Decoupled elastostatic stiffness modeling of parallel manipulators based on the rigidity principle

Analytical elastostatic stiffness modeling of parallel manipulators (PMs) based on the rigidity principle, screw theory, and strain energy while considering the flexibility of the links, joints, and actuators is proposed. The proposed model can decouple each elastic component's contribution to the mechanism's stiffness performance and is suitable for application to non-overconstrained and overconstrained PMs with sub-closed loop structures. The method is implemented as follows: 1) formulate limb constraint wrenches based on screw theory; 2) let each elastic component be flexible sequentially while the remainder are rigid and calculate the compliance matrix contribution (CMC) and the elastic deflection contribution (EDC) for each elastic component in the mechanism; and 3) obtain the total deflection and overall compliance matrix of the mechanism by summing these CMCs and EDCs. The parallelogram-type parallel manipulator (PTPM) and 3PRRR PM are used as illustrative examples to implement the proposed model and the results show that selective improvement of the stiffness performances of the elastic components can improve the linear/angular stiffness performance of the mechanism most effectively. The proposed model provides an effective approach to improve the linear/angular stiffness performances of mechanisms. (C) 2019 Elsevier Ltd. All rights reserved.