12 citations · 29 across the 9 of their papers we have counts for
10 papers
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…
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…
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…
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…
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…
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…
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…
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…