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.

翻译：运动多项式（具有非零实范数的对偶四元数多项式）描述有理运动。本文给出了约化有界运动多项式允许分解为幺正线性因子的充分必要条件，并给出了计算这些因子的算法。这些线性因子可用于构造机构，因为该分解对应于将有理运动分解为简单旋转或平移。有界运动多项式在乘以适当的实数或四元数多项式后，总是允许分解为线性因子。我们提出的可分解性准则使我们能够改进早期算法，以计算合适的实数或四元数多项式共因子。