature is still low. There are also some typos and grammar errors in the manuscript. The authors should polish the manuscript to improve its writing. The quality of the article should be increased. The contribution of the article to the literature is low and lack of novelty. Authors should examine the subject in more different to contribute to the literature. In particular, there is no comparison with similar studies in the article. It must be given as a table or paragraph. The overall quality is very poor, also the English must be strongly revised to make the paper even readable.
It shows similarities with the folow study .
Mei, J. P., & Hu, L. H. (2013). Parallel Manipulators' Analysis by Transmission Angle. In Applied Mechanics and Materials (Vol. 401, pp. 226-230). Trans Tech Publications Ltd.
Although I said it in my previous comment, there was no reply to this.
Author Response
1.Authors should emphasize contribution and novelty in the abstract. Also Authors should provide more numerical values in the abstract and conclusions sections.
Reply: Thank you for your valuable comments. We have comprehensively revised the Abstract and Conclusions to highlight the contribution and novelty of the article. The revised contents are as follows:
Abstract: For most research works, conditioning index is used to analyze the kinematic performance for a type of parallel manipulators whose traveling plate has only translation in the workspace and each limb is made up of three joints and two moving links. However, it is difficult to determine the reasonable limit value of conditioning index as the design criterion. Therefore, this paper defines two types of transmission angles to evaluate the kinematic performance of parallel manipulators, with which the direct and indirect singularities can be identified in a straightforward manner. Taking both the Diamond and Delta parallel manipulators as an example, the relationships are investigated between the angles and condition number of Jacobian which is a vital performance index for parallel manipulators throughout the workspace. Then, the simulation works are conducted to prove the effectiveness of two kinds of transmission angles for the Diamond and Delta robot. It indicates that the defined angles are well characterized compared to the condition number of Jacobian matrix in evaluating kinematic performance of the parallel manipulators and determining the workspace.
Conclusions
It may not be appropriate to only use the condition number or its modified version as the performance index of the performance evaluation or optimization design of the parallel robots. Therefore, this paper investigates two transmission angles for the optimization design of the parallel manipulators. By analyzing the kinematic singularity of the Diamond and Delta parallel manipulators, two kinds of angles are proposed to evaluate the kinematic performance of parallel manipulator. Then, the simulation works of the evaluating kinematic performance of the two kinds of parallel manipulators are conducted to verify the effectiveness of the proposed transmission angle. It indicates that the defined angles are well characterized compared to the condition number of Jacobian matrixes in evaluating kinematic performance of the parallel manipulator and determining the workspace. The two transmission angles defined in this paper makes the parallel robots not only have better motion performance, but also achieve a better workspace for parallel robot.
2. The authors really spent a lot of time preparing the article for both the previous version and the revised version. However, I think that the contribution of the article to the literature is still low. There are also some typos and grammar errors in the manuscript. The authors should polish the manuscript to improve its writing. The quality of the article should be increased. The contribution of the article to the literature is low and lack of novelty. Authors should examine the subject in more different to contribute to the literature. In particular, there is no comparison with similar studies in the article. It must be given as a table or paragraph. The overall quality is very poor, also the English must be strongly revised to make the paper even readable.
Reply: Thank you for your valuable comments. We rechecked some typos and grammar errors in the manuscript, and modified them. In addition, we provide detailed simulation results and analysis. The comparative effects of condition number and the transmission angle on the kinematic performance of the Diamond robot and Delta can be obtained from the figure. And in the figure, we give the detailed numerical change results.
3.It shows similarities with the folow study .
Mei, J. P., & Hu, L. H. (2013). Parallel Manipulators' Analysis by Transmission Angle. In Applied Mechanics and Materials (Vol. 401, pp. 226-230). Trans Tech Publications Ltd.
Although I said it in my previous comment, there was no reply to this.
Reply: Thank you for your valuable comments. Compared with the mentioned paper, we take both the Diamond and Delta parallel manipulators as example, the relationships are investigated between the angles and condition number of Jacobian. Then, the simulation works are conducted to prove the effectiveness of two kinds of transmission angles for the Diamond and Delta robot. It indicates that the defined angles are well characterized compared to the condition number of Jacobian matrix in evaluating kinematic performance of the parallel manipulators and determining the workspace.
However, the mentioned paper takes a new robot as an typical case to guarante the kinematic performance of parallel robots. It implies that they have nearly the same function with the condition number of Jacobian matrix in evaluating kinematic performance of robotics and determining a well-conditioned workspace.
Round 3
Reviewer 2 Report
I have reviewed the revised manuscript title "Transmission Angle Analysis in a Type of Parallel Manipulators". After revising my initial comments and comparing the changes, done by the authors, with them. I found that the authors addressed and answered most of the comments efficiently. Overall, the revised manuscrip is well organized and carefully prepared. The response letter was elegant and satisfactory. I thank the authors for their kind responses. The authors have sufficiently address my all comments. So, I think it is appropriate to accept the revised article. The authors have addressed all the concerns and responded to the review comments. The manuscript can be published in this journal.
