Solving the Forward Position Problem of an In-Parallel Planar Manipulator in the Gauss Plane

TL;DR

This paper addresses the problem of determining the posture of a specific in-parallel planar manipulator using algebraic methods, including complex numbers and Groebner bases, to analyze its kinematic equations.

Contribution

It introduces a novel algebraic approach with self-inversive polynomials and applies computer algebra to solve the forward position problem of the manipulator.

Findings

Polynomials are self reciprocal, indicating symmetry in solutions.

Groebner bases effectively solve the manipulator's kinematic equations.

Algebraic methods facilitate precise posture determination.

Abstract

We study determining the posture of an in-parallel planar manipulator, which has three connectors composed of revolute, prismatic and revolute joints, from specified active joint variables. We construct an ideal in the field of complex numbers, and we introduce self inversive polynomials. We provide results for an in-parallel planar manipulator, which has a base and moving platform in right triangular shape. Using Sage computer algebra system, we compute its Groebner bases. We illustrate that the single variable polynomials obtained from the Groebner bases are self reciprocal.