38 citations · 212 across the 21 of their papers we have counts for
7 papers · 1 filter
Kempe's Universality Theorem for Rational Space Curves
Zijia Li, Josef Schicho, Hans-Peter Schröcker
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.…
From the Fundamental Theorem of Algebra to Kempe's Universality Theorem
Gábor Hegedüs, Zijia Li, Josef Schicho +1
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 the…
The Rational Motion of Minimal Dual Quaternion Degree With Prescribed Trajectory
Zijia Li, Josef Schicho, Hans-Peter Schröcker
We give a constructive proof for the existence of a unique rational motion of minimal degree in the dual quaternion model of Euclidean displacements with a given rational parametri…
Factorization of Motion Polynomials
Zijia Li, Josef Schicho, Hans-Peter Schröcker
In this paper, we consider the existence of a factorization of a monic, bounded motion polynomial. We prove existence of factorizations, possibly after multiplication with a real p…
Planar Linkages Following a Prescribed Motion
Matteo Gallet, Christoph Koutschan, Zijia Li +3
Designing mechanical devices, called linkages, that draw a given plane curve has been a topic that interested engineers and mathematicians for hundreds of years, and recently also…
7R Darboux Linkages by Factorization of Motion Polynomials
Zijia Li, Josef Schicho, Hans-Peter Schröcker
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 o…
Factorization of Rational Motions: A Survey with Examples and Applications
Zijia Li, Tudor-Dan Rad, Josef Schicho +1
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 acc…