A homotopy-based method for the synthesis of defect-free mechanisms satisfying secondary design considerations

Baskar, Aravind; Bandyopadhyay, Sandipan

doi:10.1016/j.mechmachtheory.2018.12.002

Cited by 4 publications

(3 citation statements)

References 20 publications

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“…According to the Burmester theory, any two center points yield a linkage solution such that the four-position synthesis problem has ∞ 2 solutions in theory. Although there are many combinations of center points, most solutions involve defects in the circuit, branch, or order (Baskar and Bandyopadhyay, 2019;Singh et al, 2017;Tipparthi and Larochelle, 2011), which requires engineers to often spend weeks or even longer on repeated calculations and analyses to obtain satisfactory linkage solutions. Therefore, it is important to solve the problem of the poor efficiency of four-position synthesis.…”

Section: Introductionmentioning

confidence: 99%

TGA-based solutions map method for four-position synthesis of planar 4R linkage

Zhao

Xue²,

Wang³

et al. 2022

Mech. Sci.

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Abstract. In this study, the authors propose a solutions map based on a telomere genetic algorithm (TGA) to improve the efficiency of 4R-linkage synthesis. First, the points on the center curve are obtained by using projective geometry, and those of the circle curve are obtained by vector elimination. Second, the definition of the linkage type, assessment of linkage performance, and a method to identify defects in the linkage are introduced. Third, the solutions map method is proposed that can map the linkage solutions obtained by all combinations of the points on the center curve to a 3D color-coded surface to represent the distribution of solutions with different attributes of linkages in the solution domain. Fourth, we use the proposed telomere operator and pseudo-histogram method to improve the traditional genetic algorithm, and expand the domain of solutions of the solutions map by using the TGA. Finally, the linkage synthesis software BurLink is developed based on the solutions map method. The results show that the TGA-based solutions map can quickly locate the required 4R-linkage solution in the solution domain, and provides engineers with more candidate solutions than traditional methods.

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Section: Introductionmentioning

confidence: 99%

TGA-based solutions map method for four-position synthesis of planar 4R linkage

Zhao

Xue²,

Wang³

et al. 2022

Mech. Sci.

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“…The theoretical basis of the graphing method is the theory of burmester, that is to say, connecting any two groups of center points and their corresponding circle points can obtain the desired linkage solution. Although the selection of center points or circle points are optional, majority of the linkage solutions have some problems such as circuit defect, branch defect, order defect or poor motion performance (Wang et al, 2010;Baskar and Bandyopadhyay, 2019a). For the linkage motion defect, the classical defect discrimination method is to study the segmentation technique of the burmester curve (Filemon, 1972;Waldron and Strong, 1978;Gupta and Beloiu, 1998).…”

Section: Introductionmentioning

confidence: 99%

“…With the development of computer-aided design, the burmester curve mentioned above can be obtained by programming with analytic geometry, but the existence of defective linkages makes it difficult to obtain feasible solutions. In order to get the most candidate solutions, one of the approaches is to allow some task variables to change in a certain range, so as to expand the number of solutions (Zhao et al, 2016;Baskar and Bandyopadhyay, 2019b;Chanekar et al, 2013;Sun et al, 2016). Although this method can increase the number of solutions, most of the increased linkage solutions still have motion defects, so it does not fundamentally eliminate the blindness of linkage synthesis process.…”

Section: Introductionmentioning

confidence: 99%

Computer-aided synthesis of spherical and planar 4R linkages for four specified orientations

Wang

Zhang

et al. 2019

Mech. Sci.

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Abstract. According to the burmester theory, an infinite number of spherical or planar 4R linkages for a specific four-orientation task can be synthesized, but most of the linkage solutions calculated by this method are invalid because of motion defect, poor performance and others. In order to improve the synthesis efficiency, a program package based on Matlab is developed to find a satisfied linkage solution automatically and quickly. Firstly, the calculation on circle points and the center points based on the burmester theory in spherical problems is introduced. Secondly, the calculation methods of linkage defect discrimination, linkage type classification, linkage performance evaluation and solutions visualization based on the theory of spherical trigonometry are presented respectively. Thirdly, the synthesis calculation of program package is extended to the planar 4R linkage based on the theory of planar analytic geometry. Finally, the examples of the spherical synthesis problem and the planar synthesis problem based on solutions map are introduced to test the program package, the result proves this program package is effective and flexible.

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