**
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.