This paper shows the coordinates influence on singularity of a three degree-of-freedom structure, namely, three-Universal-Prismatic-Spherical (3-UPS) parallel manipulator. Rotational coordinates, which are chosen to define the orientation of the platform, affect the singularity of the manipulator. Euler parameters, which don't have any inherent geometrical singularity are utilized, however they...

A sliding mode control method is presented for Euler parameter command tracking of spacecraft maneuvers. Although only three Euler parameters are independent, desired closed-loop performance is specified on all four Euler parameters by way of four sliding surfaces in the Euler parameter error-error rate phase planes. The Euler parameters were chosen as the generalized coordinates for tracking t...

This article presents a way to draw Euler angles such that the proper operation and application becomes immediately clear. Furthermore, Euler parameters, which allow a singularity-free description of rotational motion, are discussed within the framework of quaternion algebra and are applied to the kinematics and dynamics of a rigid body. 1 Euler Angles In rigid body mechanics we need to keep tr...

Euler parameters constitute a well-known nonminimal singularity-free representation of rigid body orientation. This paper is aimed at illustrating the role of Euler parameters in robot control; namely, the kinematic control, dynamic control and impedance control problems are surveyed in a unifying perspective, where robot’s end-effector orientation displacements are described in terms of Euler ...

A position and attitude tracking control law for autonomous underwater vehicles (AUVs) in 6 degrees of freedom (DOF) is derived. The 4-parameter unit quaternion (Euler parameters) is used in a singularity-free representation of attitude. Global convergence of the closed-loop system is proven. In addition several 3-parameter representations in terms of the Euler parameters are discussed with app...

New combinatorial statistics on colored permutation groups are introduced here. We present two different generalizations of major index and descent number, one of them is combinatorial in nature and the other is algebraic. We also present Euler-Mahonian type joint distributions of our parameters.

A method of workspace modelling for spherical parallel manipulators (SPMs) of symmetrical architecture is developed by virtue of Euler parameters in the paper. The adoption of Euler parameters in the expression of spatial rotations of SPMs helps not only to eliminate the possible singularity in the rotation matrix, but also to formulate all equations in polynomials, which are more easily manipu...

Gas holdup and bubble size are important parameters for simulation and designing in bubble column reactors. Because based on these parameters, the available gas-liquid interfacial area is defined for mass transfer. In this paper, the results of applying magnetic fields on the velocity field and volume fraction of gas holdup are reported. Hydrodynamics of the bubble column in the reactors is inv...

sieve trays are widely used in the gas- liquid contactors such as distillation and absorption towers. in this article, a three-dimensional, two phase cfd model using euler-euler framework was developed to simulate a distillation tower with two sieve trays. hydrodynamic simulation of air and water system in different rates of gas phase was carried out and velocity distribution parameters, clear ...