  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.
