Kinematic analysis of a class of analytic planar 3-RPR parallel manipulators

TL;DR

This paper analyzes a specific class of planar 3-RPR parallel manipulators, focusing on their kinematic properties, singularities, and the implications for non-singular assembly-mode changes, with a simplified solution approach.

Contribution

It introduces a kinematic analysis method for a class of manipulators with congruent base and platform, including singularity characterization and analysis of second-order singularities.

Findings

Forward kinematics reduces to solving a cubic and a quadratic equation.

Singularities are identified and visualized in joint space.

Second-order singularities are characterized and analyzed.

Abstract

A class of analytic planar 3-RPR manipulators is analyzed in this paper. These manipulators have congruent base and moving platforms and the moving platform is rotated of 180 deg about an axis in the plane. The forward kinematics is reduced to the solution of a 3rd-degree polynomial and a quadratic equation in sequence. The singularities are calculated and plotted in the joint space. The second-order singularities (cups points), which play an important role in non-singular change of assembly-mode motions, are also analyzed.