Error Modeling of a Parallel Wedge Precision Positioning Stage

Abstract

The parallel wedge precision positioning stage (PW-PPS) presents a novel configuration of a parallel mechanism for precision positioning applications. Based on its specific parallel configuration, the corresponding inverse and forward kinematic models were developed and used to formulate the volumetric error model of the mechanism. The error model that considers the influence of manufacturing errors is built in two steps. In the first, the structural parameter-induced errors associated with the PW-PPS's structural parameters and input variables were considered, while in the second, the joint clearance-induced errors produced by joint clearances were taken into account. The structural parameter-induced errors were modeled based on complete differential-coefficient theory, while the joint clearance-induced errors due to joint clearances were modeled based on the virtual work and deterministic method. In the latter case, the kinetostatic model and joint error contact modes were analyzed to build a joint clearance-induced error model. The relationship between the different error sources and the output pose error of the mechanism's moving platform was obtained. Finally, considering practical values for the mechanism's parameters and errors, the error distribution in the PW-PPS's workspace was evaluated to determine the distributive rules of the various error components.