Modeling and Verification of Cable-Hole Transmission Tension Ratio Considering the Cable Lateral Extrusion

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The manuscript introduces an innovative rope-hole transmission tension ratio model that incorporates the lateral extrusion effect of the rope. An analytical solution for the tension ratio of the rope as it threads through the hole is derived using the perturbation method. The study employs a Particle Swarm Optimization (PSO) algorithm to accurately determine the rope-hole parameters and develops an adaptive tension control strategy.

To further enhance the clarity and applicability of the paper, the following refinements are suggested:

(1) For ropes with varying materials, lengths, and diameters, does the formula vary accordingly? Could supplementary clarifications be included to broaden the applicability of this methodology? (2) Clarify the distinctions between Formula (6) and Formula (17) in prose, potentially by highlighting these differences in the captions of Figures 19 and 20. (3) It would be beneficial to juxtapose the new model with existing models referenced in the literature to showcase its strengths and any potential limitations. If such a comparison is not feasible, an explanation could be provided to underscore the merits of the proposed approach.  (4) A thorough grammatical review of the entire text is recommended. Additionally, the abstract should be revised for improved grammatical accuracy and logical coherence.

Comments on the Quality of English Language

Grammar needs improvement.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

Please see my comments in the attached PDF file.

Comments for author File: Comments.pdf

Comments on the Quality of English Language

English language is mostly fine. See also my comments in the attached PDF file.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

1) The introduction of your paper does not provide sufficient background and lacks several critical references, leading to a significant gap in the contextual foundation required for this study. While you briefly mention key concepts such as the Capstan equation and the rope-pulley system, the discussion is too superficial, lacking depth in explaining the evolution of these models and their relevance to your work. For instance, the introduction refers to prior research on the Capstan equation and its modifications by Jung et al. (2008) and Lu et al. (2015) but does not sufficiently detail the limitations of these models that your study aims to address. Additionally, the references to more recent advances, such as data-driven methods or finite element models (FEMs), are mentioned without adequately integrating them into the narrative. This gives the impression of a disjointed literature review rather than a cohesive argument leading to your research question. Furthermore, you fail to cite several seminal works that are crucial for understanding the current state of rope-driven mechanisms, particularly in the context of aerospace and robotics applications, which you claim as your focus areas. The introduction should not only discuss existing models but also critically analyze their shortcomings, thus justifying the need for your proposed model. Without these improvements, the introduction remains incomplete and insufficiently grounded in the existing body of knowledge.

2) The research does exhibit certain areas that require modifications to fully align with the objectives you aim to achieve. The use of a differential equation model and the perturbation method to derive the tension ratio of the rope threading through the hole is a fine approach. But, the application of the PSO  for parameter identification raises concerns about the robustness of the solution, given the nonlinearity and potential sensitivity of the system to initial conditions. For example, you briefly mention the optimization target stabilizing within a certain iteration range but fail to explore the potential impact of different initial parameter guesses or the algorithm's sensitivity to variations in these inputs. Additionally, the experimental validation using a prototype is a necessary step, but the choice of a single rope diameter and material limits the generalizability of your findings. Expanding the experimental setup to include variations in rope materials and dimensions would strengthen the applicability of your model across different scenarios. 

3)The methods in your paper lack sufficient detail in critical areas, which could hinder understanding. For example, while you describe the differential equation for the tension distribution and the perturbation method used to obtain an analytical solution, the explanation of how these equations are derived is somewhat cursory. There is an assumption that the reader is already familiar with these mathematical techniques, which may not be the case for all audiences. Also, the description of the PSO algorithm is overly brief; you mention the algorithm's parameters but do not provide a rationale for their selection or discuss how variations in these parameters might affect the results. Additionally, the experimental setup, including the use of a high-precision stepper motor and tension sensor, is described in general terms, but the calibration processes, error margins, and potential sources of measurement uncertainty are not adequately addressed. The methods need to be described with greater precision and depth to ensure that other researchers can replicate your study accurately.

4) While you include various figures and tables, such as the tension ratio versus wrap angle and the identified parameters using the PSO, the narrative that accompanies these results is somewhat lacking in depth. For example, in Figure 9, where you present the tension ratio of the rope-hole transmission, you describe the general trends but do not delve into a more detailed analysis of why certain behaviors occur, when the wrap angle exceeds 60°. The comparison between the control methods considering and not considering lateral extrusion is insightful, yet the discussion does not fully articulate the implications of the observed differences in terms of practical applications or the potential limitations of the proposed method. Some results, such as the tension variation depicted in Figures 19 and 20, could benefit from more explicit labeling and a clearer connection to the theoretical framework presented earlier in the paper. 

