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Rigid Body Dynamics in the Mechanical Engineering Laboratory

Abstract

This paper describes a relatively simple method in which planar rigid body motion can be measured and analyzed in the context of an upper division mechanical engineering laboratory course. The overall intention of this work is to help facilitate upper division level laboratory projects in dynamics. Such projects are intended to provide students with the opportunity to i) apply and reinforce their knowledge of dynamics, ii) learn and practice modern experimental methods used to make and assess motion measurements, and iii) if possible, compare theoretical and measured results.

The instrumentation involves the use of two inexpensive sensors – a dual axis accelerometer and a rate gyro – and a data acquisition system (such as LABVIEW). The accelerometer and rate gyro are fixed to the rigid body object. The rate gyro measures the planar angular velocity, which can be integrated with respect to time to yield angular orientation of the rigid body. With the use of this measured angular orientation, the accelerations measured by the accelerometer (which are measured in two directions fixed to the rigid body) can be resolved into directions fixed in space, and consequently integrated to yield velocity and position coordinates of the point on the rigid body where the accelerometer is attached.

These experiments also highlight the importance of error estimation. Errors in acceleration and angular velocity measurement lead to errors in angular orientation and translational velocity and position components that generally grow with time (due to the time integration). An estimation of acceleration and angular velocity measurement errors can be made by calibrating the accelerometer and rate gyro using simple homemade devices.

After describing how these experiments can be set up and performed in general, this paper will describe a specific experiment done in the author’s junior mechanical engineering laboratory course. The rigid body object under study is a remote controlled car. The technique described above is used to find the position, velocity, orientation, and angular velocity of the car as a function of time. Results of the measurements and data analysis are compared with observations of the car’s motion viewed by a video camera. An examination of this laboratory experience, with a discussion of intended learning objectives, an assessment of whether they are being achieved (based on surveys), and suggestions for improvement, will be included.

The paper will conclude with some suggestions for additional rigid body motion experiments using this general method of motion measurement.

I. Introduction

Engineering educators have identified several learning objectives to be achieved in engineering laboratory courses, including (but not limited to) the development of the following abilities (quoted from 1):

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Nordenholz, T. (2008, June), Rigid Body Dynamics In The Mechanical Engineering Laboratory Paper presented at 2008 Annual Conference & Exposition, Pittsburgh, Pennsylvania. 10.18260/1-2--3282