Improving the Pose Accuracy of Planar Parallel Robots using Mechanisms of Variable Geometry

摘要

In this paper, the kinematically redundant 3(P)RRR and 3(P)RPR mechanisms were presented. In each case, an additional prismatic actuator was applied to the structure allowing one base joint to move linearly. After a description of some fundamentals of the proposed PKM, the effect of the additional DOF on the moving platform pose accuracy was clarified. An optimization of the redundant actuator position in a discrete manner was introduced. It is based on a minimization of a criterion that the authors denoted the gain (xh ) of the maximal homogenized pose error xh . Using several exemplarily chosen trajectories a significant improvement in terms of accuracy of the proposed redundant mechanisms in combination with the developed optimization procedure was demonstrated. It could be seen that the suggested index (xh ) leads to more appropriate switching patterns than the well known condition number of the Jacobian. Additional simulations demonstrated the marginal influence of the redundant actuator joint error on the moving platform pose error x. Furthermore, a comparative study on the usable workspaces, i.e. the singularity-free part of the total workspace providing a certain desired performance, of the mentioned mechanisms and their non-redundant counterparts was performed. The results demonstrate a significant increase of the useable workspace of all considered EE orientations thanks to the applied additional prismatic actuator. To further increase the overall and the operational workspace, future work will deal with the design optimization of the prismatic actuator, e.g. its orientation with respect to the x-axis of the inertial coordinate frame as well as its stroke ('length'). In addition, the simulation will be extended to PKM with higher DOF and an experimental validation of the obtained numerical results will be performed.