A robomech class parallel manipulator with three degrees of freedom

Authors

DOI:

https://doi.org/10.15587/1729-4061.2020.203131

Keywords:

parallel manipulator, RoboMech, cylindrical coordinate systems, Chebyshev and least–square approximations

Abstract

This paper presents the methods of structural-parametric synthesis and kinematic analysis of a parallel manipulator with three degrees of freedom working in a cylindrical coordinate system. This parallel manipulator belongs to a RoboMech class because it works under the set laws of motions of the end-effector and actuators, which simplifies the control system and improves its dynamics. Parallel manipulators of a RoboMech class work with certain structural schemes and geometrical parameters of their links. The considered parallel manipulator is formed by connecting the output point to a base using one passive and two active closing kinematic chains (CKC). Passive CKC have zero degree of freedom and it does not impose a geometrical constraint on the movement of the output point, so the geometrical parameters of the links of the passive CKC are freely varied. Active CKCs have active kinematic pairs and they impose geometrical constraints on the movement of the output point. The geometrical parameters of the links of the active CKCs are determined on the basis of the approximation problems of the Chebyshev and least-square approximations. For this, the equations of geometrical constraints are derived in the forms of functions of weighted differences, which are presented in the forms of generalized (Chebyshev) polynomials. This leads to linear iterative problems.

The direct and inverse problems of the kinematics of the investigated parallel manipulator are solved. In the direct kinematics problem, the coordinates of the output point are determined by the given position of the input links. In the inverse kinematics problem, the positions of the input links are determined by the coordinates of the output point. The direct and inverse problems of the kinematics of the investigated parallel manipulator are reduced to solving problems on the positions of Sylvester dyads. Numerical results of structural-parametric synthesis and kinematic analysis of the considered parallel manipulator are presented. The numerical results of the kinematic analysis show that the maximum deviation of the movement of the output point from the orthogonal trajectories is 1.65 %

Author Biographies

Zhumadil Baigunchekov, Al-Farabi Kazakh National University al-Farabi ave., 71, Almaty, Republic of Kazakhstan, 050040 Satbayev University Satpaev str., 22a, Almaty, Republic of Kazakhstan, 050013

Director

Scientific and Educational Centre of Digital Technologies and Robotics

Professor

Department of Mechanical Engineering

Azamat Mustafa, Satbayev University Satpaev str., 22a, Almaty, Republic of Kazakhstan, 050013

Doctoral Student

Institute of Industrial Engineering

Tarek Sobh, University of Bridgeport Park ave., 126, Bridgeport, CT 06604, United States of America

Professor

Sarosh Patel, University of Bridgeport Park ave., 126, Bridgeport, CT 06604, United States of America

Professor

Muratulla Utenov, Al-Farabi Kazakh National University al-Farabi ave., 71, Almaty, Republic of Kazakhstan, 050040

Professor

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Published

2020-06-30

How to Cite

Baigunchekov, Z., Mustafa, A., Sobh, T., Patel, S., & Utenov, M. (2020). A robomech class parallel manipulator with three degrees of freedom. Eastern-European Journal of Enterprise Technologies, 3(7 (105), 44–56. https://doi.org/10.15587/1729-4061.2020.203131

Issue

Vol. 3 No. 7 (105) (2020): Applied mechanics

Section

Applied mechanics

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Copyright (c) 2020 Azamat Mustafa, Zhumadil Baigunchekov, Tarek Sobh, Sarosh Patel, Muratulla Utenov

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