Form-Finding Analysis of a Class 2 Tensegrity Robot
, Oscar A. Zavala-Pérez 2,†, Gerardo I. Pérez-Soto 2,†, Juvenal Rodríguez-Reséndiz 2,† and Karla A. Camarillo-Gómez 1,*,†Round 1
Reviewer 1 Report
The manuscript is interesting and contains a new approach to the form-finding of class 2 tensegrity robots. The introduction is well written and it provides a wide background to the presented ideas. I have some concerns about the parts of the paper, which are not original, but I understand that the authors decided to show them for the completeness reasons.
I have the following remarks:
The last section of the paper should be extended - there is almost no discussion of the results and the conclusions are very brief.
In section 5 four experiments are discussed - in my opinion it would be good to show graphically the analysed configurations of the robot.
I have some concerns about the finite element model - have you tried to model beams using more than one FE per beam? Would it not improve the results?
Figure 9 is not clear enough - the tables should be created by the authors instead of printing the results directly from the software.
The title of Table 4 should be changed to "Comparison between..."
In Table 4 "Experiment 1" is mentioned twice - it should be changed to "Experiment 4".
There are quite a few language mistakes - please check the manuscript before resubmitting it (especially section 2 and 3). Some of the examples are mentioned below:
- line 137 - "and" instead of "y",
- line 81 - "r1 y r2, en los extremos restantes",
- line 139 - please, reformulate the sentence: "Furthermore, as design parameters it is known: the total mass of the robot",
- line 132 - "of the same".
Author Response
Form Finding Analysis of a Class 2 Tensegrity Robot
Reviewer 1
The manuscript is interesting and contains a new approach to the form finding of class 2 tensegrity robots. The introduction is well written and it provides a wide background to the presented ideas. I have some concerns about the parts of the paper, which are not original, but I understand that the authors decided to show them for the completeness reasons.
R.
Thank you for the comments. The preliminaries were necessary to include in order to the comprehension of the paper.
I have the following remarks:
The last section of the paper should be extended - there is almost no discussion of the results and the conclusions are very brief.
R.
Thank you for the comments. An extended explanation was added to the paper.
In section 5 four experiments are discussed - in my opinion it would be good to show graphically the analysed configurations of the robot.
R.
Thank you for the comments. The geometric configurations of the four numerical experiments were included in the paper, showed in Figures 1 – 4.
Figure 1. Experiment 1
Figure 2. Experiment 2
Figure 3. Experiment 3
Figure 4. Experiment 4
I have some concerns about the finite element model - have you tried to model beams using more than one FE per beam? Would it not improve the results?
R.
Thank you for the comments. The kinematic and the static analysis consider that the structural elements of the robot are in fact, rigid bodies. These are simulated as beams due to the characteristics of degrees of freedom of the nodes of the assembly. However, when the mechanical properties have to be assigned to each element, particularly the modulus of elasticity, this is higher compared with the applied forces. So, the small displacements generated by the loads are practically neglected, approaching the behavior of the structure as a rigid body. Then, the author's purposes for using ANSYS software are:
(a) to guarantee that the geometric configuration is stable equilibrium,
(b) to compare them with the obtained results of the proposed methodology of the forces
in the cables, springs and kinematic joint.
In conclusion, if more elements were added to the beam to discretize of the robot the results would not be better, and it only increases the computational time, and the graphical view of the results could be more complicated.
Figure 9 is not clear enough - the tables should be created by the authors instead of printing the results directly from the software.
R.
Thank you for the comments. According to the authors of this paper, the importance of Figure 9 is to show the veracity of the results by showing directly from software ANSYS. But if the reviewer and editor consider that it is necessary to substitute the Figure 9 by Tables, the authors can do it. Still, the images presented in Figure 9 had high resolution.
The tables requested by the reviewer are presented below in Tables 1-4.
Table 1. Data information for experiment 1
Table 2. Data information for experiment 2
Table 3. Data information for experiment 3
Table 4. Data information for experiment 4
The title of Table 4 should be changed to "Comparison between..."
R.
Thank you for the comments. The word has been changed.
In Table 4 "Experiment 1" is mentioned twice - it should be changed to "Experiment 4".
R.
Thank you for the comments. The label has been changed.
There are quite a few language mistakes - please check the manuscript before resubmitting it (especially section 2 and 3). Some of the examples are mentioned below:
- line 137 - "and" instead of "y",
- line 81 - "r1 y r2, en los extremos restantes",
- line 139 - please, reformulate the sentence: "Furthermore, as design parameters it is known: the total mass of the robot",
- line 132 - "of the same".
R.
