Position Equations of a 3RPR Planar Manipulator

TL;DR

This paper derives parametric position equations for a 3RPR planar manipulator using isometries and loop-closure equations, providing a mathematical framework for analyzing its kinematics.

Contribution

It introduces a novel approach to formulating position equations of a 3RPR manipulator based on isometries and loop-closure in the Gauss plane.

Findings

Derived explicit parametric equations for the manipulator's position.

Provided insights into the geometric relationships using isometries.

Enhanced understanding of the manipulator's kinematic behavior.

Abstract

We study parametric equations, which describe the position of an in-parallel planar manipulator. We discuss isometries in the Gauss plane, then we write the loop-closure equations in terms of the rotations as the parameters.