A Generic Numerical Method for Mechanical System Kinematics and Dynamics Modeling

Abstract

The theory and basic numerical procedures of unified approach for kinematic analysis and optimization, as well as for force analysis and modeling of the nonlinear dynamics of spatial poly-contour mechanical systems are presented. Matrix transformation methods and Newton-Euler equations are used for deriving the kinematic and dynamic equations of motion. The resulting nonlinear kinematic model is common for the analysis and synthesis problems. Nonlinear programming techniques are used for solution of the kinematic equations. A new method of treating the nonlinear explicit form dynamic equations is presented. Generalized forces, reactions, internal forces, etc., obeying principles of proportionality and superposition, are derived as a function of generalized velocities and accelerations. The nonlinear model is focused on solution of special problems, including, for example, friction forces in the pairs. On the basis of the discretized nonlinear dynamic equations, a new numerical method for mechanical system motion control and optimization is suggested.