On the position analysis of a new spherical parallel robot with orientation applications

In this paper, we propose a new spherical parallel robot for celestial orientation, and rehabilitation applications (TV satellite dish, tracking systems, solar panels, cameras, telescopes, table of the machine tools, ankle, shoulder, wrist and etc.). The proposed robot can completely rotate about an axis. After describing the robot and its inverse position analysis, using the genetic algorithm, the dimensional optimization to maximize the workspace of the robot is performed. The workspace analysis shows that the proposed robot has a relatively large workspace. Also, singularity analysis represents that the manipulator is a singularity-free workspace. It is a great advantage of the proposed robot. Next, an optimal approach is proposed for solving the direct position problem of the robot. According to the geometry of the robot, two coupled trigonometric equations are obtained through using a special form of Rodrigues' rotation formula. Next, the two coupled equations are transformed to a 8-degrees polynomial using the Sylvester's Dialytic elimination method. Finally, a numerical example for the robot with an asymmetric structure is given with eight real solutions. Therefore, the polynomial being minimal and the proposed approach is optimal. This greatly decreases computational time, which is necessary for dynamics, control and simulation.