Determination of Maximal Singularity-Free Workspace of Parallel Mechanisms Using Constructive Geometric Approach
This paper proposes a novel approach to obtain the maximal singularity-free regions of planar parallel mechanisms which is based on a constructive geometric reasoning. The proposed approach consists of two algorithms. First, the borders of the singularity-free region corresponding to an arbitrary start point of the moving platform is obtained. Then, the second algorithm aims to find the center of the maximal singularity-free circle which is obtained using the so-called offset curve algorithm. As a case study, the procedure is applied to a 3-PRR planar parallel mechanism and results are given in order to graphically illustrate the effectiveness of the proposed algorithm. The proposed approach can be directly applied to obtain the maximal singularity-free circle of similar parallel mechanisms, which is not the case for other approaches proposed in the literature which is limited to a given parallel mechanism, namely, 3-RPR. Moreover, as the main feature of the proposed approach, it can be implemented both in a CAD system or in a computer algebra system where non-convex and re-entrant curves can be considered.
KeywordsParallel mechanisms Singularity-free workspace Geometric approach Offset curve algorithm.
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