论文标题
不研究条件的双重四元素多项式的分解
Factorization of Dual Quaternion Polynomials Without Study's Condition
论文作者
论文摘要
在本文中，我们研究了双重四季度在线性因子中的多项式分解。虽然较早的结果假定范数多项式是真实的（“运动多项式”），但我们只需要在原始部分中没有实际多项式因子，而规范多项式在双重数字上的因素是偶像二次因素。这种显然必要的条件也足以存在因素化。我们提出了一种算法来计算这些多项式的因素化，并将其用于新的机制构造，这些机制无法通过现有的运动多项式分解算法获得。当它们产生具有旋转或翻译关节的机制时，我们的方法产生了由“垂直darboux关节”组成的机制。它们表现出机械缺陷，因此我们探索了用圆柱关节代替它们的方法，同时保持整体机制受到充分约束。
In this paper we investigate factorizations of polynomials over the ring of dual quaternions into linear factors. While earlier results assume that the norm polynomial is real ("motion polynomials"), we only require the absence of real polynomial factors in the primal part and factorizability of the norm polynomial over the dual numbers into monic quadratic factors. This obviously necessary condition is also sufficient for existence of factorizations. We present an algorithm to compute factorizations of these polynomials and use it for new constructions of mechanisms which cannot be obtained by existing factorization algorithms for motion polynomials. While they produce mechanisms with rotational or translational joints, our approach yields mechanisms consisting of "vertical Darboux joints". They exhibit mechanical deficiencies so that we explore ways to replace them by cylindrical joints while keeping the overall mechanism sufficiently constrained.
