June 16, 2002
June 16, 2002
June 19, 2002
7.1182.1 - 7.1182.11
The Role of the Kinetic Diagram in the Teaching of Introductory Rigid-Body Dynamics – Past, Present, and Future Glenn Kraige Department of Engineering Science and Mechanics Virginia Polytechnic Institute and State University Blacksburg, VA 24061 USA
The introductory engineering dynamics course is widely regarded as one of the most difficult courses that the undergraduate engineering student takes. Further, the rigid-body area of this dynamics course is considered much more difficult than the particle area. One reason for the latter statement is that we have not yet progressed to the best steady-state teaching strategy in the area of rigid-body kinetics. The purpose of this paper is to review the history and current state of affairs in this narrow area and then to advocate a better strategy. Recommendations are made in regard to both diagrams and corresponding equations of motion.
Dynamics did not become a significant issue until the beginning of the machine age. Mechanicists were accustomed to a zero on the right-hand side of the governing equations in statics, so the first direction of particle dynamics was to include a -ma term on the left side of dynamics equations so that the right-hand zero could be retained. Although sometimes referred to as D’Alembert’s Principle, this technique should be called dynamic equilibrium (D’Alembert’s Principle is a virtual-work principle). This -ma term has been called an inertia force, an effective force, a reversed effective force, etc. The technical community eventually took the position that dynamics should not be treated as a special case of statics, but rather the other way around. In other words, we soon placed the ma term on the right side of the equations of motion and included only real (contact and body) forces on the left side. Some textbooks went through a period in which a kinetic diagram (sometimes called a resultant-force diagram) was drawn (in addition to the free-body diagram (FBD)). This diagram merely showed an ma vector (or its components). The usual arrangement was to draw the FBD and then write an equal sign with the kinetic diagram (KD) to the right. Such practice seems to have been largely terminated for particle dynamics.
It is the author’s position that, with the conventional teaching of particle dynamics as outlined above, we are in the steady-state, terminal teaching configuration. We note that the teaching of particle statics and particle dynamics is now of identical format. There is the same type of FBD showing only real forces, followed by application of governing equations. The only difference is that, for particle dynamics, the right-hand sides of the governing equations are not zero.
Proceedings of the 2002 American Society for Engineering Education Annual Conference & Exposition Copyright © 2002, American Society for Engineering Education
Kraige, L. G. (2002, June), The Role Of The Kinetic Diagram In The Teaching Of Introductory Rigid Body Dynamics Past, Present, And Future Paper presented at 2002 Annual Conference, Montreal, Canada. 10.18260/1-2--10358
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