Higher-Order Flexible Configurations of Planar Parallel Manipulators Constructed by Averaging
arXiv:2605.02434
Abstract
This paper investigates singular configurations of planar 3-RPR parallel manipulators, which result from applying the averaging technique to solution pairs of their direct kinematic problem. Without computing the zeros of the corresponding degree 6 polynomial we parametrize the input pairs and determine their relative orientation in a way that the flexion order of the averaged configurations increases. Moreover, the obtained results are visualized for concrete examples. The presented methodology can also be used for studying the spherical and spatial analogues of planar 3-RPR parallel manipulators.
This manuscript represents the full complementary version of the paper of the same title submitted to the International Conference on Geometry and Graphics 2026 (ICGG 2026)