Mechatronic Model of a Compliant 3PRS Parallel Manipulator

Round 1

Reviewer 1 Report

The present work developed a mechatronic model of a compliant 3PRS parallel manipulator through integrating the inverse and direct kinematics, the inverse dynamic problem of the manipulator, and the dynamics of the actuators and the control. This work is generally well-in written and of the interest of the readers. I would like to recommend for its acceptance after the following comments are addressed:

1. How to determine the locations and shapes of the joints? 

2. Will the stress concentration around the joint significantly affect the behavior of the manipulator, for instance, the damage and fatigue? And is this also a possible reason for the inconsistency of the numerical and experimental results?

3. How to guarantee the optimality of the design? 

4. I would recommend the authors present some of the FEA analysis results, not only to compare with analytical and experimental results but also to illustrate the key configurations of the manipulator.

5. Whether the current work can be applied to design manipulators with 4, 5, or even more legs? 

6. Please supply some prospects or interesting applications of the present work.

Author Response

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Author Response File: Author Response.pdf

Reviewer 2 Report

This is a good research paper which integrates the inverse and direct kinematics, the inverse dynamic problem of the manipulator and the dynamics of the actuators as well as the control. There are some issues which should be sorted before the publishing of the paper.

Paper lacks a more thorough literature review about modelling of compliant 3PRS parallel manipulators. There is a lot of research concerning the above noted mechanisms which is only partially given in a paper. Furthermore, it is important that the authors point out the novelty of their approach as well difference to approach used by other authors.

The paper can be shorter as much of the model kinematics is already presented in paper

Ruiz, A., Campa, F.J., Roldán-Paraponiaris, C., Altuzarra, O. and Pinto, C., 2016. Experimental validation of the kinematic design of 3-PRS compliant parallel mechanisms. Mechatronics, 39, pp.77-88.

The authors should present just the final equations and reference the noted paper as source. Only the new content should be presented in this paper.

There is some text on Spanish language in the paper text (lines 306-308). The text should be given in English.

Author Response

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Author Response File: Author Response.pdf

Reviewer 3 Report

This paper gives detailed models for a compliant 3PRS manipulator and its related controls. It proposes a method to couple the kinematic and dynamic models to arrive at an overall control scheme in joint space. The execution of work appears sophisticated. However, methodology and context of work deserve more exlpanations and the model formulations should be simplified, wherever possible.
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Major remarks:

* The state-of-the-art section is very short and more should be said about similar works. In general, compliance in mechanisms can be achieved via flexibility in links and/or joints. The authors should include a more extensive state of the art study which covers both classes of mechanisms (with link and joint flexibility) and clearly motivate why they select a mechanism with link flexibility and model it as flexible joints via the pseudo rigid model. The authors should consider citing the following works (not only):
        * [1DOF Survey] Grioli G, Wolf S, Garabini M, et al. Variable stiffness actuators: The user’s point of view. The International Journal of Robotics Research. 2015;34(6):727-743. doi:10.1177/0278364914566515
        * [2DOF Application] Stoeffler, C., Kumar, S., Peters, H., Brüls, O., Müller, A., Kirchner, F.: Conceptual design of a variable stiffness mechanism in a humanoid ankle using parallel redundant actuation. In: 2018 IEEE-RAS 18th International Conference on Humanoid Robots (Humanoids), pp. 462–468. IEEE, Beijing (2018)
        * [2DOF Survey] Stoeffler C., Kumar S., Müller A. (2021) A Comparative Study on 2-DOF Variable Stiffness Mechanisms. In: Lenarčič J., Siciliano B. (eds) Advances in Robot Kinematics 2020. ARK 2020. Springer Proceedings in Advanced Robotics, vol 15. Springer, Cham. https://doi.org/10.1007/978-3-030-50975-0_32
        * [2DOF Application] Lemerle, S., Catalano, M. G., Bicchi, A., & Grioli, G. (2021). A Configurable Architecture for Two Degree-of-Freedom Variable Stiffness Actuators to Match the Compliant Behavior of Human Joints. Frontiers in Robotics and AI, 8, 10.

