Dynamics of Mechanisms and Machine Systems in Accelerating Reference Frames

Abstract

Matrix equations of motion are derived for a general machine system in an accelerating reference frame. These equations are highly-nonlinear in the displacements of inertial elements and describe the dynamics of large motions. This analysis permits study of dynamic interactions between the moving elements of a machine and the motion of the machine body. The latter may undergo general translation and rotation as a result of internal and external forces. Power-conserving transformations relating inertial, kinematic, and generalized velocities provide a highly formal procedure for kinematic and dynamic analyses and produce explicit equations in generalized variables which are efficient for numerical solution. The theory is applied to study a machine with a four-bar linkage and driveshaft elasticity mounted on a spring-damper suspension. In this example, torsional oscillations in the drive are compared to those obtained with the machine body fixed in inertial space.