2.3RAJul 19, 2015
From the Fundamental Theorem of Algebra to Kempe's Universality TheoremGábor Hegedüs, Zijia Li, Josef Schicho et al.
This article provides a gentle introduction for a general mathematical audience to the factorization theory of motion polynomials and its application in mechanism science. This theory connects in a rather unexpected way a seemingly abstract mathematical topic, the non-unique factorization of certain polynomials over the ring of dual quaternions, with engineering applications. Four years after its introduction, it is already clear how beneficial it has been to both fields.
9.2AGJun 18, 2012
The Theory of Bonds: A New Method for the Analysis of LinkagesGábor Hegedüs, Josef Schicho, Hans-Peter Schröcker
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 one-parametric mobility. We demonstrate the usefulness of bond theory by giving a new and transparent proof for the well-known classification of overconstrained 5R linkages.
10.8RAFeb 1, 2012
Factorization of Rational Curves in the Study Quadric and Revolute LinkagesGábor Hegedüs, Josef Schicho, Hans-Peter Schröcker
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 quaternions. Low degree examples include the Bennett mechanisms and contain new types of overconstrained 6R-chains as sub-mechanisms.