## FUNDAMENTALS OF KINEMATICS AND DYNAMICS OF MACHINES AND MECHANISMS

CONTENTS
• Introduction
• Kinematic Analysis of Mechanisms
• Force Analysis of Mechanisms
• Cams
• Gears
• Introduction to Linear Vibrations

INTRODUCTION TO THIS BOOK :

This subject is a continuation of statics and dynamics, which is taken by students
in their freshman or sophomore years. In kinematics and dynamics of machines and
mechanisms, however, the emphasis shifts from studying general concepts with
illustrative examples to developing methods and performing analyses of real  designs.
This shift in emphasis is important, since it entails dealing with complex  objects
and utilizing different tools to analyze these objects.
The objective of kinematics is to develop various means of transforming motion
to achieve a specific kind needed in applications. For example, an object is to be
moved from point A to point B along some path. The first question in solving this
problem is usually: What kind of a mechanism (if any) can be used to perform this
function? And the second question is: How does one design such a mechanism?
The objective of dynamics is analysis of the behavior of a given machine or
mechanism when subjected to dynamic forces. For the above example, when the
mechanism is already known, then external forces are applied and its motion is
studied. The determination of forces induced in machine components by the motion
is part of this analysis.
As a subject, the kinematics and dynamics of machines and mechanisms is
disconnected from other subjects (except statics and dynamics) in the Mechanical
Engineering curriculum. This absence of links to other subjects may create the false
impression that there are no constraints, apart from the kinematic ones, imposed on
the design of mechanisms. Look again at the problem of moving an object from A
to B. In designing a mechanism, the size, shape, and weight of the object all constitute
input into the design process. All of these will affect the size of the mechanism.
There are other considerations as well, such as, for example, what the allowable
speed of approaching point B should be. The outcome of this inquiry may affect
either the configuration or the type of the mechanism. Within the subject of kinematics
and dynamics of machines and mechanisms such requirements cannot be
justifiably formulated; they can, however, be posed as a learning exercise.

Force Analysis of
Mechanisms

INTRODUCTION

The design of mechanisms and their components requires information about forces
acting on these components. Some mechanisms are designed to perform a  specific
kinematic function (like the windshield wiper mechanism, Figure 1.4), others to
transfer energy (like the internal combustion engine). However, in any mechanism,
identification of forces is needed to determine the proper dimensions of components.
The power supplied to the input link flows through the mechanism to the output
link. Associated with this power flow is a force flow. The objective of the force
analysis of mechanisms is to find the transformation of forces from the input to the
output links. This transformation of forces depends on the position of the mechanism;
in other words, it is a function of time. Thus, it is important to find out how these
forces change during one cycle in order to find their maxima.
One should differentiate between two types of forces: external and internal. The
former are forces that are applied to the links from external (with respect to the
mechanism) sources — driving forces, resistance forces — whereas the latter are
forces acting between the joints (they are called constraint or reaction forces).
The motion of a mechanism is caused by the known external forces, and can be f
ound by formulating and solving the differential equation describing the dynamic
equilibrium of the mechanism at any moment in time. This approach to motion
analysis is called direct dynamics. An alternative approach is to assume that the
motion is known (in other words, the motion of the input link is given as a function
of time). Then, as a result of kinematic analysis, the accelerations of all links are
known, and thus the inertial forces associated with these links. These inertial forces
can be treated as known external forces, and the force analysis is then reduced to
solving equilibrium equations for the mechanism at any given position. This
approach to force analysis is called inverse dynamics. It is important to keep in mind
that inverse dynamics is based on the assumption of known motion, whereas in fact
such motion can be found only from direct dynamics analysis. However, in many
situations the much simpler inverse dynamics approach is sufficient as a first approximation

This approach is considered in this book.
To summarize, it is assumed here that the forces acting on the input link are
given as a function of time (or link position) and the inertial (dynamic) forces are
also known as a result of kinematic analysis of motion. The objective of force analysis
then is to find the internal and resistance forces. The method of solution is to perform
static analysis of a mechanism in a number of fixed positions over the region of