A Screw Theory-Based Approach for Conservative Stiffness Mapping of 3-PRS Parallel Mechanism

This study presents a hierarchical semi-analytical approach for conservative stiffness modeling of the 3-PRS parallel mechanism based on the screw theory. Firstly, considering all the elastic links and joints, the compact explicit stiffness expression is derived based on the tensor transformation between local compliance matrices and global compliance. Then, the conservative stiffness mapping is formulated by taking the change of geometry of the mechanism due to the external forces into account. Finally, the results obtained from the analysis of a type of Z3 head show that the discrepancy between the proposed model and the Finite Element Analysis (FEA) model is lower than 8.21%, demonstrating the proposed model’s accuracy and effectiveness. The proposed model is hugely efficient for predicting the distributions of stiffness performances within the entire workspace and guiding the optimal functional design at the initial conceptual design stage.