Spatial Straight Line Linkages by Factorization of Motion Polynomials

TL;DR

This paper introduces a novel method for designing overconstrained spatial linkages with straight line trajectories using motion polynomial factorization, resulting in complex linkages with unique motion capabilities.

Contribution

It presents a new approach to construct spatial linkages with non-translational end-effector motion via motion polynomial factorization, expanding the design possibilities.

Findings

Constructed linkages with four revolute and two prismatic joints.

Developed a linkage with seven revolute joints performing a Darboux motion.

Demonstrated the effectiveness of motion polynomial factorization in linkage design.

Abstract

We use the recently introduced factorization of motion polynomials for constructing overconstrained spatial linkages with a straight line trajectory. Unlike previous examples, the end-effector motion is not translational and the link graph is a cycle. In particular, we obtain a number of linkages with four revolute and two prismatic joints and a remarkable linkage with seven revolute joints one of whose joints performs a Darboux motion.