Abstract
This work focuses on the geometric synthesis of planar 3-RPR parallel mechanisms in order to guarantee a singularity-free workspace for a desired orientation range. The effects of the orientation angle, the minimal leg length as well as the base shape on the singularity-free workspace are analyzed using the Gauss divergence theorem. The results show that for every orientation angle, there exists an optimal minimal leg length which leads to the maximal singularity-free workspace. If the optimal minimal leg lengths are used, the equilateral triangle base yields the maximal singularity-free workspace for any orientation angle. However, for a prescribed working range of the orientation angle, the optimal minimal leg length may be different from the individual optimal minimal leg lengths. Based on the optimal minimal leg length determined for a prescribed working range of the orientation angle, a geometric synthesis procedure is proposed in order to guarantee a singularity-free workspace.
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