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Teaching Multi-Body Dynamics in an Undergraduate Curriculum: An Intuitive and Explicit Formalism Based on Parasitic Elements Abstract

Typical undergraduate mechanical engineering curricula in North America do not include a course in multi-body dynamics. A rigid body dynamics course covering single-body kinetics is usually completed in early semesters, and often the material is not revisited before graduation. Students typically graduate without a sense of how to simulate the forward dynamics of even simple multi-body systems such as slider-crank or four-bar mechanisms. Engineers should have some increased depth of understanding in this area even if they will exclusively use specialized commercial software after graduation.

A physically intuitive, explicit multi-body formalism is presented that will allow senior students to review and refresh their knowledge of dynamics, understand how to handle constraint forces, and write their own forward dynamics simulation code using software such as MATLAB. The formalism is based on the use of parasitic (stiff) springs to allow a small but finite relaxation of ideal joint constraints. Stiff springs break dependencies among the generalized coordinates of connected bodies and thereby allow derivation of a set of explicit first-order ordinary differential equations. Joint forces are found from parasitic spring deflections. Moreover, a consistent set of initial conditions can be generated without resorting to nonlinear equation solution.

The formulation and its advantages are demonstrated using a double pendulum and a slider-crank mechanism case study. The formulation gives the student a practical tool for dynamic analysis of mechanisms and prepares him or her for more advanced study of topics such as Lagrange’s equations and Lagrange multipliers.

Introduction

The absence of multi-body dynamics in the typical North American mechanical engineering curriculum is a gap that has received surprisingly little attention. The typical graduating mechanical engineer in North America cannot write a coherent set of governing dynamic equations for a slider-crank or four-bar mechanism, and then explain how these equations might be solved. These are simple multi-body systems and fundamental building blocks of mechanical systems, and contain multiple rigid bodies. In the rigid body dynamics course that is usually completed in early semesters, single bodies are the focus. A sampling of five undergraduate curricula in North America shows a pattern of only introductory exposure to kinematics and kinetics, and only early on in the program1,2,3,4,5. Typical dynamics-related course offerings include: rigid body dynamics (kinematics and kinetics of particles and single bodies) theory of mechanisms and machines (graphical and analytical methods for kinematics of planar mechanisms; instantaneous determination of static and dynamic loads resulting from prescribed motion) vibrations (free-body diagrams and equations of motion for simple mass-spring-damper systems)

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Rideout, G. (2008, June), Teaching Multibody Dynamics In An Undergraduate Curriculum – An Intuitive And Explicit Formalism Based On Parasitic Elements Paper presented at 2008 Annual Conference & Exposition, Pittsburgh, Pennsylvania. 10.18260/1-2--3115