Dynamics and Synthesis of Kinematic Chains with Impact and Clearance

Abstract

The dynamics and synthesis of open and closed kinematic chains with frictional impact and joint clearance is studied. The impact between rigid bodies with friction is investigated. A new model of impact with friction is presented. The coefficient of rolling friction is defined and the moment of rolling friction is introduced to the impact equations. The influence of the moment of rolling friction and the geometrical characteristics of the links on the energy dissipated by friction during the impact is analyzed. The effect of prismatic joint inertia on the dynamics of kinematic chains is analyzed. The effect of the prismatic joint inertia on the position of the application point of the joint contact forces is investigated. The influence of the joint inertia on the dynamic response of a spatial robot arm with feedback control is analyzed. Also, the influence of the joint inertia on the dynamic parameters of a planar mechanism is exemplified using inverse dynamics. Furthermore, a planar rigid-link mechanism with rotating prismatic joint and clearance is modeled. The influence of the clearance gap size, crank speed, friction, and impact parameters on the dynamics of the system is analyzed. Nonlinear dynamics tools are applied to analyze the data captured from the connecting rod of the mechanism. Finally, a new structural synthesis of spatial mechanisms is developed based on the system group classification. Spatial system groups of different families with one, two, and three independent contours are presented. The advantage of the analysis of spatial mechanisms based on the system group classification lies in its simplicity. The solution of mechanisms can be obtained by composing the partial solutions of system groups. For the previous models of impact with friction, the effect of the rolling friction was neglected. In this dissertation, the moment of rolling friction is defined and introduced to the impact equations. Prismatic joint inertia must be included for modeling high-speed machine tools, manipulators, and robots. This problem is important, because in some cases the moment of inertia of the prismatic joints is comparable to the moment of inertia of the links and may significantly influence the dynamics of the system at high speeds. Periodic motion is observed for the mechanism with rotating prismatic joint and no clearance. The response of the mechanism with joint clearance is chaotic at relatively high crank speeds. Also, a general method is presented in order to determine all the configurations of complex spatial system groups and to automate the process.