Equations of Motion for a Mechanism with Rigid Links

Abstract

Until now, it was presumed that the motion law of a mechanism is known: it was assumed that the law is the program law necessary for the execution of a working proccess. In a real machine the actual motion differs from the program motion. This difference is primarily related to the properties of the engine, setting the machine in motion and generating driving forces applied to input links. The output velocity of the engine depends on the magnitude of the generalized driving force, and this must be taken into account when designing a machine assembly. It is necessary to integrate the system of differential equations of the mechanical system together with the engine characteristic. Usually, differential equations of motion for a mechanism are in the form of Lagrange’s equations of the second kind.