Factorization of Rational Curves in the Study Quadric and Revolute Linkages

TL;DR

This paper presents a method to construct linkages with prescribed rational motion paths using polynomial factorization over dual quaternions, leading to new overconstrained mechanisms.

Contribution

It introduces a novel approach to design linkages for specific motions via polynomial factorization in dual quaternion algebra, including new overconstrained 6R-chains.

Findings

Constructed linkages for generic rational curves in Euclidean displacements group.

Includes examples such as Bennett mechanisms and new overconstrained 6R-chains.

Demonstrates the effectiveness of polynomial factorization over dual quaternions in linkage design.

Abstract

Given a generic rational curve $C$ in the group of Euclidean displacements we construct a linkage such that the constrained motion of one of the links is exactly $C$. Our construction is based on the factorization of polynomials over dual quaternions. Low degree examples include the Bennett mechanisms and contain new types of overconstrained 6R-chains as sub-mechanisms.