The Kinematic Analysis of a Symmetrical Three-Degree-of-Freedom Planar Parallel Manipulator

TL;DR

This paper analyzes the kinematics of a symmetrical three-DOF planar parallel manipulator, introducing the concept of aspects to handle multiple solutions and demonstrating the existence of non-singular assembly-mode changing trajectories.

Contribution

It introduces the notion of aspects for kinematic analysis and shows that non-singular assembly-mode changing trajectories exist for this type of manipulator.

Findings

Multiple inverse and direct kinematic solutions identified.

Aspects enable separation of inverse kinematic solutions.

Existence of non-singular assembly-mode changing trajectories demonstrated.

Abstract

Presented in this paper is the kinematic analysis of a symmetrical three-degree-of-freedom planar parallel manipulator. In opposite to serial manipulators, parallel manipulators can admit not only multiple inverse kinematic solutions, but also multiple direct kinematic solutions. This property produces more complicated kinematic models but allows more flexibility in trajectory planning. To take into account this property, the notion of aspects, i.e. the maximal singularity-free domains, was introduced, based on the notion of working modes, which makes it possible to separate the inverse kinematic solutions. The aim of this paper is to show that a non-singular assembly-mode changing trajectory exist for a symmetrical planar parallel manipulator, with equilateral base and platform triangle.