A uniform procedure is described for establishing the dynamic equation of motion for machines with single or multiple degrees of freedom. The procedure, which utilizes the independent kinematic loops of the machine, is readily programmed for a digital computer. The basic program is largely independent of the specific machine being analyzed and is capable of treating input forces, internal springs and dampers, all of which may depend nonlinearly upon position, velocity, or time. As an example, the dynamic performance of a Stirling cycle engine is analyzed without recourse to simplifying approximations usually made in engine analysis (i.e., constant crank speed, use of approximate “rotating” and “reciprocating” weights, neglect of higher harmonics in piston motion). It is shown that the method not only predicts transient behavior, but is capable of predicting steady (long-term) behavior without loss of accuracy, or excessive computer costs. The method described satisfies the major criteria of generality, accuracy, and economy, required of a truly practical design tool.
Dynamic performance estimation: A design tool for mechatronic scanners
