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 ...

Interpolating trajectories of points and geometric entities is an important problem for kinematics. To describe these trajectories, several algorithms have been proposed using matrices, quaternions, dual-quaternions, the Study quadric; last one allows embedding motors as 8D vectors into projective space P7, where interpolation rotations translations becomes a linear problem. Furthermore, confor...

Quaternions have been a popular tool in 3D computer graphics for more than 20 years. However, classical quaternions are restricted to the representation of rotations, whereas in graphical applications we typically work with rotation composed with translation (i.e., a rigid transformation). Dual quaternions represent rigid transformations in the same way as classical quaternions represent rotati...

Abstract. We formulate Lorentz group representations in which ordinary complex numbers are replaced by linear functions of real quaternions and introduce dotted and undotted quaternionic one-dimensional spinors. To extend to parity the space-time transformations, we combine these one-dimensional spinors into bi-dimensional column vectors. From the transformation properties of the two-component ...

In this paper, we propose two methods based on quaternions to compute the angles of inclination and the angular velocity with 6 degrees of freedom using the measurements of a 3-axis accelerometer and a 3-axis magnetometer. Each method has singularities which occur during the computation of the orientation of the device in the 3-dimensional space. We propose solutions to avoid these singularitie...

Colour image representation using real quaternions has shown to be very useful for linear and morphological colour filtering. This paper deals with the extension of first derivatives-based structure tensor for various quaternionic colour image representations. Classical corner and edge features are obtained from eigenvalues of the quaternionic colour structure tensors. We study the properties o...

In [He], Herstein conjectured that odd-order subgroups of division rings K were cyclic, and he proved this to be the case when K is the division ring of the real quaternions. Herstein’s conjecture was settled negatively in [Am]. As part of his complete classification of finite groups in division rings, Amitsur showed that the smallest noncyclic odd-order group that can be embedded in a division...

1 Quaternions and the three-dimensional sphere 3 1.1 Hamiltion’s quaternions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2 The Lie group S . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.2.1 The normalizer of Q8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.3 The exponential map for S . . . . . . . . . . . . . . . . ....

Two solutions of the homogeneous matrix equation AX=ZB, that allows a simultaneous computation of the transformations from robot world to robot base and from robot tool to robot wrist coordinate frames, are proposed. The presented methods introduce the Kronecker product and dual quaternions to solve the rotations and translations problem, simultaneously, with no propagation error. The experimen...