The Mechanical interference-free workspace of the planar parallel robots using geometric approach

In spite of several advantages of parallel robots, they generally have limited workspace. Therefore, it is of paramount importance to obtain the workspace by considering the mechanical interference. In this paper, the mechanical interference in planar parallel mechanisms, including interference between links and, collision between links and obstacles and between end-effector and obstacles, are investigated using geometrical reasoning. For this purpose, a new geometric method is proposed for collision detection in the workspace of planar parallel mechanisms based on the lines segment intersection. In this method, the configurations of the planar parallel robot are obtained in the entire workspace. Then, the interference of links with each other and obstacles, which are respectively modeled by line segment and polygon, are determined. Finally, the collision-free workspace of the parallel robot is obtained for a specified orientation of the moving platform. Moreover, in this paper, an index is presented which can be used for examining the workspace by considering mechanical interference. The foregoing index provides some insight into obtaining a well-conditioned workspace. For the sake of validation, this method is implemented on two planar parallel robots, namely as 3-RRR and 3-PRR, for different working modes. The obtained results reveal that the ratio of the practical workspace to the theoretical workspace is decreased upon increasing the orientation of the end-effector for both clockwise and counterclockwise directions. Furthermore, due to differences in the number of the moving links, the mechanical interference-free workspace of 3-RRR parallel robot is usually more limited than 3-PRR parallel robot.