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Session 2668

Using MATLAB to Animate the Generation of a Space Centrode in Kinematics

Glynn P. Adams, Ing-Chang Jong University of Arkansas

Abstract

Computer animations are valuable tools for demonstrating and teaching dynamics of mech- anisms. Several software packages are commercially available t o aid in this effort. The work presented in this paper is intended to complement, the animation capabilities of existing soft- ware by using the MATLAB programming language to animate a specific four-bar linkage and display the space centrode of the coupler during the animation. The linkage presented here is a crank-rocker mechanism, which can be assembled in a colinear configuration. This linkage was selected because of the interesting nature of the coupler link space centrode and the motion of the output, link. The position solution for the linkage is obtained with a. Newton-Ra.phson method and the use of kinematic coefficients. The details of this approach are presented as is the specific MATLAB code required to produce the position solution and the animation.

Introduction

One of the main impediments to learning dynamics of mechanisms is the visualization of the mechanism motion. Several commercially available software p a c k a g e s such as Working Model and Analytix allow users t o create mechanisms with various constraints and produce animations of the resulting motion. The packages provide a valuable asset for helping stu- dents to realize the kinematics associated with a wide variety of mechanisms. However, computer programs written for specific mechanisms and specific purposes can serve as ex- cellent complements to these software packages The animation of a specific mechanism involves both computer programming and numerical methods. The objective of this paper is to share the programming strategy with instructors who may contemplate animating a linkage and the generation of a space centrode using MATLAB. Consider the four-bar linkage in Fig. 1, which can be assembled in a collinear configuration. For example, we can choose rl = 0.3 m, r2 = 0.5 III, r:< = 1.0 III, and r4 = 1.2 m. The crank AB, coupler BD, and output DE all become collinear along the ground link when (?I = r. Animation of this mechanism and generation of the space centrode of the coupler are particularly interesting for the following reasons: l The crank must make two revolutions to completely define the motion of the output.

l The space centrode of the coupler contains two asymptotes.

The analytical study of the space centrode and its asymptotes was presented by Jong, et nP.

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Adams, G. P., & Jong, I. (1997, June), Using Matlab To Animate The Generation Of A Space Centrode In Kinematics Paper presented at 1997 Annual Conference, Milwaukee, Wisconsin. 10.18260/1-2--6878