Direct Kinematics, Inverse Kinematics, and Motion Planning of 1-DoF Rational Linkages

TL;DR

This paper introduces algorithms for trajectory planning of 1-DoF rational linkages using dual quaternions, including direct and inverse kinematics, and demonstrates their application through a laboratory experiment.

Contribution

It presents a unified approach for trajectory planning of rational single-loop mechanisms with 1-DoF using dual quaternion representation and novel inverse kinematics methods.

Findings

Effective algorithms for direct and inverse kinematics are developed.

The approach enables smooth tool travel via arc-length reparameterization.

Experimental validation confirms practical applicability.

Abstract

This study presents a set of algorithms that deal with trajectory planning of rational single-loop mechanisms with one degree of freedom (DoF). Benefiting from a dual quaternion representation of a rational motion, a formula for direct (forward) kinematics, a numerical inverse kinematics algorithm, and the generation of a driving-joint trajectory are provided. A novel approach using the Gauss-Newton search for the one-parameter inverse kinematics problem is presented. Additionally, a method for performing smooth equidistant travel of the tool is provided by applying arc-length reparameterization. This general approach can be applied to one-DoF mechanisms with four to seven joints characterized by a rational motion, without any additional geometrical analysis. An experiment was performed to demonstrate the usage in a laboratory setup.