Higher-Order Flexible Configurations of Planar Parallel Manipulators Constructed by Averaging

TL;DR

This paper explores singular configurations of planar 3-RPR parallel manipulators using averaging techniques, providing a parametrization method that increases flexion order without solving high-degree polynomials.

Contribution

It introduces a novel averaging-based parametrization approach for analyzing singular configurations, applicable to planar, spherical, and spatial manipulators.

Findings

Parametrization increases flexion order of averaged configurations.

Visualization of singular configurations for specific examples.

Method applicable to spherical and spatial manipulator analogues.

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.