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X KINEMATICS OF RIGID BODY

45 Kinematics of Rigid Body: Basic Concepts

We developed the relationships governing the displacement,
velocity, and acceleration of particles if they moved along straight or
curved paths. In rigid body kinematics we use these same
relationships but must also account for the rotational motion of the
body. Thus rigid body kinematics involves both linear and angular
displacements, velocities, and accelerations.
We need to describe the motion of rigid bodies for two important
reasons. First, we frequently need to generate, transmit, or control
certain motions by the use of cams, gears, and linkages of various
types. Here we must analyze the displacement, velocity, and
acceleration of the motion to determine the design geometry of the
mechanical parts. Furthermore, as a result of the motion generated,
forces may be developed which must be accounted for in the design of
the parts.
Second, we must often determine the motion of a rigid body
caused by the forces applied to it. Calculation of the motion of a
rocket under the influence of its thrust and gravitational attraction is
an example of such a problem.
We need to apply the principles of rigid body kinematics in both
situations. This chapter covers the kinematics of rigid body motion
which may be analyzed as occurring in a single plane.
Rigid Body Assumption. In the general case, we defined a rigid
body as a system of particles for which the distances between the
particles remain unchanged. Thus, if each particle of such a body is
located by a position vector from reference axes attached to and
rotating with the body, there will be no change in any position vector
as measured from these axes. This is, of course, an ideal case since all
solid materials change shape to some extent when forces are applied
to them.
Nevertheless, if the movements associated with the changes in
shape are very small compared with the movements of the body as a
whole, then the assumption of rigidity is usually acceptable. The
displacements due to the flutter of an aircraft wing, for instance, do
not affect the description of the flight path of the aircraft as a whole,

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