5) The conclusions of your paper require more robust support from the data. You conclude that the tension ratio model considering the rope lateral extrusion significantly improves the motion control accuracy of rope-driven mechanisms, and while your experimental results do show a reduction in transmission error and improved tension control, the evidence presented does not fully substantiate the magnitude of improvement claimed. For example, you assert that the motion control error is reduced by an order of magnitude, but the discussion does not  assess the variability or consistency of this improvement across different conditions. Also, While the PSO-identified parameters are presented as effective in capturing the system's behavior, there is little discussion on the potential limitations of this approach, in cases where different rope materials or environmental conditions might affect the outcomes. 

6) Moderate editing of English language required. The paper's language quality is generally understandable, but there are several instances where clarity, conciseness, and grammatical accuracy could be improved.

7) After carefully reviewing all the formulas in the document, I did not detect any explicit errors in them. 

8) I do have several concerns regarding the study, spanning scientific and technical aspects:

- The study heavily relies on theoretical models, such as the differential equations and the perturbation method, without providing sufficient experimental validation across a range of conditions. While the study does include some experimental validation, it is limited in scope. The use of only one rope material and diameter limits the generalizability of the findings.

- As previously mentioned, the methods section needs more detailed descriptions,  regarding the selection of parameters for the PSO. The lack of discussion about the sensitivity of these parameters and the robustness of the optimization process raises concerns about the reproducibility of the results.

- The paper claims "significant" improvements in motion control accuracy, claiming reductions in error by an order of magnitude. But, the data presented does not fully substantiate this claim across different scenarios, and there is little discussion about the limitations or potential variability in these results. The conclusions should be more carefully aligned with the evidence provided.

- There is insufficient discussion about potential sources of error in both the theoretical modeling and the experimental setup. For example, factors like measurement uncertainty, environmental conditions, and assumptions made in the model (the simplifications in the rope's mechanical properties) are not analyzed. 

- While self-citation is not unethical, it can raise ethical concerns if done too much or without proper context. In this study, several self-citations were identified. 

9) The originality and novelty of your article are, at best, average. The approach primarily builds on existing models and methodologies rather than introducing entirely new concepts or groundbreaking innovations. The use of the perturbation method and the PSO algorithm, while effective, are well-established techniques in mechanical engineering and optimization, thus limiting the study's claim to novelty. Also, the experimental validation is narrow in scope, focusing on a single rope material and diameter, which restricts the generalizability and impact of your findings. 

8) The significance and impact of your article are moderate. The overall impact is somewhat limited due to the narrow scope of the study. The research does not offer transformative advancements that would have a substantial impact across a wide range of applications. 

9) The level of presentation in your article is adequate but could be improved in several key areas to have better understanding and engagement. The clarity of explanations and the depth of detail provided in the methodology and results sections are somewhat lacking. 

10) The scientific soundness of your article is average. The technical content generally makes sense and is based on established principles in mechanical engineering and control theory. 

11) The interest level of your article is likely to be average for readers within the specific field of rope-driven mechanisms and mechanical engineering. 

12) The overall merit of your article is average. Its impact on the broader scientific community is limited. To increase its significance, the study would need to either propose novel theoretical frameworks, demonstrate broader applicability, or provide more extensive experimental validation across diverse conditions. 

13) Most of the cited papers are relevant but, there are a few references that appear to be less relevant to the specific focus on rope-hole transmission mechanisms and the associated tension models. Papers 22 and 23 Are Not Really Relevant. Recommended Articles to Be Added:

- Costello, M. F., & Lachenmayr, D. J. (2000). Tension, friction, and winding models for tethered aerostats. Journal of Guidance, Control, and Dynamics, 23(1), 128-136. doi: 10.2514/2.4500. This article can be cited in the Introduction or Mechanical Model of Rope-Hole Contact Surface sections, as it provides relevant insights into tension and friction models that can be applied to the understanding of rope dynamics in constrained environments, similar to what your study aims to address.

