12 citations · 30 across the 12 of their papers we have counts for
13 papers
Computer-Aided Design of Rational Motions for 4R and 6R Spatial Mechanism Synthesis
Daniel Huczala, Severinas Zube, Martin Pfurner +2
This paper focuses on geometric methods for generating rational motions used in the design of single-loop rational linkages, 1-degree-of-freedom mechanisms that can execute prescri…
Quadratic Motion Polynomials With Irregular Factorizations
Daren A. Thimm, Zijia Li, Hans-Peter Schröcker +1
Motion polynomials are a specific type of polynomial over a Clifford algebra that can conveniently describe rational motions. There exists an algorithm for the factorization of mot…
Rational Linkages: From Poses to 3D-printed Prototypes
Daniel Huczala, Johannes Siegele, Daren A. Thimm +2
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 mot…
Quadratic Spinor Polynomials with Infinitely Many Factorizations
Zijia Li, Hans-Peter Schröcker, Johannes Siegele +1
Spinor polynomials are polynomials with coefficients in the even sub-algebra of conformal geometric algebra whose norm polynomial is real. They describe rational conformal motions.…
A Geometric Algorithm for the Factorization of Spinor Polynomials
Zijia Li, Hans-Peter Schröcker, Johannes Siegele
We present a new algorithm to decompose generic spinor polynomials into linear factors. Spinor polynomials are certain polynomials with coefficients in the geometric algebra of dim…
An Overconstrained Vertical Darboux Mechanism
Johannes Siegele, Martin Pfurner
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 ver…
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…
Analysis of a 3-RUU Parallel Manipulator
Thomas Stigger, Johannes Siegele, Daniel F. Scharler +2
The aim of this paper is to give a detailed examination of the input and output singularities of a 3-RUU parallel manipulator in the translational operation mode. This task is achi…
Factorization of Quaternionic Polynomials of Bi-Degree (n,1)
Johanna Lercher, Daniel F. Scharler, Hans-Peter Schröcker +1
We consider polynomials of bi-degree over the skew field of quaternions where the indeterminates commute with each other and with all coefficients. Polynomials of this type…
Factorization of Dual Quaternion Polynomials Without Study's Condition
Johannes Siegele, Martin Pfurner, Hans-Peter Schröcker
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 ("mo…
Space Kinematics and Projective Differential Geometry Over the Ring of Dual Numbers
Johannes Siegele, Hans-Peter Schröcker, Martin Pfurner
We study an isomorphism between the group of rigid body displacements and the group of dual quaternions modulo the dual number multiplicative group from the viewpoint of differenti…
Quadratic Split Quaternion Polynomials: Factorization and Geometry
Daniel F. Scharler, Johannes Siegele, Hans-Peter Schröcker
We investigate factorizability of a quadratic split quaternion polynomial. In addition to inequality conditions for existence of such factorization, we provide lucid geometric inte…
Rational Motions with Generic Trajectories of Low Degree
Johannes Siegele, Daniel F. Scharler, Hans-Peter Schröcker
The trajectories of a rational motion given by a polynomial of degree n in the dual quaternion model of rigid body displacements are generically of degree 2n. In this article we st…