Thank you for the comments. The previous observations have been attended.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
The paper “Form Finding Analysis of a Class 2 Tensegrity Robot” Oscar A. Zavala-Pérez, Carlos G. Manríquez-Padilla, Gerardo I. Pérez-Soto 1, Juvenal Rodríguez-Reséndiz, and Karla A. Camarillo-Gómez proposed a form-finding analysis of a class 2 tensegrity robot. the analysis of the workspace is carried out through the results of the kinematic analysis, subsequently, from the static analysis, equilibrium positions are found within the calculated workspace. The authors also use software ANSYS for a result verification.
1) The novelty of the paper is not clear, and it should rewrite in the abstract, and the reviewer did not understand the contribution of this paper. Also what results did the authors get, it should be clarified?
2) In introduction part, the authors should cite those relevant papers to emphasis what the novelty of this paper. Such as
1. https://ieeexplore.ieee.org/document/8351924
‘Development of a SMA-fishing-line-McKibben bending actuator’.
2. https://www.liebertpub.com/doi/10.1089/soro.2018.0034
‘A Soft, Steerable Continuum Robot That Grows via Tip Extension’.
3. https://www.tandfonline.com/doi/full/10.1080/01691864.2018.1476179
‘Design and control of a novel variable stiffness soft arm’.
4. https://ieeexplore.ieee.org/document/8730312
‘Design and Development of a Novel SMA Actuated Multi-DOF Soft Robot’
3) In the second part, the design principle of the structure should be clarified, and why did the authors want to design this structure, and what is novelty of this structure?
4) The English grammar errors and others, such as,
Line 139 ‘Furthermore, as design parameters it is known: the total mass of the robot.’
Line 81 ‘r1 y r2, en los extremos restantes’
The authors should check the paper carefully.
5) The results are not clearly, and did the simulation results verify the design and modeling?
Author Response
Form Finding Analysis of a Class 2 Tensegrity Robot
Reviewer 2
The paper “Form Finding Analysis of a Class 2 Tensegrity Robot” Oscar A. Zavala-Pérez, Carlos G. Manríquez-Padilla, Gerardo I. Pérez-Soto 1, Juvenal Rodríguez-Reséndiz, and Karla A. Camarillo-Gómez proposed a form-finding analysis of a class 2 tensegrity robot. the analysis of the workspace is carried out through the results of the kinematic analysis, subsequently, from the static analysis, equilibrium positions are found within the calculated workspace. The authors also use software ANSYS for a result verification.
R.
Thank you for the comments.
1) The novelty of the paper is not clear, and it should rewrite in the abstract, and the reviewer did not understand the contribution of this paper.
R.
Thank you for the comments. In this paper, a new form--finding analysis methodology for a class 2 tensegrity robot is proposed. The methodology consists of two steps: first, the analysis of the possible geometric configurations of the robot is carried out through the results of the kinematic position analysis; second, from the static analysis, the equilibrium positions of the robot are founded which represents its workspace. Both kinematics and static analysis were resolved in a closed--form using basic tools of linear algebra instead of the strategies used in literature. Four numerical experiments are presented using the finite element analysis software ANSYS$^\copyright$. Additionally, a comparison between the results of the form-finding analysis methodology proposed and the ANSYS results are presented.
Also what results did the authors get, it should be clarified?
R.
Thank you for the comments. The main result of this paper is the new methodology of the form-finding analysis for the class 2 tensegrity robot. Based on the proposed methodology, the following results are obtained for the case of study:
(a) The closed-form solution of the kinematic and static analysis of the robot tensegrity.
(b) The solution of the form-finding analysis which represents the workspace of the class 2 tensegrity robot.
(c) The comparison of the results obtained by the proposed methodology using the FEM software ANSYS.
2) In introduction part, the authors should cite those relevant papers to emphasis what the novelty of this paper. Such as
1. https://ieeexplore.ieee.org/document/8351924
‘Development of a SMA-fishing-line-McKibben bending actuator’.
2. https://www.liebertpub.com/doi/10.1089/soro.2018.0034
‘A Soft, Steerable Continuum Robot That Grows via Tip Extension’.
3. https://www.tandfonline.com/doi/full/10.1080/01691864.2018.1476179
‘Design and control of a novel variable stiffness soft arm’. Hao
4. https://ieeexplore.ieee.org/document/8730312
‘Design and Development of a Novel SMA Actuated Multi-DOF Soft Robot’
R.
Thank you for the comments. The references were included in the introduction section.
3) In the second part, the design principle of the structure should be clarified, and why did the authors want to design this structure, and what is novelty of this structure?
R.