* The novelty of the approach does not become clear with regard to author's previous works (e.g. [10] and [11]).

* In CAD diagram of Fig. 1, no actuators are shown which gives an impression that the mechanism is passive which is not the case. The figure should be revised.  
 
* The term "mechatronic model" is used often and in different contexts (e.g. complete system or actuators) but it is left open to the reader what these models encompass. A clear definition of and a differentiation to dynamic and kinematic models would be helpful.

* The presentation of the mechatronic model is cumbersome and the description of Fig. 3 is incomplete: Subscripts "c" are not explained (probably commanded) and there is no criterion given for calling the "compliant 3PRS model". Also the phrase: "As the force required to deform the compliant mechanism is higher than for a conventional mechanism, it is advisable to model the stiffness of the actuator and its transmission chain, as it may happens that a given transmission is less rigid than the compliant mechanism itself." can be misleading. It should rather be explained by means of Figure 3 how kinematics and kinetostatics/dynamics are used to solve the coupled problem of the compliant mechanism.

* There are many vector expressions used to derive the different kinematic relations, what can become daunting to the reader. The reviewer believes that using a more general formulation e.g. in terms of transformation matrices can improve the readability of the paper. The details could be moved to the appendix.

* There is a specific terminology, such as "mobile platform subsystem" that appears in the derivation of kinematic and dynamic equations. It would be desirable to stick with the common formulation of joint, task and configuration space.

* The experiment results are only given in joint space and the model fidelity cannot be verified in this manner. What about the motion of the platform? Also the phase shift and therefore the difference between Figure 8 and 9 is not clear.

* Joint space stiffness is given by relating to an older paper, but it should be discussed why it can be assumed to be linear.

* Some english phrases should be revised to proper formulations e.g. L.193: "Doing the dot product of Eq. (28) by PBi and rearranging". There is also a spanish phrase.

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Minor remarks:
* The term Jacobian should be written in capitalized form throughout the paper.
* typo "Boltzmann-Hammel equations" -> "Boltzmann-Hamel equations"
* L.39: typo "ans" -> "and".
* L.49: It can be mentioned earlier what is encountered by "mechatronic model"
* L.59: The term "disturbance" confuses here, as it may appear that the forces are unwanted.
* L.69: typo "intro de" -> "into the"
* L.73: type "as it may happens" -> "as it may happen"
* E.2: According to Figure 1, there is also a z-offset of the points B_i relative to the platform. Is the frame P here shifted for a simpler model?
* E.3: sine and cosine should either be fully written, or the notation must be explained in the text
* E.4: There appears a "?" inside the equation and index 1 is missing
* L.117: Eq.(6) not yet given
* L.135: This should be expressed differently
* L.154: typo "Fig. 4" -> "Fig. 5" 
* L.161: typo "unity vectors" -> "unit vectors"
* L.162: typo "m_i0 is the characteristic vector of the vertical planes" -> "m_i0 are the characteristic vectors of the vertical planes"
* L.162: What is meant by "characteristic vectors"? Are they not unit vectors?
* L.166: typo "unity vectors" -> "unit vectors"
* L.168: typo "those vectors are expressed premultiplying by the rotation matrix" -> "those vectors are expressed by premultiplying with the rotation matrix"
* E.26: How is this equation finally obtained? Would it not be appropriate to simply use the matrix logarithm of the relative rotation matrix?
* E.28: The hat operator must be explained, since it is not very common
* L.222: missing word
* L.228: typo one "the" too much
* L.239: typo "obtention" -> "obtainment"
* E.62: Even if obvious, subscripts and M_plat and g must be explained
* L.261: typo "obtained premultiplying by" -> "obtained by premultiplying"
* L.306-308: This phrase is in Spanish!
* Table 1: k_r, k_sf and k_st have wrong dimension
* L.393: typo "obtention" -> "obtainment"

Author Response

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Author Response File: Author Response.pdf

Round 2

Reviewer 3 Report

The authors have revised the paper addressing the reviewer's concerns and hence the paper can be accepted in the present form.