2022/09/06 by Zijia Li, Li, Zijia, Hans-Peter Schröcker +3 · 1 citation
Engineering · Mathematics · #12D05 15A66 16S36 30C15 70B10 #Algebraic and Geometric Analysis #Dynamics and Control of Mechanical Systems #FOS: Computer and information sciences #FOS: Mathematics #Rings and Algebras (math.RA) #Robotic Mechanisms and Dynamics #Robotics (cs.RO)
paper · pdf · doi:10.48550/arxiv.2209.02306
openalex publication_date 2022/09/06 · openalex created_date 2022/09/30 · openalex updated_date 2026/08/01
Motion polynomials (polynomials over the dual quaternions with nonzero real norm) describe rational motions. We present a necessary and sufficient condition for reduced bounded motion polynomials to admit factorizations into monic linear factors, and we give an algorithm to compute them. We can use those linear factors to construct mechanisms because the factorization corresponds to the decomposition of the rational motion into simple rotations or translations. Bounded motion polynomials always admit a factorization into linear factors after multiplying with a suitable real or quaternion polynomial. Our criterion for factorizability allows us to improve on earlier algorithms to compute a suitable real or quaternion polynomial co-factor.