相关论文: Factorization of Rational Curves in the Study Quad…

The paper presents an optimal synthesis of overconstrained linkages, based on the factorization of rational curves (representing one parametric motions) contained in Study's quadric. The group of Euclidean displacements is embedded in a…

We prove that every bounded rational space curve of degree d and circularity c can be drawn by a linkage with 9/2 d - 6c + 1 revolute joints. Our proof is based on two ingredients. The first one is the factorization theory of motion…

We propose a geometric explanation for the observation that generic quadratic polynomials over split quaternions may have up to six different factorizations while generic polynomials over Hamiltonian quaternions only have two. Split…

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…

We consider bivariate polynomials over the skew field of quaternions, where the indeterminates commute with all coefficients and with each other. We analyze existence of univariate factorizations, that is, factorizations with univariate…

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…

We present an algorithm to compute all factorizations into linear factors of univariate polynomials over the split quaternions, provided such a factorization exists. Failure of the algorithm is equivalent to non-factorizability for which we…

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…

We use the recently introduced factorization of motion polynomials for constructing overconstrained spatial linkages with a straight line trajectory. Unlike previous examples, the end-effector motion is not translational and the link graph…

We use the recently introduced factorization theory of motion polynomials over the dual quaternions for the synthesis of closed kinematic loops with six revolute joints that visit four prescribed poses. Our approach admits either no or a…

Motion polynomials are a specific type of polynomial over a Clifford algebra that can conveniently describe rational motions. There exists an algorithm for the factorization of motion polynomials that works in generic cases. It hinges on…

The trajectories of a rational motion given by a polynomial of degree n in the dual quaternion model of rigid body displacements are generically of degree 2n. In this article we study those exceptional motions whose trajectory degree is…

This paper gives new and elementary combinatorial topological proofs of the classification of unoriented and oriented rational knots and links. These proofs are based on the known classification of alternating knots through flyping, and the…

We discuss existence of factorizations with linear factors for (left) polynomials over certain associative real involutive algebras, most notably over Clifford algebras. Because of their relevance to kinematics and mechanism science, we put…

In this paper, we construct two types of 7R closed single loop linkages by combining different factorizations of a general (non-vertical) Darboux motion. These factorizations are obtained by extensions of a factorization algorithm for a…

This paper investigates the construction of rational motions of a minimal quaternionic degree that generate a prescribed plane trajectory (a ``rational torse''). Using the algebraic framework of dual quaternions, we formulate the problem as…

Rational transformations of polynomials are extensively studied in the context of finite fields, especially for the construction of irreducible polynomials. In this paper, we consider the factorization of rational transformations with…

We investigate the local contribution of the braid monodromy factorization in the context of the links obtained by the closure of these braids. We consider plane curves which are arrangements of lines and conics as well as some algebraic…

We investigate constrained quantum motion on curves and surfaces using connection factorization methods. We show that Laplace operators admit an exact half-connection factorization generated by connection one-forms. The first-order part of…

Let $D$ be an oriented classical or virtual link diagram with directed universe $\vec{U}$. Let $C$ denote a set of directed Euler circuits, one in each connected component of $U$. There is then an associated looped interlacement graph…