A semi-analytical approach for stiffness modeling of PKM by considering compliance of machine frame with complex geometry

Stiffness modeling is one of the most significant issues in the design of parallel kinematic machine （PKM）. This paper presents a semi-analytical approach that enables the stiffness of PKM with complex machine frame geometry to be estimated effectively. This approach can be implemented by three steps： （i） decomposition of the entire system into two sub-systems associated with the parallel mechanism and the machine frame respectively; （ii） stiffness modeling of each sub-system using the analytical approach and the finite element analysis; and （iii） generation of the stiffness model of the entire system by means of linear superposition. In the modeling process of each sub-system, the virtual work principle and overall deflection Jacobian are employed with special attention to the bending rigidity of the constrained passive limb and the interface stiffness of the machine frame. The stiffness distribution of a 5-DOF hybrid robot named TriVariant-B is investigated as an example to illustrate the effectiveness of this approach. The contributions of component rigidities to that of the system are evaluated using global indices. It shows that the results achieved by this approach have a good match to those obtained through finite element analysis and experiments.