Geometric Modeling and Free-elimination Computing Method for the Forward Kinematics Analysis of Planar Parallel Manipulators

doi:10.3901/JME.2018.19.027

Abstract

Abstract: In order to cope with the requirements of the coordinate establishment and elimination process, in the process of the modelling and computing for the forward kinematic analysis of general planar parallel manipulators, a geometric modeling and free-elimination computing method for the forward kinematics of planar parallel manipulators is proposed using conformal geometric algebra (CGA). Under the frame of CGA, two of the three coordinates in the moving platform are formulated by the intersecting, dissecting and dual of the basic geometric entities; in terms with the area sign of the moving triangular platform, the characteristic polynomial equation is derived by a sequence of geometric algebra operation and simplification; a high-degree polynomial equation for planar parallel manipulators of any link parameters is deduced by tangent-half-angle substitution, Euler-angle substitution or no substitution. The derivation of the characteristic polynomial is free of coordinate and no elimination process and no assumption are required. Numerical examples are given to validate the correctness of the procedure and that the proposed algorithm is feasible to all cases of planar parallel manipulators including the special and general structures. At last, the results show that the proposed algorithm has a readily numerical robustness and provides a new sight for the theoretical solution to the kinematics of planar parallel manipulators.

Key words: conformal geometric algebra, forward kinematics, free-elimination computing, geometric modeling, planar parallel manipulators

CLC Number:

TH112

ZHANG Ying, WEI Shimin, LI Duanling, LIAO Qizheng. Geometric Modeling and Free-elimination Computing Method for the Forward Kinematics Analysis of Planar Parallel Manipulators[J]. Journal of Mechanical Engineering, 2018, 54(19): 27-33.

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