- Wang, X., & Huang, R. (2017). Analytical and experimental investigation on frictional behavior of cables in cable-driven parallel robots. Mechanism and Machine Theory, 116, 289-302. doi: 10.1016/j.mechmachtheory.2017.06.007. This article could be included in the Introduction or Tension Ratio Model of Rope-hole Transmission sections. It provides a detailed analysis of frictional behavior in cable-driven systems, which is highly relevant to the discussion of tension ratios. 

Comments on the Quality of English Language

General suggestions:

- In the reference list, ensure that all journal names are formatted

- Abreviations should be standardized.

- All references should be punctuated, with the use of periods and commas in the author and title sections.

- Use the Oxford comma for lists throughout the document.

- Review the document for subject-verb agreement issues, especially in complex sentences where multiple subjects are present.

 

Below are specific recommendations for improvement of the quality of article language:

 

Page 1 

- The phrase "Due to the uncertain elements such as local deformation friction and etc." should be revised to "Due to uncertain factors such as local deformation, friction, and other effects."

- "Rope-hole transmission errors" should be rephrased as "errors in rope-hole transmission."

- The sentence "To improve the transmission accuracy of rope-driven mechanisms a tension distribution model considering the rope lateral extrusion effect is established" should include a comma after "mechanisms."

- "A rope-hole transmission experimental device is manufactured to verify" should be "A rope-hole transmission experimental device was constructed to verify."

 

Page 2

- "Therefore rope-driven mechanisms are mostly used within confined space" should be revised to "Therefore, rope-driven mechanisms are predominantly used in confined spaces."

- "To ensure the rope transmission precision of the rope-driven mechanism" should be "To ensure the precision of rope transmission in the rope-driven mechanism."

- Page 2 - Introduction - The sentence "Researchers do not consider the rope bending stiffness in the Capstan equation thereby causing the failure of the boundary conditions" needs a comma after "equation" and should be rephrased for clarity: "Researchers often overlook rope bending stiffness in the Capstan equation, leading to inaccurate boundary conditions."

- Page 2 - Introduction - The phrase "further revised the rope transmission ratio model under the factors such as bending stiffness shear stiffness and initial tension" should include commas: "further revised the rope transmission ratio model to account for factors such as bending stiffness, shear stiffness, and initial tension."

 

Page 3

- "Therefore it is necessary to develop a rope transmission model considering diameter variation of the rope with extrusion" should be revised to "Thus, it is necessary to develop a rope transmission model that considers diameter variations of the rope due to extrusion."

- "To solve the above problems a tension ratio model and servo transmission properties of the rope-hole transmission considering the rope lateral extrusion is proposed and verified" should be "To address these problems, a tension ratio model and the servo transmission properties of the rope-hole transmission, considering the rope lateral extrusion, are proposed and verified."

 

Page 4

- "With the extrusion on the contact surface the diameter of the rope in contact with the hole is smaller than that of the rope outside the hole" should be revised to "Due to the extrusion on the contact surface, the diameter of the rope in contact with the hole is smaller than that of the rope outside the hole."

- The phrase "This phenomenon is similar to the ploughing effect in mechanical processing" should be rephrased for clarity: "This phenomenon resembles the ploughing effect observed in mechanical processing."

 

Page 5

- "The rope mass in the hole is small enough and can be ignored" should be "The rope mass within the hole is negligible and can be ignored."

- "Therefore the balance equation of the rope element force in Fig. 4 can be written as" should be "Thus, the force balance equation for the rope element in Fig. 4 can be expressed as."

- The term "Therefore in Eq. (2)" should be revised to "Hence, in Eq. (2)."

 

Page 6

- The phrase "Eq. (8) is an implicit nonlinear differential equation without an analytical solution" should be rephrased for clarity: "Equation (8) is an implicit nonlinear differential equation that lacks an analytical solution."

- "Therefore a perturbation method is employed to obtain an approximate analytical solution for the tension distribution and tension ratio" should be revised to "Thus, a perturbation method is employed to derive an approximate analytical solution for the tension distribution and ratio."

 

Page 7

- The phrase "Therefore a dimensionless small parameter can be separated from the rope diameter ρ" should be revised to "Hence, a dimensionless small parameter can be isolated from the rope diameter ρ."

- The phrase "Since C and ρ’ can be considered as terms unrelated to ϕ Eq. (14) and Eq. (15) can be regarded as linear constant coefficient differential equations with analytical solutions" should be revised to "Since C and ρ’ can be considered independent of ϕ, Eqs. (14) and (15) can be treated as linear constant coefficient differential equations with analytical solutions."

