An approach for obtaining unique kinematic solutions of a spherical parallel manipulator

Abstract

In this paper an approach for obtaining unique solutions to forward and inverse kinematics of a spherical parallel manipulator (SPM) system with revolute joints is proposed. Kinematic analysis of a general SPM with revolute joints is revisited and the proposed approach is formulated in the form of easy-to-follow algorithms that are described in detail. A graphical verification method using SPM computer-aideddesign (CAD) models is presented together with numerical and experimental examples that confirm the correctness of the proposed approach. It is expected that this approach can be applied to SPMs with different geometries and can be useful in designing real-time control systems of SPMs.

Constrained Orientation Control of a Spherical Parallel Manipulator via Online Convex Optimization

“…Therefore, eight possible solutions are provided for the inverse kinematic problem. In this paper, the algorithm presented in [18] (to which we refer the reader for details), is used. This algorithm is defined in order to employ only one of the eight solutions at each sampling instant, also maintaining the same working mode during the whole robot motion.…”

“…Thus, there is a need for general control laws that can directly take these constraints into account. In [17], an off-line framework was proposed for generating optimal motor trajectories for general 3-DOF RRR SPMs, based on the kinematics analysis reported in [18]. A feasible configuration space for the SPM was first defined by using numerical procedures, in order to guarantee the absence of singularities and collisions between links during the motion of the manipulator.…”

“…In this configuration the axes of base and top joints are aligned as u 1 = −v 3 , u 2 = −v 1 , u 3 = −v 2 and the SPM top mobile and base platforms are parallel to each other. The angles in θ are set from the vertical plane generated by the z axis and vectors u i , to the plane of the corresponding proximal links in the servomotor counterclockwise direction, as shown in [18].…”

Numerical Optimal Control of a Spherical Parallel Manipulator Based on Unique Kinematic Solutions

“…Assuming that the same home SPM assembly and coordinate system are considered for obtaining unique solutions to the manipulator kinematics, vector θ can be found knowing vectors v i , i = 1, 2, 3, corresponding to the current orientation of the SPM top mobile platform, by determining unique inverse kinematic solutions, as proposed by the authors in [41].…”

“…Experimental demonstration of the proposed framework using a 3D printed prototype of the Agile Wrist SPM with three servomotors is given in Section VI, which also includes a discussion of the results. The first phase of the framework proposed in this paper is a development of the authors' preliminary work [41], that also reported an approach for obtaining a unique inverse kinematic solution, a graphical verification method using SolidWorks CAD software and numerical examples considering a specific Agile Wrist SPM.…”