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C H A P T E R 7
Kinematics of Rigid Bodies
7.1 INTRODUCTION
In this chapter the kinematics of rigid bodies are presented. Section 7.1 is concerned with in-
troduction to various important definitions and concepts in the kinematics of rigid bodies. e
instantaneous center of rotation in plane motion is briefly introduced in Section 7.2. More de-
tails presentation and application in motion analysis may be found in textbooks on kinematics
and dynamics of machinery, for example in [1–3]. Position vector in a rotating frame of refer-
ence is presented in Section 7.3. Rate of change of a vector with respect to a rotating frame of
reference is dealt with in Section 7.4. e 3D motion of a point in a rigid body with respect to a
rotating frame is considered in Section 7.5 in which three representative examples are included
to illustrate the steps in the solution.
In a system of particles or rigid bodies, arguably the most fundamental concept is the
degrees-of-freedom (dof) in spaces. By the dof of a system or rigid body one means the minimum
number of independent coordinates that are required to completely describe the position of the
system. It is independent of the coordinate system adopted in a particular situation. For example,
if the system in a Cartesian coordinate system has 6 dof then it has the same number of dof in
a spherical coordinate system. For a rigid body in 3D space, there are 3 translational dof, and 3
rotational dof, as shown in Figure 7.1. For a rigid body in a 2D space there are 2 translational
dof and 1 rotational dof.
A rigid body may, in general, experiences either one or more of the various types of motion
to be included in the following.
(a) Translation is the motion in which any straight line inside the body maintains the same
direction, as shown in Figure 7.2a. Clearly, all particles in the rigid body move in parallel
paths. However, if these paths are curved lines such motion is called curvilinear translation,
as shown in Figure 7.2b.
(b) Rotation about a fixed axis is the motion in which the particles of the rigid body move in
parallel planes along the circles centered on the same fixed axis, which is called the axis of
rotation, as indicated in Figure 7.3.
(c) General plane motion is one which is neither a rotation nor a translation, as shown in Fig-
ure 7.4.