相关论文: Four-Pose Synthesis of Angle-Symmetric 6R Linkages

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…

In this paper, we consider a special kind of overconstrained 6R closed linkages which we call angle-symmetric 6R linkages. These are linkages with the property that the rotation angles are equal for each of the three pairs of opposite…

Given a generic rational curve $C$ in the group of Euclidean displacements we construct a linkage such that the constrained motion of one of the links is exactly $C$. Our construction is based on the factorization of polynomials over dual…

We characterise the kinematic image of the constraint variety of a 2R dyad as a regular ruled quadric in a 3-space that contains a "null quadrilateral". Three prescribed poses determine, in general, two such quadrics. This allows us to…

In this paper, a set of tools is introduced that simplifies the synthesis and rapid-prototyping of single-loop rational kinematic chains. It allows the user to perform rational motion interpolation of up to four given poses and yields the…

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…

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…

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…

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…

In this article, we will construct an overconstrained closed-loop linkage consisting of four revolute and one cylindrical joint. It is obtained by factorization of a prescribed vertical Darboux motion. We will investigate the kinematic…

In this paper we introduce a new technique, based on dual quaternions, for the analysis of closed linkages with revolute joints: the theory of bonds. The bond structure comprises a lot of information on closed revolute chains with a…

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…

Synthesis problems for linkages in kinematics often yield large structured parameterized polynomial systems which generically have far fewer solutions than traditional upper bounds would suggest. This paper describes statistical models for…

We present a closed-loop 8R mechanism with two degrees of freedom whose motion exhibits curious properties. In any point of a two-dimensional component of its configuration variety it is possible to fix every second joint while retaining…

This study presents a set of algorithms that deal with trajectory planning of rational single-loop mechanisms with one degree of freedom (DoF). Benefiting from a dual quaternion representation of a rational motion, a formula for direct…

This work focuses on pose-following, a variant of path-following in which the goal is to steer the system's position and attitude along a path with a moving frame attached to it. Full body motion control, while accounting for the additional…

This note is a complete library of symbolic parametrized expressions for both real and complexified configuration spaces of a planar 4-bar linkage. Building upon the previous work from Izmestiev (2015), this library expands on the…

This paper presents new six solutions for sixth degree polynomial equation in general forms basing on new theorems, where the possibility to calculate the six roots of any sixth degree equation nearly simultaneously. The proposed roots for…

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…