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IX KINEMATICS

Introduction
Kinematics is the branch of dynamics which describes the
motion of bodies without reference to the forces which either cause
the motion or are generated as a result of the motion. Kinematics
treats only the geometric aspects of the motion. Some engineering
applications of kinematics include the design of cams, gears, linkages,
and other machine elements to control or produce certain desired
motions, and the calculation of flight trajectories for aircraft, rockets,
and spacecraft.
The motion of particles (or rigid bodies) can be described by
using coordinates measured from fixed reference axes (absolute-
motion analysis) or by using coordinates measured from moving
reference axes (relative-motion analysis). Both descriptions will be
developed and applied in the articles which follow.

38 Kinematics of Particle

We begin our study of kinematics by first discussing in this
chapter the motions of points or particles. A particle is a body whose
physical dimensions are so small compared with the radius of
curvature of its path that we may treat the motion of the particle as
that of a point. For example, the wingspan of a jet transport flying
between Los Angeles and New York is of no consequence compared
with the radius of curvature of its flight path, and thus the treatment of
the airplane as a particle or point is an acceptable approximation.
We can describe the motion of a particle in a number of ways,
and the choice of the most convenient or appropriate way depends a
great deal on experience and on how the data are given. Let us obtain
an overview of the several methods developed in this chapter by
referring to Fig. 2-1, which shows a particle P moving along some
general path in space. If the particle is confined to a specified path, as
with a bead sliding along a fixed wire, its motion is said to be
constrained. If there are no physical guides, the motion is said to be
unconstrained. A small rock tied to the end of a string and whirled in
a circle undergoes constrained motion until the string breaks, after
which instant its motion is unconstrained.
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