76 citations · 271 across the 28 of their papers we have counts for
30 papers
Bivariate quaternionic factorizations and surfaces that decompose into two circles
Johanna Frischauf, Niels Lubbes, Hans-Peter Schröcker
We present an algebraic and geometric condition for bivariate quaternionic polynomials of arbitrary bidegree to have a univariate linear left or right factor. We apply this quatern…
Bistable Quad-Nets Composed of Four-Bar Linkages
Gudrun Szewieczek, Daniel Huczala, Martin Pfurner +1
We study a novel type of mechanical structures, composed of spatial four-bar linkages, that are bistable, that is, they allow for two distinct configurations. These structures have…
A Complete Characterization of Pythagorean Hodograph Preserving Mappings
Amedeo Altavilla, Hans-Peter Schröcker, Zbyněk Šír +1
We fully characterize the mappings that send every Pythagorean-hodograph (PH) curve to a PH curve. We prove that in any dimension, such mappings are precisely the conformal fun…
Rational Motions of Minimal Quaternionic Degree with Prescribed Line Trajectories
Zülal Derin Yaqub, Hans-Peter Schröcker
In this paper, we study how to find rational motions that move a line along a given rational ruled surface. Our goal is to find motions with the lowest possible degree using dual q…
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…
Three Paths to Rational Curves with Rational Arc Length
Hans-Peter Schröcker, Zbyněk Šìr
We solve the so far open problem of constructing all spatial rational curves with rational arc length functions. More precisely, we present three different methods for this constru…
Optimal interpolation with spatial rational Pythagorean hodograph curves
Hans-Peter Schröcker, Zbyněk Šìr
Using a residuum approach, we provide a complete description of the space of the rational spatial curves of given tangent directions. The rational Pythagorean hodograph curves are…
A Multi-Bennett 8R Mechanism Obtained From Factorization of Bivariate Motion Polynomials
Johanna Frischauf, Martin Pfurner, Daniel F. Scharler +1
We present a closed-loop 8R mechanism with two degrees of freedom whose motion exhibits curious properties. In any point of a two-dimensional component of its configuration variety…
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…
Rational Framing Motions and Spatial Rational Pythagorean Hodograph Curves
Bahar Kalkan, Daniel F. Scharler, Hans-Peter Schröcker +1
We propose a new method for constructing rational spatial Pythagorean Hodograph (PH) curves based on determining a suitable rational framing motion. While the spherical component o…
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…
An Algorithm for the Factorization of Split Quaternion Polynomials
Daniel F. Scharler, Hans-Peter Schröcker
We present an algorithm to compute all factorizations into linear factors of univariate polynomials over the split quaternions, provided such a factorization exists. Failure of the…
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…
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 Kinematic Image of RR, PR, and RP Dyads
Tudor-Dan Rad, Daniel F. Scharler, Hans-Peter Schröcker
We provide necessary and sufficient conditions for admissible transformations in the projectivised dual quaternion model of rigid body displacements and we characterise constraint…
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…
The Kinematic Image of 2R Dyads and Exact Synthesis of 5R Linkages
Tudor-Dan Rad, Hans-Peter Schröcker
We characterise the kinematic image of the constraint variety of a 2R dyad as a regular ruled quadric in a 3-space that contains a "null quadrilateral". Three prescribed poses dete…
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…
Guaranteed Collision Detection With Toleranced Motions
Hans-Peter Schröcker, Matthias J. Weber
We present a method for guaranteed collision detection with toleranced motions. The basic idea is to consider the motion as a curve in the 12-dimensional space of affine displaceme…
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…