Factorization of Rational Motions: A Survey with Examples and Applications

TL;DR

This survey reviews the development of rational motion factorization since 2012, illustrating its applications in mechanism science with examples, algorithms, and new synthesis methods for specific linkages.

Contribution

It provides an accessible overview of motion factorization, including pseudo-code, practical examples, and recent advancements in mechanism synthesis.

Findings

Presented a generic factorization algorithm with pseudo-code

Demonstrated synthesis of Bennett linkages using factorization

Explored non-generic factorization for circular and elliptic translations

Abstract

Since its introduction in 2012, the factorization theory for rational motions quickly evolved and found applications in theoretical and applied mechanism science. We provide an accessible introduction to motion factorization with many examples, summarize recent developments and hint at some new applications. In particular, we provide pseudo-code for the generic factorization algorithm, demonstrate how to find a replacement linkage for a special case in the synthesis of Bennett mechanisms and, as an example of non-generic factorization, synthesize open chains for circular and elliptic translations.