Generalized Equations of Motion for the Dynamic Analysis of Elastic Mechanism Systems

[+] Author and Article Information
D. A. Turcic

Department of Mechanical Engineering and Mechanics, Drexel University, Philadelphia, PA 19104

Ashok Midha

School of Mechanical Engineering, Purdue University, West Lafayette, Ind. 47907

J. Dyn. Sys., Meas., Control 106(4), 243-248 (Dec 01, 1984) (6 pages) doi:10.1115/1.3140680 History: Received May 17, 1983; Online July 21, 2009


Until recently, vibration effects have generally been neglected in the design of high-speed machines and mechanisms. This has been primarily due to the complexity of the mathematical analysis of mechanisms with elastic links. With the advent of high-speed computers and structural dynamics techniques, such as finite element analysis, this is no longer regarded as such a formidable task. To date, with few exceptions, the analysis of elastic mechanism systems have been limited to a single type of mechanism (i.e., a four-bar or slider-crank) modeled with a small number of simple finite elements (usually beam elements). This paper develops the generalized equations of motion for elastic mechanism systems by utilizing finite element theory. The derivation and final form of the equations of motion provide the capability to model a general two- or three-dimensional complex elastic mechanism, to include the nonlinear rigid-body and elastic motion coupling terms in a general representation, and to allow any finite element type to be utilized in the model. A discussion of a solution method, applications, as well as an experimental investigation of an elastic four-bar mechanism will be presented in subsequent publications.

Copyright © 1984 by ASME
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