Kinetostatic Modeling and Workspace Analysis of Redundant Actuated n-4R Compliant Parallel Pointing Mechanism

The workspace of the compliant parallel mechanism (CPM) is generally limited due to the small deformation range of flexible hinges, which are usually at the micro/nano scale. This paper takes the 2-DOFs <i>n</i>-4R compliant parallel pointing mechanism (<i>n</i>-4R CPPM) as the object and optimizes the workspace performance of the mechanism through redundant actuation, aiming to maximize the workspace. First, the kinetostatic model and the flexible hinge displacement model of the redundant actuated <i>n</i>-4R CPPM are established, successively. The former model reveals the relationships between the output displacements and the input forces/displacements, while the latter relates the flexible hinge deformation and the input forces/displacements. Second, a space pointing trajectory is chosen to validate the accuracy of the kinetostatic model of the redundant actuated 3-4R CPPM through finite element (FE) simulation. The results show that the relative error between the analytical and the FE results does not exceed 2.1%, and the high consistency indicates the accuracy of the kinetostatic model. Finally, the workspace performance of the 3-4R and 4-4R CPPMs is successively optimized through redundant actuation. The results indicate that, compared with the non-redundant actuation case, the workspace can be effectively enlarged and become more symmetric by means of the redundant actuation. The maximum achievable pitch angle <i>ψ_a</i> and the <i>y</i>-direction motion range of the mobile platform both increase by 100%. Moreover, it is shown that the workspace in the non-redundant actuated case is a subset of the workspace in the redundant actuated case, and the position-workspace shape changes from planar to 3-D.