Determination of the maximal singularity-free workspace of 3-DOF parallel mechanisms with a 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 associated with an arbitrary starting point of the moving platform are obtained. Then, the second algorithm finds the center of themaximal singularity-free circle, which is obtained using the so-called offset curve algorithm. The procedure is applied to a 3-PRR planar parallel mechanism as an example and the obtained results illustrate graphically the effectiveness of the proposed algorithm. The proposed approach can be directly applied to obtain themaximal singularity-free circle of similar parallel mechanisms, which is not the case for other approaches proposed in the literature that are limited to a given parallelmechanism, namely, the 3-RPR planar parallelmechanism. Moreover, as the main feature of the proposed approach, it can be implemented both in a CAD system and in a computer algebra system where non-convex and reentrant curves can be considered. (C) 2014 Elsevier Ltd. All rights reserved.