Dynamics modeling of slipping collision of robot and impact response under different stiffness

In order to ascertain the affect of stiffness on slipping collision of flexible arm, the kinematics model was established by hybrid coordinate method, and flexible deformation was decoupled by using the assumed modes. Contact-impact model was established by using the Hertz impact theory and nonlinear spring-damper theory, collision dynamics of flexible arm was derived through Lagrange equations. The fourth-order Runge-Kutta numerical solution algorithm with variable step-size and precision was designed for solving dynamical equation. Simulation of the impact responses of flexible arm collision under different stiffness were completed, and curves of contact force, joint angle, angle velocity and elastic deformation were given. Based on comparative analysis, with bending stiffness increasing, contact force enlarged and the phase of peak force advanced, the flexible arm joint angle turned smaller, vibration of elastic deformation and angular velocity became lower. Material structural damping had obvious inhibition on the elastic deformation vibration. The model and solving algorithm of this paper are proved effective.