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The book takes the subject from an introductory level through advanced topics needed to properly design, model, analyze, specify, and manufacture cam-follower systems.
Cam Design and Manufacturing Handbook
(Dynamics of Cam Systems)

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   by Robert L. Norton
Published By:
Industrial Press Inc.
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DYNAMICS OF CAM SYSTEMS—

MODELING FUNDAMENTALS

 

8.0 INTRODUCTION

This chapter presents a review of the fundamentals of dynamic modeling in order to establish a base of information on which to develop the tools for the dynamic analysis of cam-follower systems in succeeding chapters.

 

8.1 NEWTON’S LAWS OF MOTION

Dynamic force analysis involves the application of Newton ’s three laws of motion which are:

 

1 A body at rest tends to remain at rest and a body in motion will tend to maintain its velocity unless acted upon by an external force.

 

2 The time rate of change of momentum of a body is equal to the magnitude of the applied force and acts in the direction of the force.

 

3 For every action force, there is an equal and opposite reaction force.

 

The second law is expressed in terms of rate of change of momentum , P = m v , where m is mass and v is velocity. Mass m is assumed to be constant in this analysis. The time rate of change of m v is m a , where a is the acceleration of the mass center.

 

F = m a (8.1)

 

F is the resultant of all forces on the system acting at the mass center.

 

We can differentiate between two subclasses of dynamics problems depending upon which quantities are known and which are to be found. The “ forward dynamics problem ” is the one in which we know everything about the external loads (forces and/or torques) being exerted on the system, and we wish to determine the accelerations, velocities, and displacements that result from the application of those forces and torques. This subclass is typical of problems such as determining the acceleration of a block sliding down a plane, acted upon by gravity. Given F and m , solve for a.

 

The second subclass of dynamics problem, called the “ inverse dynamics problem ,” is one in which we know the (desired) accelerations, velocities, and displacements to be imposed upon our system and wish to solve for the magnitudes and directions of the forces and torques that are necessary to provide the desired motions and which result from them. This inverse dynamics case is sometimes also called kinetostatics . Given a and m , solve for F . Whichever subclass of problem is addressed, it is important to realize that they are both dynamics problems. Each merely solves F = m a for a different variable. To do so we should first review some fundamental geometric principles and mass properties that are needed for the calculations.

 

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