In this paper we introduce a new technique, based on dual quaternions, for the analysis of closed linkages with revolute joints: the theory of bonds. The bond structure comprises a lot of information on closed revolute chains with a one-parametric mobility. We demonstrate the usefulness of bond theory by giving a new and transparent proof for the well-known classification of overconstrained 5R ...

We define motion polynomials as polynomials with coefficients in the dual quaternions and study their factorizations. The motion polynomials correspond to motions in 3D space, and factoring into linear factors means to compose the motion into translations and rotations. This allows to realize the motion by a linkage with revolute or prismatic joints. This is joint work with G. Hegedüs (Univ. Ob...

This paper proposes a new non-linear differential equation for the six degrees of freedom (6-DOF) relative rigid bodies motion. A representation theorem is provided 6-DOF motion in arbitrary non-inertial reference frame. The problem two spacecraft specific case Keplerian confocal orbits proposed. result an analytical method without secular terms and singularities. Tensors dual algebra quaternio...

Kinematics studies the motion of bodies without consideration of the forces or moments that cause the motion. Robot kinematics refers the analytical study of the motion of a robot manipulator. Formulating the suitable kinematics models for a robot mechanism is very crucial for analyzing the behaviour of industrial manipulators. There are mainly two different spaces used in kinematics modelling ...

We explore discrete approaches in LQG where all fields, the gravitational tetrad, and the matter and energy fields, are encoded implicitly in a graph instead of being additional data. Our graph should therefore be richer than a simple simplicial decomposition. It has to embed geometrical information and the standard model. We start from Lisi’s model. We build a trivalent graph which is an F4 la...

Interior point methods can be extended to a number of cones (self-dual homogeneous cones) • Rn (linear programming) • vectorized symmetric matrices over real numbers (semidefinite programming) • vectorized Hermitian matrices over complex numbers • vectorized Hermitian matrices over quaternions • vectorized Hermitian 3×3 matrices over octonions Grötschel, Lovász and Schrijver [3]: semidefinite p...

Conformal geometric algebra (CGA) is a framework that allows the representation of objects, such as points, planes and spheres, deformations, translations, rotations dilations uniform vectors, called multivectors. In this work, we demonstrate merits multivector usage with novel, integrated rigged character simulation based on CGA. framework, for first time, one may perform real-time cuts tears ...

There are two kinds of dual split type air-conditioner. One is of using two compressors for two indoor units; the other has only one compressor for two indoor units. The EER and refrigerating capacity of the former kind are just the same as the single split type's. But to one compressor dual split type system, there are two working ways: 1. compressor and both two indoor units operating, and 2....