Thank you for the comments. The tensegrity robot used as a case of study in this paper was presented in:
Manríquez--Padilla, C.G.; Camarillo--Gómez, K.A.; Pérez--Soto G.I.; Rodríguez--Reséndiz J.; Crane, C.D., III. “Development and Kinematic Position Analysis of a Novel Class 2 Tensegrity Robot”. Proceedings of the ASME 2018 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, Quebec City, Quebec, Canada, 26–-29 August 2018.
This robot is one of the few presented in the literature as a class 2 tensegrity robot, and the inspiration of its design is for biomechanical applications; however, the comprehensive understanding of this robot is too interesting for the authors.
A brief explanation of the motivation is added in the second part of the paper to attend the observation of the reviewer.
4) The English grammar errors and others, such as, Line 139 ‘Furthermore, as design parameters it is known: the total mass of the robot.’
Line 81 ‘r1 y r2, en los extremos restantes’
The authors should check the paper carefully.
R.
Thank you for the comments. The authors of the paper have already updated the paper grammar.
5) The results are not clearly, and did the simulation results verify the design and modeling?
R.
Thank you for the comments. The main result of this paper is the new methodology of the form-finding analysis for the class 2 tensegrity robot. Based on the proposed methodology, the following results are obtained for the case of study:
(a) The closed-form solution of the kinematic and static analysis of the robot tensegrity.
(b) The solution of the form-finding analysis which represents the workspace of the class 2 tensegrity robot.
(c) The comparison of the results obtained by the proposed methodology using the FEM software ANSYS.
The simulation of the class 2 tensegrity robot in the FEM software ANSYS proves the results of the proposed methodology; also, it verifies that the robot is in equilibrium with the geometric configuration analyzed.
Author Response File: Author Response.pdf
Reviewer 3 Report
This paper aims to present the form-finding analysis of a class 2 tensegrity robot. First, the Denavit–Hartenberg parameters used for direct kinematics analysis of the workspace and then joint angles were obtained for inverse kinematics. Finally, from the static analysis, equilibrium positions are found and compared with a numerical experiment is using the finite element analysis software ANSYS.
The paper can be further processed for publication considering the following:
1- The joint angles and are not shown properly in the images.
2- More explanations are required for simulating the kinematics and static force simulation results. Please clarify to readers how to implement the simulation from the equations.
3- There are some typographical errors that should be corrected as: in line 137 “ y with’
Author Response
Form Finding Analysis of a Class 2 Tensegrity Robot
Reviewer 3
This paper aims to present the form-finding analysis of a class 2 tensegrity robot. First, the Denavit–Hartenberg parameters used for direct kinematics analysis of the workspace and then joint angles were obtained for inverse kinematics. Finally, from the static analysis, equilibrium positions are found and compared with a numerical experiment is using the finite element analysis software ANSYS.
R.
Thank you for the comments.
The paper can be further processed for publication considering the following:
1- The joint angles and are not shown properly in the images.
Thank you for the comments. Notice that the joint angles are implicit int he paper when using the Denavit-Hartenberg parameters, this is, the angle $\theta_1$ is measured around the $z_0$ axis; and the angle $\theta_2$ is measured around $Z_1$ axis showed in Figure 2; also is wide explained in the reference:
Manríquez--Padilla, C.G.; Camarillo--Gómez, K.A.; Pérez--Soto G.I.; Rodríguez--Reséndiz J.; Crane, C.D., III. “Development and Kinematic Position Analysis of a Novel Class 2 Tensegrity Robot”. Proceedings of the ASME 2018 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, Quebec City, Quebec, Canada, 26–-29 August 2018.
2- More explanations are required for simulating the kinematics and static force simulation results. Please clarify to readers how to implement the simulation from the equations.
R.
Thank you for the comments. By substituting the parameters listed in Table 2 in the forward kinematic of position equations (6-13) it can obtain the coordinates of M, M_1, M_2, r_1, and r_2 showed in Figure 2, as well as the middle points of the superior base known by design B_1, B_2, B_3, B_4, $\Sigma_0$ and G. With the aforementioned information, the equation (25) can be computed resulting a matrix points showed in Figures 6 and 7.
A paragraph was added in section 4.2 to attend the reviewer observation.
3- There are some typographical errors that should be corrected as: in line
137 “ y with’
R.
Thank you for the comments. The observation has been resolved.
Author Response File: Author Response.pdf
Round 2
Reviewer 1 Report
I would like to thank the Authors for addressing my comments. I would recommend the article for publication in the present form.
Reviewer 2 Report
Recommendation: In my opinion, this manuscript can be considered for publication.
Reviewer 3 Report
No
