This paper presents a synthesis methodology for parallel robots based on the dual quaternion synthesis of serial constrained robots, that is, serial robots with less than six degrees of freedom. This methodology uses a dual quaternion formulation of the kinematics equations. The goal of the synthesis problem is to determine the dimensions of the robot from a specification of its workspace. The ...

This work studies the zeros of slice functions over algebra dual quaternions and it comprises applications to problem factorizing motion polynomials. The class an alternative $*$-algebra $A$ was defined by Ghiloni Perotti in 2011, extending regular introduced Gentili Struppa 2006. Both classes strictly include polynomials $A$. We focus on case when is $\mathbb{DH}$. specific properties this all...

In this paper, firstly the ruled surface drawn by Darboux vector is expressed as a quaternion. Then, spatial quaternionic definition of striction curve given and integral invariants are calculated. Finally, which corresponds to dual derived with help quaternions obtained.

Some of the most brilliant mathematical discoveries of the 1800s were pushed aside for over a century in favor of the vector analysis and linear algebra that we are all familiar with. However, these old ideas have recently been rediscovered in the field of computer graphics by researchers who understand how they can unify many of the geometric operations that are used every day. This talk intro...

Using split-quaternions, we find explicit SDYM SU(1, 1) instanton solutions in S2 −×S 2 + which is the conformal compactification of the semi-Euclidean 4-spacetime R 2+2 of split-signature (−,−,+,+). The noncompact Lie group SU(1, 1) is naturally introduced as an appropriate gauge group for SDYM instantons in S2 −×S 2 +. It is shown that SDYM and ASDYM SU(1, 1) instanton solutions in S2 −×S 2 +...

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 one-parametric family of solutions. We suggest strategies for picking good solutions from this family.