Jacobian-based singularity analysis of a 3-CRRR spatial parallel robot

This paper discusses the singularity analysis of a spatial parallel robot. The robot is a 3-CRRR three-degree of freedom mechanism proposed to improve the dynamic stability of robotic manipulation tasks. First, kinematic equations of the robot are analyzed to extract Jacobian matrices of the mechanism. For exploring singular points of the workspace, rank deficiency of the Jacobian matrices is investigated through an interval-based numerical solution. To determine the search space of the numerical solution, the workspace boundaries are achieved using SolidWorks software. Then, a cube is considered which contains the whole workspace of the mechanism. In this search space, a computer algorithm is written to find the points and neighborhoods around which singularities happened. To increase the neighborhood accuracy, an error function is defined. In the next step of the interval-based algorithm, this function is optimized after reaching a predetermined threshold. The second step is accomplished using Genetic Algorithm applying multiobjective optimization in MATLAB software. The results and their accuracy show that there is one singularity neighborhood around the boundary of the robot workspace as well as another exact singular point which is out of the workspace. These findings can be used in the nonsingular planning of the mechanism while manipulating objects.