An Improved Fourier-Based Method for Path Generation of Planar Four-Bar Linkages without Prescribed Timing

Round 1

Reviewer 1 Report

I think the paper is very elaborate and very well referenced. Just make some observations that may or may not be considered.

- The notation of expression (11) is very interesting.

- In figure (1) I would put the vector arrows to the segments a b, c and d, so that the meaning of equation (13) can be seen. Or instead of using the sides, use the vertices AB+BC=AD+DC and it would not be necessary to draw arrows. Even the figures would gain clarity.

- In equation (17), the central equation, is c squared correct?

- From equation (19) it becomes a little difficult to follow the reasoning, since you have to understand the cited references. But it seems necessary.

- Instead of clockwise rotation and counterclockwise rotation I prefer to say antitrigonometric rotation and trigonometric rotation. Drawing on a crystal the rotation from x to y (trigonometric or counterclockwise) if you look at it from the other side it turns out like clockwise, but nevertheless it is still trigonometric (from x to y, obtaining z).

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 2 Report

This manuscript presents a point-to-point combination method based on Fourier coefficients for better accuracy by assigning time to the analysis points authors claim that this can increase the computation efficiency on path generation of four-bar linkage systems. Overall, the manuscript is well written with detailed mathematical and conceptual explanation of the proposed approach and the comparison shows the efficacy compared to existing methods. The numerical implantation was done in various benchmark problems. However, this reviewer suggests authors to address the following to further improve the manuscript quality.

-          Remove “among the mechanisms” as it sounds redundant.

-          Instead of reference [1] – this is trivial information so reference is necessary, this reviewer thinks information given in lines 34~41, where authors provide deficiencies of each method requires references as it might be controversial.

-          placement of each angle parameter in figures 1 & 2 could be updated for better readability.

-          While the Images in all seem to be in an adequate resolution, it could be vastly enhanced via vector graphics, especially figures that contain flowcharts (Figure 5 & 6).

-          Line 324, reference error should be fixed.

-        Authors claim that the proposed method is computationally ‘efficient’ compared to previous methods by one order of magnitude. It would be better to include a table or chart that visually compares the computation efficiency.

I do not se any significant issues with the English quality.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf