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Session 1668

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

R. R. Reynolds and I. C. Jong University of Arkansas

Abstract

The software package MATHEMATICA provides a highly interactive computing environment in which scientific and engineering problems can be solved and the solutions displayed in a variety of ways. As such, it provides an efficient and concise means of solving and animating the motion of mechanisms. As part of an overall effort to provide multimedia tools for modern teaching, this paper uses some basic commands in the MATHEMATICA environment for animating a specific mechanism. The paper provides a complete program listing. A sequence of sample animation frames is included to illustrate the motion of a four-bar linkage and the plotting of the space centrode of its coupler.

Introduction

The study of the dynamics of mechanisms typically requires the student to visualize how a series of static configurations evolves in time. This requirement involves an intuitive leap that can be problematic for some people. This potential problem can be minimized or avoided by using an animation of the mechanism as a teaching tool. Unfortunately, animations have typically been difficult to create. The prevalence of commercial analysis software makes the creation and display of graphical aids much simpler now than it has been in the past. MATHEMATICA1 allows users to create programs using a high-level programming language and to manipulate and display data easily. This software provides an extensive library of subroutines, which can be used to solve problems with a minimum of programming effort. These subroutines include numerical integration, root-finding, and curve fitting. It is an excellent package for seamlessly integrating numerical computations, data analysis, and presentation. The graphics capabilities of MATHEMATICA include two and three dimensional curve and surface graphing, density plots, and the ability to create a wide range of primitive graphics entities (e.g., lines, circles, arcs, etc.). In addition to these capabilities, the program interface permits the user to animate any sequence of graphics entities. Thus, by simply generating a series of images that depict the motion of the linkage mechanism and its velocity center over a range of positions, we may animate the motion of the linkage as if it were moving in real-time by issuing the animate option. Recently Jong and Onggowijaya2 used QuickBASIC to animate the generation of the space centrode of a coupler as a complement to WORKING MODEL. Adams and Jong3 also animated the space centrode using the MATLAB software. For the purpose of comparison, the generation of the same space centrode is solved and animated here using the MATHEMATICA program. A selection of sample animation frames is included in Appendix A, and a listing of the complete yet brief MATHEMATICA program used to create this animation is given in Appendix B, where various helpful comments are inserted as comments between the marks (* and *).

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Reynolds, R. R., & Jong, I. (1997, June), Using Mathematica To Animate The Generation Of A Space Centrode In Kinematics Paper presented at 1997 Annual Conference, Milwaukee, Wisconsin. 10.18260/1-2--6877