From the Fundamental Theorem of Algebra to Kempe's Universality Theorem
It addresses a foundational problem in mechanism science by linking abstract algebra to practical applications, but is incremental as it builds on existing theory.
The paper introduces factorization theory of motion polynomials, connecting non-unique factorization over dual quaternions to mechanism science, and highlights its beneficial impact on both mathematics and engineering over four years.
This article provides a gentle introduction for a general mathematical audience to the factorization theory of motion polynomials and its application in mechanism science. This theory connects in a rather unexpected way a seemingly abstract mathematical topic, the non-unique factorization of certain polynomials over the ring of dual quaternions, with engineering applications. Four years after its introduction, it is already clear how beneficial it has been to both fields.