Nonsmooth dynamic modeling and simulation of spatial mechanisms with frictional translational clearance joints

This paper presents a nonsmooth dynamic approach of modeling and computation for spatial mechanism including spatial frictional translational joints (SFTJs) with small clearances. In this research, the dynamic formulation is derived in the Lie group setting, which leads to a coordinate-free and compact formulation. In the following, the normal contact interaction between the slider and guide is described by the complementarity relations between the constraint force in the normal direction. The tangent contact interaction in the SFTJ is characterized by the Coulomb's friction law in the type of a set-valued map. Based on the horizontal linear complementarity problem (HLCP), the non-smooth dynamics can be established and calculated by combining the Lemke's algorithm and the RK-MK time integration algorithm. Finally, A spatial crank-slider mechanism with SFTJs is shown as a numerical case. The simulation results demonstrate the correctness and effectiveness of the proposed method which can capture the nonsmooth dynamical behavior of the system.