Motion generation of spherical four-bar mechanism using harmonic characteristic parameters

Sun, Jiachang; Lu, Chao; Chu, Jinkui

doi:10.1016/j.mechmachtheory.2015.08.020

Cited by 16 publications

(4 citation statements)

References 21 publications

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“…It is observed when the crank r 2 is aligned with r 3 , as shown in Fig. 9(a), it is necessary to fulfill the inequality (31). When r 2 is aligned with r 1 (see Fig.…”

Section: ) Constraintsmentioning

confidence: 99%

“…The least-square optimization scheme has been applied to the path generation dimensional synthesis in [28], to the function generation dimensional synthesis in [29], and to the motion generation dimensional synthesis in [30] of spherical four-bar mechanisms. In the motion generation dimensional synthesis of spherical four-bar mechanisms, sequential quadratic programming (SQP) is employed in [31] to solve the mechanism synthesis problem handled with the aid of harmonic analysis.…”

Section: Introductionmentioning

confidence: 99%

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Nature-Inspired Intelligent Synthesis of a Spherical Mechanism for Passive Ankle Rehabilitation Using Differential Evolution

et al. 2023

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The ankle rehabilitation in certain injuries requires passive movements to aid in the prompt recovery of ankle movement. In the last years, parallel ankle rehabilitation robots with multiple degrees of freedom have been the most studied for providing such movements in a controlled way. Nevertheless, the high cost does not make it viable for home healthcare. Then, this paper presents an optimization approach where a spherical mechanism of one-degree-of-freedom is proposed as a low-cost ankle rehabilitation device to provide the passive rehabilitation exercise for plantar flexion/dorsiflexion and adduction/abduction ankle movements. The approach is formulated as a mono-objective constraint optimization problem where the relative motion angle of the mechanism, the Grashof criterion, the force transmission, and the rehabilitation routine are included. The link lengths of the mechanism parameterized in Cartesian coordinates are found by the two most representative differential evolution variants. The statistical analysis of optimizers indicates that the DE/rand/1/bin finds, on average, more promising solutions through algorithm executions than the DE/best/1/bin. The numerical simulation results and the motion simulation of the CAD model illustrate the obtained ankle rehabilitation mechanism, indicating that the percentage error between the desired rehabilitation path and the curve generated by the coupler point of the mechanism is in the interval [0.036, 0.437]%. Manufacturing the ankle rehabilitation mechanism with a 3D printer validates the optimization approach and verifies the resulting mechanism.

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“…It is observed when the crank r 2 is aligned with r 3 , as shown in Fig. 9(a), it is necessary to fulfill the inequality (31). When r 2 is aligned with r 1 (see Fig.…”

Section: ) Constraintsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Nature-Inspired Intelligent Synthesis of a Spherical Mechanism for Passive Ankle Rehabilitation Using Differential Evolution

et al. 2023

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“…Mechanism synthesis includes function, motion and path generation [1]. The most studied problems are path synthesis of four-bar mechanism, where the coupler can pass a series of desired points with or without prescribed timing [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20], and function and path combined synthesis of six-bar double dwell mechanism, where the coupler can pass through a series of desired points and the output link can realize the desired angles during the dwell portion [14,21,22]. The six-bar dwell mechanism works as an alternative of cam mechanism and to meet certain requirements which are hardly satisfied by four-bar mechanism sometimes [22].…”

Section: Introductionmentioning

confidence: 99%

Path and function synthesis of multi-bar mechanisms using beetle antennae search algorithm

Zhao

et al. 2020

Filomat

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Beetle antennae search algorithm (BAS) is based on the searching behavior of longhorn beetles. This newly proposed metaheuristic algorithm is used in the path and function synthesis of multi-bar mechanism. The optimization results are compared with that of other metaheuristic algorithms like genetic algorithm (GA), particle swarm optimization (PSO) and differential evolution (DE) et al. While BAS uses only one group of initial parameters to search the best result, the convergence and efficiency are tested with eight case studies results. Newly added parameter q increases the possibility to find better results during iterations and deals with a higher number of independent parameters efficiently. Revised BAS exhibits good performance both in path synthesis of four-bar mechanism with or without prescribed timing, while optimized parameters increases from 6 to 34, and extends to path and function combined synthesis of Stephenson III six-bar double dwell mechanism with 14 parameters.

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“…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. Considering that modern computers can obtain massive solutions quickly and discriminate the defective linkage solutions in turn later (Myszka et al, 2009;Tipparthi and Larochelle, 2011;Bai, 2017), the method of type map (Han and Cao, 2019) is gradually applied in some linkage synthesis software, such as Synthetic (Su and McCarthy, 2005), Lincages (Erdman and Loftness, 2005), Sphinx (the latest version is SphinxPC) (Ruth and McCarthy, 1999;McCarthy, 2013) and the software developed by Han et al (2013). Among them, specially, Sphinx is the first software to solve the spherical G. Wang et al: Computer-aided synthesis of spherical and planar 4R linkages problems.…”

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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Motion generation of spherical four-bar mechanism using harmonic characteristic parameters

Cited by 16 publications

References 21 publications

Nature-Inspired Intelligent Synthesis of a Spherical Mechanism for Passive Ankle Rehabilitation Using Differential Evolution

Nature-Inspired Intelligent Synthesis of a Spherical Mechanism for Passive Ankle Rehabilitation Using Differential Evolution

Path and function synthesis of multi-bar mechanisms using beetle antennae search algorithm

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

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