Optimization of a Truss Structure Used to Design of the Manipulator Arm from a Set of Components
, Zbyněk Paška 1, Martin Fusek 1, Zdenko Bobovsky 2, Alžbeta Sapietová 3, Vladimír Mostýn 2 and Dagmar Ličová 1,*Round 1
Reviewer 1 Report
In this paper the authors proposed a methodology based on the Genetic Algorithm (GA) in order to find the optimal truss structure from a set of components. The method is firstly verified for the optimization of a 2D truss structure and then used to carry out the structural optimization of a manipulator arm. This is designed with three different models: (i) a truss structure with ideal rod, (ii) a truss structure with flat or L-shaped metallic components, (iii) a three-dimensional solid. The optimization and structural analysis is carried out for each model via the Finite Element Method (FEM) and comparisons are made in terms of maximum deflection, structural weight and equivalent stresses.
The manuscript is interesting, fits well with the aim of the “Applied Sciences” Journal, and can be accepted for publication after the described major revisions.
(1) First of all, the manuscript needs some polishing from a language perspective. Various statements throughout the paper are badly written and need revision. Please, perform a careful check of the manuscript, maybe with the help of a native English speaker.
(2) Equation (9) reports the criteria adopted for the sorting of components. At lines 115-116, it is written: “For the sorting we used the sorting length ls and the sorting force Ps”. However, it is not clear what these parameters, ls and Ps, correspond. Please, specify.
(3) Few lines below, it is written: “Meeting condition Equation (9) for C significantly simplifies the optimization process, because all criteria Equation (1), Equation (2) have the same gradient direction as the component labels in C”. It is not clear to me, how these sorting conditions imply that criteria in Eqs. (1) and (2) have the same gradient directions. More details should be included here.
(4) At lines 156-158, the results arising from the twenty GA analyses on the 2D truss example are reported in terms of truss weight. From the results, it seems that there is a certain variability among the results, from a minimum weight of 2490 kg to a maximum of 3033 kg, corresponding to an increase of about 22%). This variation suggests that the method might not be able to overcome local minima. A discussion about this should be provided. Also, the standard deviation of these weight values should be provided as well, besides the average value (2586.9 kg).
(5) Table 2 provides a comparison between the GA proposed in this paper and previous published papers [27, 39, 25]. More details about the methods provided in these reference should be provided, so that readers are not expected to go and read the full papers to have an idea of the analysis performed by previous authors. Also, reference [39] is reported twice in Table 2, once with asterisk, and once without. Please, explain the difference between the two analyses.
(6) Section 3.3.5 is title “stiffness correction” but it should be titled “strength correction”.
(7) At lines 301-302, it is written: “The components 1–5, 19, and 20 did not meet the criteria defined in Section 3.2, so components 6–19 were used”. Specify which criteria are not met. Also, it is not clear whether component 19 does not satisfy the criteria or whether it has been used for the analysis.
(8) Strength criteria for the truss structure shown in Equation (2) seem to suggest that buckling of compressed rods is not taken into account, as the equivalent stress is only compared to the yield stress. Is it correct? In this case, some rods could undergo buckling and might need larger cross-section, thus leading to a larger structure weight.
(9) At line 360, the authors say that “nonlinear static structural analysis” is carried out on model 2. More details should be provided about this analysis. Is it performed under load- or displacement-control mode? How large is the final value of the force/displacement? How material and geometrical non-linearities are taken into account within the analysis?
(10) Table 7 shows that in model 2, all component classes exhibit some points where the acting stress exceeds the yield stress, thus not satisfying strength criteria. It is clear that this is mostly due to the stress intensification due to the holes within the components. However, the authors should at least discuss this occurrence.
(11) Figure 13 shows the resulting geometry from topological optimization for model 3. Additional figures showing the deformed mesh upon the application of the load, as well as a contour plot showing the distribution of stresses across the solid, should be inserted.
(12) Table 8 says that the maximum equivalent stress in model 3 is about 8 MPa. However, a value of 14.8 MPa is reported in Table 9. Which is the correct one?
(13) Speaking about the 1st natural frequency of the models, the authors write: “For Model 1, the value is not given because it depends on the shape of the cross-section, which is not included in the truss structure”. However, in section 3.5, it was reported to be equal to 7.67 Hz. The difference in these value of vibrational frequencies between the models (7.67 Hz for model 1, 199 Hz for model 2, and 425 Hz for model 3) should be given more attention. It seems that a different optimization technique has the potential to lead to completely different dynamic characteristics of the structure.
According to what said above, the reviewer’s opinion is that the manuscript can be accepted for publication after the described major revisions.
Author Response
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Reviewer 2 Report
The authors present a component optimization of a truss structure using known Genetic algorithm. They also show an numerical example of the proposed approach and they present results for several parameters and functions. Furthermore, the paper is well written and easy to follow.
However, I think that this study there is no new contribution since their proposed approach is based on the existing methods (i.e. GA). Therefore, this work is in a way a routine task. For this reason, there are still changes to made prior to publication.
In the Introduction section do not describe the contributions of the paper well.
Furthermore, the authors could provide a detailed comparison of the proposed approach with other approaches. Please try to add such a discussion.
More work is needed for the conclusion section in terms of the significance and applicability of the proposed approach. More discussion for future work.
Author Response
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Reviewer 3 Report
The paper presents a genetic algorithms based approach for the development of a robotic arm. The research is comprehensive and very detailed, however it is not clear to this reviewer which is the application domain and the requirements that moved this approach. In the sense that: the final weight of the arm is important but also its manoeuvrability. Can the approach be extended to different design requirements and applications? Can it be used to generate designs with multiple segments (typical for robotic manipulator)? How the Authors pan to develop the manipulator? Are the Authors going to 3D print the design or build it with the set of components presented in the paper? In the later case, how are those component compatible with the generated design?
Author Response
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Round 2
Reviewer 1 Report
The authors have addressed most of my previous points. However, some final revisions are necessary, before the paper can be accepted for publication. Namely:
(1) In Eq. (11), C=[Aj, j=1...Nc] should be C*=[Aj, j=1...Nc].
(2) Figure 13 shows the first mode shape of Model 2, with a frequency of 239 Hz. However, (i) the mode shape seems to affect only localized portions of the structure, with only some components which vibrate, whereas this first mode shape is expected to affect the whole structure. Why is that not the case? (ii) The frequency is 199 Hz in Table 9, and not 239 Hz (as reported at line 443 and Figure 13). Correct the inconsistency.
(3) The maximum equivalent stress of Model 3 is reported to be 8 MPa (10.7 MPa) in Table 8, but it is 14.8 MPa in Table 9. I already reported this inconsistency in my previous review, at point (12). Although authors replied that the explanation of the problem was added, I wasn't able to find any statement addressing this issue in the paper, which thus remains unsolved.
(4) In Table 9, model 3 reports both the first and second value of the frequencies. Please, report only the first one (140 Hz).
Author Response
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Reviewer 2 Report
Thank you for the revision. All my comments were applied. Thus I recommend publishing this work in present form.
Author Response
The reviewer recommends publishing without comments.