 

Page 8

- The phrase "and the servo control law of the rope-hole transmission is designed according to the adaptive control algorithm in Chapter 4" should be revised to "The servo control law for the rope-hole transmission is developed using the adaptive control algorithm presented in Chapter 4."

- Control Frame for the Rope-drive End Tension: "and the tension ratio of the rope-hole transmission can be calculated combined with the towed weight" should be revised to "and the tension ratio of the rope-hole transmission can be calculated in conjunction with the towed weight."

 

Page 9

- The phrase "the specific calculation process is shown in Fig. 6" should be "the detailed calculation process is depicted in Fig. 6."

- The sentence "In the latter case the global optimum value obtained by the particle swarm is the identified parameter" should include a comma after "case."

 

Page 10

- The phrase "The vision camera adopts a 40-megapixel color industrial camera" should be revised to "A 40-megapixel color industrial camera is used for visual measurement."

- "The physicochemical property of the rope is stable with the low radial stiffness and high axial stiffness" should be rephrased for clarity: "The rope exhibits stable physicochemical properties, with low radial stiffness and high axial stiffness."

- The sentence "It can be seen that the lateral compression of the rope increases with the increase of the rope-hole wrap angle" should be revised to "It is observed that the lateral compression of the rope increases with the rope-hole wrap angle."

 

Page 11

- The phrase "In this paper the wrap angle of the rope segment is measured by a visual camera" should include a comma after "paper."

- The sentence "When iterations steps exceeds 550 the structural parameters calculated by the PSO algorithm are basically constant values" should be revised to "After 550 iterations, the structural parameters calculated by the PSO algorithm stabilize to nearly constant values."

 

Page 12

- The phrase "This paper verifies the tracking ability of the adaptive control method considering the rope-hole resistance with two typical signals" should be revised to "The tracking ability of the adaptive control method, considering rope-hole resistance, is validated in this study using two typical signals."

- "However when the desired signal is time-varying it is difficult to tracking the trajectory due to the variation of the resistance at the rope-hole contact area caused by the variation of rope tension and inertia force" should be revised to "However, when the desired signal varies with time, tracking the trajectory becomes challenging due to changes in resistance at the rope-hole contact area, resulting from variations in rope tension and inertia forces."

 

Page 13

- The phrase "The phenomenon indicates that the dynamic model of rope-driven mechanisms without considering the rope lateral extrusion is less effective" should be revised to "This indicates that the dynamic model of rope-driven mechanisms, when not considering lateral extrusion, is less effective."

- "The primary reason is the improved accuracy of rope-hole compensation increasing the rope tension variation" should be revised to "The primary reason is that the improved accuracy of rope-hole compensation increases rope tension variation."

 

Page 14

- The phrase "The motion control method which considers the rope extrusion resistance can effectively reduce disturbances caused by the model uncertainty and discontinuity" should be revised to "The motion control method that accounts for rope extrusion resistance effectively reduces disturbances caused by model uncertainty and discontinuity."

- The sentence "A extrusion resistance model for the rope threading through the hole is established based on the phenomenon of rope lateral extrusion" should be revised to "An extrusion resistance model for the rope threading through the hole is established based on the phenomenon of lateral rope extrusion."

- The phrase "Experimental results demonstrate that the tension ratio model considering the rope lateral extrusion can accurately compensate" should include a comma after "demonstrate."

 

Page 15

- The phrase "significantly improves both the steady-state and transient properties of the mechanism" should be revised to "significantly improves both the steady-state and transient response characteristics of the mechanism."

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

Comments and Suggestions for Authors

The authors have revised the manuscript according to my comments. I have no further comments to make.

Comments on the Quality of English Language

The manuscript writing style is acceptable.

Reviewer 3 Report

Comments and Suggestions for Authors

After reviewing the revised submission, I am pleased to see that the authors have effectively addressed the concerns raised in the previous review. The improvements made enhance the clarity and presentation of the research. The paper now offers a clearer explanation of the rope-hole transmission mechanisms, with stronger connections between theory and practice. Additionally, the experimental validation has been expanded, providing a more solid foundation for the conclusions. The revisions have increased the novelty and impact of the work, aligning it with the standards expected for publication in Machines. Given these improvements, I recommend accepting the paper for publication.

Comments on the Quality of English Language

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