Stiffness Modeling of Parallel Robots (en Inglés) - Alexandr Klimchik

The book focuses on the stiffness modeling of serial and parallel manipulators It presents fundamentals and enhancements for Virtual Joint Modelling (VJM), Matrix Structural Analysis (MSA) and Finite Element Analysis (FEA). The described techniques consider complex kinematics with numerous passive joints, different types of loadings, including essential loadings leading to critical changes in the manipulator configurations, linear and non-linear stiffness analysis, conventional and non-linear compliance error compensation and stiffness parameters estimation from virtual experiments.    

Presented enhancement for the VJM integrates in the stiffness analysis external force/torque applied to the end-point, internal preloading in the joints, and auxiliary forces/torques applied to intermediate points. The proposed technique includes computing an equilibrium configuration corresponding to the external/internal loading and allows obtaining the full-scale non-linear force-deflection relation for any given workspace point. This enables the designer to evaluate critical forces that may provoke non-linear behaviours of the manipulators, such as sudden failure due to elastic instability (buckling). The presented enhancement to the MSA allows users to carry out stiffness analysis for serial underactuated structures and over-constrained ones with multiple closed loops.   

To increase the model accuracy of the VJM and MSA techniques a dedicated FEA-based stiffness model parameters identification technique is introduced in the book. It is based on the virtual experiments in the CAD/CAE environment and allows the VJM and MSA to achieve accuracy comparable with FEA, but it essentially reduces the computational effort, eliminating repetitive re-meshing through the workspace. All considered stiffness modelling techniques, kinematic particularities and loading conditions are illustrated with practical examples and related analysis.