Workspace of 3-RRR parallel robot using the combination of interval analysis and refinement methods by considering the limitation of active joints movement

In this paper, two new algorithms are presented for calculating the workspace of parallel robot considering the limitation of active joints movement by combining interval analysis with two refinement methods. In proposed methods, the kinematic expressions of the chains are calculated based on the joint coordinates and geometrical constraints governing the kinematic chains of the parallel robot. In the following, two methods are presented for calculating the workspace of parallel robot by combining the concepts of interval analysis with two refinement algorithms, namely mean value form and slope form. The two presented algorithms and the interval analysis method without refinement operation are implemented on the 3-RRR planar parallel robot and the constant-orientation workspaces are obtained for different limitation of active joints movement. For the sake of comparison, the constant-orientation workspace of 3-RRR parallel robot is also obtained using the geometric method, and it is shown that if refinement is used in the interval analysis, the workspace of the parallel robot is entirely consistent with the results of the geometric method.