Computational method for dynamic analysis of constrained mechanical systems using partial velocity matrix transformation

Abstract

A computational method for the dynamic analysis of a constrained mechanical system is presented in this paper. The partial velocity matrix, which is the null space of the Jacobian of the constraint equations, is used as the key ingredient for the derivation of reduced equations of motion. The acceleration constraint equations are solved simultaneously with the equations of motion. Thus, the total number of equations to be integrated is equivalent to that of the pseudo generalized coordinates, which denote all the variables employed to describe the configuration of the system of concern. Two well-known conventional methods are briefly introduced and compared with the present method. Three numerical examples are solved to demonstrate the solution accuracy, the computational efficiency, and the numerical stability of the present method.

W-1-1-1 Multibody Dynamics Research in Korea

“…[n reLative coordinate fbrmulation [4], joint coordinates [5,6] are mainly used lnstead of Cartesian coordinates. Kane's method and partiat velocity matrix in constrained multibody systems are presented in referen ¢ es [7][8][9][10].…”

F-6-4-2 Linearization and Vibration Analysis of Constrained Multibody Systems with Constant Generalized Speeds

“…Fuehrer and Wallrapp [1l presented a linearization method based on matrix computation, but they did not suggest a general multibody formulation. A linearization method was introduced by Sohoni and Whitesell [2] [5] and pania] velocity matrix [6]. In addition, they suggested a method ef deterrnining independent coordinates, The above methods, however, cannot be applied to the system driven by constant genera]izedspeeds.…”