Pick and place trajectory planning of planar 3-RRR parallel manipulator in the presence of joint clearance

In this paper, the pick and place trajectory planning of a planar 3-RRR parallel manipulator is studied in the presence of joint clearance, which is one of the main sources of error in the positioning accuracy. Joint clearance can be modeled as a massless virtual link, with its direction determined from dynamic analysis. A 3-4-5 interpolating polynomial is used to plan the trajectories for the manipulator in the vertical and horizontal planes, in the presence of clearances. We compare the trajectories with those in the ideal cases, i.e., without clearances at the joints, and demonstrate that one can easily compensate for the errors in the trajectories by appropriate changes of the inputs. A similar method works for the compensation of the errors due to clearances at the joints, in trajectory planning of any parallel manipulator with any running speeds and payloads.