Position Analysis of the RRP-3(SS) Multi-Loop Spatial Structure

TL;DR

This paper develops a mathematical approach for analyzing the position of a complex multi-loop spatial structure, providing solutions to its kinematic equations and demonstrating applications to robotic manipulators.

Contribution

It introduces a set of compatibility equations and an algebraic elimination method to solve the forward kinematics of a multi-loop spatial structure with 28 solutions.

Findings

28 solutions in the complex domain for the structure's position

Application to the Tricept manipulator's forward kinematics

Numerical validation with two case studies

Abstract

The paper presents the position analysis of a spatial structure composed of two platforms mutually connected by one RRP and three SS serial kinematic chains, where R, P, and S stand for revolute, prismatic, and spherical kinematic pair respectively. A set of three compatibility equations is laid down that, following algebraic elimination, results in a 28th-order univariate algebraic equation, which in turn provides the addressed problem with 28 solutions in the complex domain. Among the applications of the results presented in this paper is the solution to the forward kinematics of the Tricept, a well-known in-parallel-actuated spatial manipulator. Numerical examples show adoption of the proposed method in dealing with two case studies.