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Session 1620

Simulation and Animation of Kinematic and Dynamic Machinery Systems with MATLAB Cole J. Brooking, Donald A. Smith University of Washington / University of Wyoming

Abstract This paper describes the application of MATLAB1 to the problem of determining the motions and forces in kinematic (prescribed motion) and dynamic (prescribed driving force) machinery systems and the animation of the system motions. Depending on the specific information which is required, the machinery system motions are determined from the kinematic loop equations utilizing velocity or acceleration constraints. This treats the motion problem as an ordinary differential equations, initial value problem. For kinematic machinery systems, the reaction force problem is uncoupled from the motion problem. For dynamic machinery systems, the motion and reaction force problems are directly coupled. MATLAB has proven to be a very effective tool for both defining these problems in a mathematical model and for the solution of that model.

In addition to the numerical capabilities of MATLAB, the graphics utilities, and in particular the enhanced handle graphics of MATLAB 5, provide a means of displaying the motions of these machinery systems in the form of a short animation. This animation is very effective in helping the contemporary, visually oriented, student understand the motions associated with machinery systems.

Introduction Earlier work 2,3 focused on representing kinematic and dynamic machinery system models as a set of coupled nonlinear ordinary differential equations, and, for specific kinematic systems, the animation of the motion of the system 4. More recently, several faculty at the U.S. Naval Academy reported the use of MATLAB graphics capabilities to animate aspects of their systems engineering courses 5. This latter work was the inspiration to extend previous efforts with kinematic and dynamic machinery systems by incorporating the numerical integration of the system differential equations with an animation capability, the major topic of this paper.

The System Model In order to minimize detail and focus on the animation aspect of the present work a velocity based kinematic simulation of a four bar linkage will be considered. The kinematic skeleton of a typical mechanism is shown in Fig. 1.

This figure is what appears on the monitor for one of the devices simulated and animated with MATLAB. The mechanism is represented mathematically by a set of vectors which form a closed loop. Vector R1 goes from the fixed pivot of the output link on the right to the fixed pivot of the input crankshaft on the left. Vector R2 goes from the fixed pivot of the crankshaft to the crank-coupler connection. Vector R3 represents the coupler and vector R4 represents the follower, both of these latter vectors following a generally clockwise loop direction. The position constraint equation is then

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Smith, D. A., & Brooking, C. J. (1998, June), Simulation And Animation Of Kinematic And Dynamic Machinery Systems With Matlab Paper presented at 1998 Annual Conference, Seattle, Washington. 10.18260/1-2--7406