38 citations · 212 across the 21 of their papers we have counts for
21 papers
The integral closure of a primary ideal is not always primary
Nan Li, Zijia Li, Zhi-Hong Yang +1
In 1936, Krull asked if the integral closure of a primary ideal is still primary. Fifty years later, Huneke partially answered this question by giving a primary polynomial ideal wh…
Motion Polynomials Admitting a Factorization with Linear Factors
Zijia Li, Hans-Peter Schröcker, Mikhail Skopenkov +1
Motion polynomials (polynomials over the dual quaternions with nonzero real norm) describe rational motions. We present a necessary and sufficient condition for reduced bounded mot…
The Study Variety of Conformal Kinematics
Bahar Kalkan, Zijia Li, Hans-Peter Schröcker +1
We introduce the Study variety of conformal kinematics and investigate some of its properties. The Study variety is a projective variety of dimension ten and degree twelve in real…
Classification of higher Mobility closed-loop Linkages
Tiago Duarte Guerreiro, Zijia Li, Josef Schicho
We provide a complete classification of paradoxical closed-loop -linkages, where , of mobility or higher, containing revolute, prismatic or helical joints. We also…
Mechanism Singularities Revisited from an Algebraic Viewpoint
Zijia Li, Andreas Müller
It has become obvious that certain singular phenomena cannot be explained by a mere investigation of the configuration space, defined as the solution set of the loop closure equati…
A Survey on the Theory of Bonds
Zijia Li, Josef Schicho, Hans-Peter Schröcker
Many researchers tried to understand/explain the geometric reasons for paradoxical mobility of a mechanical linkage, i.e. the situation when a linkage allows more motions than expe…
The Geometry of Quadratic Quaternion Polynomials in Euclidean and Non-Euclidean Planes
Zijia Li, Josef Schicho, Hans-Peter Schröcker
We propose a geometric explanation for the observation that generic quadratic polynomials over split quaternions may have up to six different factorizations while generic polynomia…
Factorization Results for Left Polynomials in Some Associative Real Algebras: State of the Art, Applications, and Open Questions
Zijia Li, Daniel F. Scharler, Hans-Peter Schröcker
We discuss existence of factorizations with linear factors for (left) polynomials over certain associative real involutive algebras, most notably over Clifford algebras. Because of…
Degree-optimal moving frames for rational curves
Hoon Hong, Zachary Hough, Irina A. Kogan +1
A at a rational curve is a basis of vectors moving along the curve. When the rational curve is given parametrically by a row vector of u…
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…
Spatial Straight Line Linkages by Factorization of Motion Polynomials
Zijia Li, Josef Schicho, Hans-Peter Schröcker
We use the recently introduced factorization of motion polynomials for constructing overconstrained spatial linkages with a straight line trajectory. Unlike previous examples, the…
A Technique for Deriving Equational Conditions on the Denavit-Hartenberg Parameters of 6R Linkages that are Necessary for Movability
Zijia Li, Josef Schicho
A closed 6R linkage is generically rigid. Special cases may be mobile. Many families of mobile 6R linkages have been characterised in terms of the invariant Denavit-Hartenberg para…
An algebraic study of linkages with helical joints
Hamid Abban, Zijia Li, Josef Schicho
Methods from algebra and algebraic geometry have been used in various ways to study linkages in kinematics. These methods have failed so far for the study of linkages with helical…
The Theory of Bonds II: Closed 6R Linkages with Maximal Genus
Gábor Hegedüs, Zijia Li, Josef Schicho +1
In this paper, we introduce a method that allows to produce necessary conditions on the Denavit--Hartenberg parameters for the mobility of a closed linkage with six rotational join…
Classification of Angle-Symmetric 6R Linkage
Zijia Li, Josef Schicho
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 an…