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Direct Kinematics of a 3-PRRS Type Parallel Manipulator

Zhumadil Zh. Baigunchekov 1 and Rustem A. Kaiyrov 2
1. Al-Farabi Kazakh National University, Satbayev University, Almaty, Kazakhstan
2. Al-Farabi Kazakh National University, Almaty, Kazakhstan

Abstract—This paper is devoted to solving the direct kinematics of a novel 3-PRRS type parallel manipulator with six-degrees-of-freedom, where P, R, and S are prismatic, revolute and spherical kinematic pairs respectively. This parallel manipulator is formed by connecting a moving platform with a fixed platform (base) through three closing kinematic chains of a PRRS type in which the prismatic kinematic pairs and their adjacent revolute kinematic pairs are active and they are located on a fixed platform. The constant and variable parameters of the considered parallel manipulator characterizing its geometry and kinematics respectively are determined. In the direct kinematics, the positions of the moving platform are determined by the known constant parameters of the links and the given variable parameters of the active kinematic pairs. An analysis of the obtained equations of the direct kinematics showed that the variable parameters of the active prismatic kinematic pairs are set free, and these equations are reduced to a 16th –order polynomial equation with the passive kinematic pairs variables. Numerical examples of the considered parallel manipulator’s direct kinematics are presented, and the results showed that the direct kinematics equations have four solutions corresponding to the four assemblies of the parallel manipulator.

Index Terms—parallel manipulator, moving and fixed platforms, direct kinematics

Cite: Zhumadil Zh. Baigunchekov and Rustem A. Kaiyrov, "Direct Kinematics of a 3-PRRS Type Parallel Manipulator," International Journal of Mechanical Engineering and Robotics Research, Vol. 9, No. 7, pp. 967-972, July 2020. DOI: 10.18178/ijmerr.9.7.967-972

Copyright © 2020 by the authors. This is an open access article distributed under the Creative Commons Attribution License (CC BY-NC-ND 4.0), which permits use, distribution and reproduction in any medium, provided that the article is properly cited, the use is non-commercial and no modifications or adaptations are made.