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CHAPTER 2
VELOCITY
KINEMATICS OF MACHINERY
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KINEMATICS OF MACHINERY
Introduction
In the design of mechanical system, a designer must
have thorough understanding of kinematics of
mechanism.
Kinematics is the study of displacement, rotation,
speed, velocity and acceleration of each link at
various positions during the operating cycle.
Using these information, a designer can compute
forces and thereby dimensions of all the links.
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The kinematic analysis of the mechanism can be
performed either by graphical or by analytical
method.
The graphical method, though less accurate, is
preferred as it gives the motion characteristics of all
the links.
KINEMATICS OF MACHINERY
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VELOCITY ANALYSIS
The change of position of a link with reference to
some fixed frame of coordinates is called
displacement.
The rate of change of displacement of a link with
reference to time, i.e. the time derivative of
displacement, is commonly referred as velocity of
link.
Depending upon the type of motion, the velocity is
classified into two types, namely linear velocity
and angular velocity.
KINEMATICS OF MACHINERY
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Linear velocity: It is the rate of change of velocity of
a body along a straight line with respect to time. Its
units are m/s.
Angular velocity: It is the rate of change of angular
position of a body with respect to time. Its units are
rad/s.
The relationship between velocity v and angular
velocity ω is: V = rω,
Where r = distance of point undergoing displacement
from the centre of rotation.
KINEMATICS OF MACHINERY
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In kinematic analysis, the velocities of various links
can be determined by the following methods:
1. Relative velocity method
2. Instantaneous centre method
KINEMATICS OF MACHINERY
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Relative Velocity Method
KINEMATICS OF MACHINERY
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Instantaneous Centre Method
KINEMATICS OF MACHINERY
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When two links form a turning pair, the instantaneous centre is
assumed to be located at the centre of the pair [Fig.(a)]
In case of sliding pair, the instantaneous centre lies at infinity
in the direction perpendicular to the path of motion of the
slider [Fig.(b)]
When two links make a pure rolling contact, the point of
contact at a given instant is taken as instantaneous centre
[Fig. (c)].
KINEMATICS OF MACHINERY
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Arnold Kennedy Theorem
KINEMATICS OF MACHINERY
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Locating Instantaneous Centres
KINEMATICS OF MACHINERY
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KINEMATICS OF MACHINERY
Numericals from
Chapter : Velocity
End of Chapter
