Optimization of the workspace of a 3R planar parallel manipulator

This paper presents a fast and reliable method to optimize the workspace of a 3R planar parallel manipulator. The ratio between the lengths of the first two links of each limb of a 3R parallel manipulator is changed whereas the other parameters and the outer boundary of the whole manipulator are kept the same during the optimization process. In this method, first, enough number (not necessarily very large) of points is generated in the workspace and then techniques of computational geometry are applied to determine the boundary of the workspace. The modified gift wrapper algorithm is used to determine the boundary. It is shown that, for a given mechanism, increasing the ratio of the length of the second link relative to the length of the first link increases the workspace. However, at certain value, gaps start to appear within the workspace which mean discontinuity in the workspace. Increasing the ratio, the workspace becomes separated regions.