A Method for Solving the Additional Stiffness Introduced by Flexible Joints in Stewart Platform Based on FEM Modal Analysis

Round 1

Reviewer 1 Report

The following issues presented in the work require clarification:

1. How were the formulas defining the form, the generalized quality matrix of the system M and the generalized stiffness matrix obtained, using what methods and equations (Newtonian, Lagrange, or other)?

2. What does m – quality of upper platform, mean in the M matrix. What is the physical interpretation of this parameter?

3. What are M15, M51, M24, M42. What is the physical interpretation of these parameters. (Eq. (3))

4. How can the authors explain the positive and negative values ​​of K matrix elements outside the main diagonal? (Eq. (6))

5. Equations (8a) and (8b) have no physical or theoretical sense. I need explanation, please.

6. Negative parameter values ​​on the K_R matrix diagonal and positive values ​​outside the diagonal indicate that the system is unstable (Eq. (10)). Therefore, the physical is unrealizable. Please comment.

 

Author Response

Thank you for your review, the first round of manuscript has been revised, please check it.

Author Response File: Author Response.pdf

Reviewer 2 Report

This work seems interesting and is very attractive; however, certain aspects have been neglected.

1.- Take into account misspellings, Newtone is repeated over and over again instead of Newton.

 

2.-Introduction

Line 33. "..the application of the mechanism has spread across many fields such as biomedical devices, aerospace engineering and industrial manufacturing", but bibliographic Ref. [3,4,5] are not related to biomedical experiments.

Line 53. "and rebound forces are generated during the process [25]". In reference [25] it has not been possible to verify the rebound effect.

Line 65. ” many researchers preferred to neglect the stiffness effect of Flexible joints during the theoretical study on Stewart configuration mechanisms [7-10,26,27]”.  This statement could not be verified in all the references indicated.

Please carefully check that all references are relevant and used correctly.

3.- Theoretical analysis

Line 149: Line 149: The abbreviations that are entered for the first time must be defined, eg. SPS (Spherical – prismatic – spherical) and UPS (Universal-prismatic – spherical).

Línea 145. It is not well understood, the sentence must be clarified: “When the flexible joints are adopted, the bending stiffness of the flexible joints will be imposed into the platform system”.

Linea 157. It is necessary to clarify why the damping effect is initially ignored.

Línea 181. "..and when the load masses are symmetric about the X and Y axes, the ….". What happens when the symmetry is lost?

Line 201 and 203: Ksi = KsDiag, It is called in two different ways.

Line 203-205. "Through theoretical derivation, it can be proved that the stiffness matrix ?? satisfies the following parameter characteristics: ??11 = ??22; ??44 = ??55; ??15 = ??51 = −??24 = −??42". The wording should be improved, clarifying what is derived and the theoretical formulation of the derivative.

Line 207. Symmetry features need some clarification, for example: the axes and planes of symmetry.

There are works by other researchers that deal with the subject that have not been taken into account and that can enrich the work, especially in the discussion section (they introduce, for example, viscous friction  in the model), eg.

"Modeling and design of flexure jointed Stewart platforms for control purposes"by  J.E. McInroy.

"Dynamic stability index and vibration analysis of a flexible Stewart platform". By Mukherjee, P (Mukherjee, Parthajit) ; Dasgupta, B (Dasgupta, Bhaskar) ; Mallik, AK (Mallik, A. K.) 

 

4.- FEM simulation

The experiment must be traceable, however, not all characteristics of the legs are specified, for example, Young's modulus, Poasson's coefficient, or the type of material, etc.

For the experiment to be traceable, it is necessary to specify the mechanical characteristics of the flexible joint that they introduce into the FEM.

The figure 3 show colors, but it is not known to which frequency each color belongs. It is convenient to add the modal analysis frequency scale.

Line 322-323. "..the corresponding mass characteristics of the legs are attached". Are you referring to stiffness or mass? Is it possible that you are referring to stiffness?

The FEM image similar to figure 3 but without the rectangular mass is missing.

 

5.- Dynamics tests.

The technical characteristics of the accelerometers (sensitivity, model, brand, mass, etc.) and the analyzer with which the tests are carried out are missing.

6.- Discusion.

A discussion section is missing, in which: (1) the results are discussed, (2) the possibilities of scaling the model are indicated, (3) difficulties in applying it to other sectors, (4) possibilities for improvement of the model, (5) if the presumption of ignoring the damping has been good or not, (6) if the results are statistically significant, (7) compare with the results obtained by other researchers, (8) maximum dynamic load carrying capacity, (9) different Stewart platform models, etc.

Many starting assumptions are checked with the validation of the theoretical model, but it is necessary to discuss if these assumptions are scalable and to specify in which conditions they will not be fulfilled.

It is a pity, because the work is very attractive, possible from an in-depth discussion, other more enriching conclusions would have been obtained, such as the little influence of the damping in the system, the assumptions of considering the stiffness of flexible joints collinear with the platform legs, etc

7.- Conclusion

This section needs to be rewritten. Most of this section represents a summary of the work. The summary of the work is part of the abstract, but not of the conclusions.

Only two paragraphs out of all can be acceptable as conclusions: 

(1) "It shows that the 6th-order natural frequencies of the system obtained by the two approaches are quite consistent, with a maximum deviation of 3.12%, which proves the correctness of the theoretical method proposed in this paper", and (2) "Comparing with the theoretical results, it intuitively shows the maximum deviation between the actual natural frequencies of the platform prototype and the theoretical results does not exceed 5%, which further proves the effectiveness of the proposed method in practical engineering".

A system of 6 DOF is not the same as a system of order 6. The order is referred to the differential equation of the system.

Behavior under the influence of maximum dynamic load rating????

Author Response

Thank you for your review, the manuscript has been revised, please check.

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

Dear authors,
Congratulations on your paper.
Nothing to comment.