Analytical Solution of the Forward Displacement Problem for Spherical Parallel Manipulators

TL;DR

This paper presents an analytical quaternion-based method to solve the forward displacement problem in spherical parallel manipulators, utilizing algebraic geometry techniques for exact solutions and demonstrating its application through a case study.

Contribution

Introduces a novel analytical approach using quaternion algebra and algebraic geometry to solve the forward displacement problem in spherical parallel manipulators.

Findings

Exact solutions obtained for specific SPM configurations.

Method effectively reduces the problem to solving quadrics in four variables.

Case study validates the analytical approach.

Abstract

In this paper, an analytical method that solves the forward displacement problem of several common spherical parallel manipulators (SPMs) is presented. The method uses the the quaternion algebra to restate the problem as a system of four quadrics in four variables and uses an algebraic geometry result by Dixon from 1908 to solve. In addition, a case study is presented for a specific SPM.