Theory of Machines and Mechanisms, Third Edition

Chapter 15: Dynamic Force Analysis (Planar)

15.1 INTRODUCTION

In the previous chapter we studied the forces in machine systems in which all forces on the bodies were in balance, and therefore the systems were in either static or dynamic equilibrium. However, in real machines this is seldom, if ever, the case except when the machine is stopped. We learned in Chapter 4 that even though the input crank of a machine may be driven at constant speed, this does not mean that all points of the input crank have constant velocity vectors or even that other members of the machine will operate at constant speeds; there will be accelerations and therefore machines with moving parts having mass will not be in equilibrium.

Of course, techniques for static-force analysis are important, not only because stationary structures must be designed to withstand their imposed loads, but also because they introduce concepts and approaches that can be built upon and extended to nonequilibrium situations. That provides the purpose of this and the following chapter: to learn how much acceleration will result from a system of unbalanced forces and also to learn how these dynamic forces can be assessed for systems that are not in equilibrium.

15.2 CENTROID AND CENTER OF MASS

We recall from Section 14.2 that Newton's laws set forth the relationships between the net unbalanced force on a particle, its mass, and its acceleration. For that chapter, because we were only studying systems in equilibrium, we made use of the relationship for entire rigid bodies,...

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