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 ...

Using the ranks and Moore-Penrose inverses of involved matrices, in this paper we establish some necessary sufficient solvability conditions for a system Sylvester-type quaternion matrix equations, give an expression general solution to when it is solvable. As application system, consider special symmetry solution, named η-Hermitian equations. Moreover, present algorithm numerical example verif...

Quaternion quantum mechanics is examined at the level of unbroken SU(2) gauge symmetry. A general quaternionic phase expression is derived from formal properties of the quaternion algebra. pacs 03.65.Bz, 03.65.Ca,11.15.Kc, 02.30.+g 1 Quaternion Quantum Mechanics Quantum mechanics defined over general algebras have been conjectured since 1934 [1]. In 1936 Birkoff and von Neumann noted that the p...

The problem of integrating rotations and angular velocity from a known timeand space-dependent curvature is met in the dynamic analysis of non-linear spatial beams, if the numerical formulation is based on curvature, as in [1]. To avoid singularities and make the formulation more convenient, rotational quaternions q̂ are used for the parametrization of rotations. The relation between the curvatu...

In the literature we find a variety of mathematical approaches for solving problems in robotics which we will review now briefly. Denavit and Hartenberg [60] introduced the mostly used kinematic notation for lower pair mechanisms based on matrix algebra, Walker [243] used the epsilon algebra for the treatment of the manipulator kinematics, Gu and Luh [99] utilized dual– matrices for computing t...

‎Let $n$ and $k$ be two positive integers‎, ‎$kleq n$ and $A$ be an $n$-square quaternion matrix‎. ‎In this paper‎, ‎some results on the $k-$numerical range of $A$ are investigated‎. ‎Moreover‎, ‎the notions of $k$-numerical radius‎, ‎right $k$-spectral radius and $k$-norm of $A$ are introduced‎, ‎and some of their algebraic properties are studied‎.

Let λ1, · · · , λn be random eigenvalues coming from the beta-Laguerre ensemble with parameter p, which is a generalization of the real, complex and quaternion Wishart matrices of parameter (n, p). In the case that the sample size n is much smaller than the dimension of the population distribution p, a common situation in modern data, we approximate the beta-Laguerre ensemble by a beta-Hermite ...