Factorization of Rational Motions: A Survey with Examples and Applications
This is an incremental survey paper that synthesizes existing knowledge for researchers in mechanism science, offering examples and applications without introducing new methods.
The paper provides an introduction and survey of factorization theory for rational motions, summarizing recent developments and demonstrating applications in mechanism science, such as synthesizing linkages for Bennett mechanisms and open chains for translations.
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.