Forward Kinematic Analysis of Parallel Mechanisms in Seven-Dimensional Kinematic Space by Considering Limitation of Passive Joints motion

Abstract

In this paper, a new and systematic algorithm is presented for the forward kinematic analysis of parallel mechanisms (PMs) by considering joint motion limitations. The proposed algorithm is based on Euler parameters, the so-called linear implicitization algorithm and interval analysis in seven-dimensional kinematic space. Interval arithmetic computations and solving system of nonlinear interval equations are performed by means of INTLAB and RealPaver software, respectively. The ranges of passive joints motion of PMs are given as input to the algorithm, and feasible solutions of the forward kinematic problem (FKP) are the output of the algorithm. The advantages of combining seven-dimensional kinematic space and interval analysis in the FKP of PM are twofold: eliminating the trigonometric expressions from equations and considering the ranges of passive joints motion. The main contribution of this paper can be regarded as the synergy of seven-dimensional kinematic space and interval analysis which is used to the end of refining the solutions of FKP of PMs by taking into account passive joints limitation. As case studies, the proposed algorithm is implemented and verified, namely the 3-RPR and 4-PUU PMs.