A regularized approach for frictional impact dynamics of flexible multi-link manipulator arms considering the dynamic stiffening effect

The present study offers a regularized approach for multi-link flexible manipulator arms with frictional impacts. The complex risks of global dynamics simulation, which involve nonlinear frictional impact, stick-slip, and foreshortening deformation, as well as multi-scale numerical problems, were implemented. The system is described as an assembly of flexible links connected by rotary joints. The stretching, bending, and the torsional deformations of the flexible links were considered in addition to the flexibility and mass of the joint. The introduction of a contact force potential energy approach transformed the non-differentiable functions of the normal and tangential frictions into differentiable ones, thereby generating Lagrange equations for the general recursive formulation of the systems. A numerical simulation for the double pendulum and spatial manipulator arms collision with targets was generated, thereby allowing the calculation of the frequent switching between the stick/sliding and forward/backward sliding. Several normal contact and friction models were adopted, and their corresponding results were analyzed. The generated ordinary differential equations of the proposed smoothed algorithm were solved using explicit solvers to verify any improvements in the global computational efficiency of the frictional collision dynamics for the flexible manipulator arms.