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Synthesis of Four-Bar Linkage with Adjustable Crank Length for Multi-Path Generation

Sayat Ibrayev 1, Assylbek Jomartov 1, Amandyk Tuleshov1, Nutpulla Jamalov 1, Aidos Ibrayev 1,2, Gaukhar Mukhambetkalieva 1,2, Gulnur Aidasheva 1,2, and Aziz Kamal 1,2
1. Institute Mechanics and Mechanical Engineering, Almaty, 050010, Kazakhstan
2. al-Farabi Kazakh National University, Almaty, 050040, Kazakhstan

Abstract—Synthesis of planar mechanism with adjustable crank length for generating multiple paths is presented. Least-square approximation problem is considered which allows carrying out approximate synthesis with unlimited number of desired coupler point positions and with unlimited number of prescribed trajectories. By reducing the task to synthesis of two-element link with variable binary link length, which is called RPR-module, the analytical solution is obtained to determine not only constant design parameters (mechanism link lengths) but the adjusting parameter values as well. Thus the number of design variables for non-linear optimization (applied to find the remaining parameters) will be decreased significantly. The applied method is exemplified by synthesis of the mechanism for variable straight line generation, where the required height of the end-effector is adjusted by adjusting the crank length. Combined with random search technique the method allows to find all local minimums of the optimized goal function and thus allows to take full advantage from the considered mechanism structure during design. 

Index Terms—adjustable mechanism, approximate synthesis, trajectories generation, least-square approximation

Cite: Sayat Ibrayev, Assylbek Jomartov, Amandyk Tuleshov, Nutpulla Jamalov, Aidos Ibrayev, Gaukhar Mukhambetkalieva, Gulnur Aidasheva, and Aziz Kamal, "Synthesis of Four-Bar Linkage with Adjustable Crank Length for Multi-Path Generation" International Journal of Mechanical Engineering and Robotics Research, Vol. 9, No. 4, pp. 489-495, April 2020. DOI: 10.18178/ijmerr.9.4.489-495