KVelocity analysis in Kinematics Of Machines.

1. KINEMATICS OF MACHINES
UNIT 2

2. VELOCITY ANALYSIS
• Analysis of mechanisms is the study of motions & forces concerning
their different parts.
• The study of velocity analysis involves the linear velocities of various
points on different links of a mechanism as well as the angular
velocities of the links.
• The velocity analysis is the prerequisite for acceleration analysis
which further leads to force analysis of various links of a mechanism.
• Velocities and accelerations in machines can be determined either
analytically or graphically.
• Graphical method is more direct & is accurate to an acceptable
degree.(Relative velocity & Instantaneous centre method)

3. ABSOLUTE & RELATIVE MOTIONS
• All motions are relative since an arbitrary set of axes or planes is required
to define a motion.
• Usually, the earth is taken to be a fixed reference plane and all motions relative to
it are termed absolute motions.
• Now, suppose a man moves inside the train. Then, the motion of the man will be
described in two different ways with different meanings.
1. Motion of the man relative to the train – it is equivalent to the motion of the
man assuming the train to be stationary.
2. Motion of the man or absolute motion of the man or motion of the man relative
to the earth = Motion of man relative to the train + Motion of train relative to the
earth.

4. VECTORS

5. ADDITION & SUBTRACTION OF VECTORS

7. MOTION OF A LINK
Let a rigid link OA, of length r, rotate about a fixed point with a uniform angular velocity ω rad/s in the counter-
clockwise direction Fig.(a). OA turns through a small angle δθ in a small interval of time δt. Then A will travel
along the arc AA’ as shown in Fig.(b).
Thus, velocity of A is ωr and is
perpendicular to OA. This can be
represented by a vector oa.
Also, the magnitude of the instantaneous linear velocity of a point
on a rotating body is proportional to its distance from the axis
of rotation

8. FOUR LINK MECHANISM
• AB is the driver rotating at an angular speed of ω rad/s in the clockwise direction if it is a crank or moving at
this angular velocity at this instant if it is rocker.
• It is required to find the absolute velocity of C (or velocity of C relative to A).
The velocity of any point relative to any other point on a fixed link is
always zero. Thus, all the points on a fixed link are represented by one point
in the velocity diagram.(A and D)
Above equation can be written as,

9. Intermediate point E
Offset point F
Velocity images: (helpful in analyzing complicated shapes of the linkages)
While drawing the velocity images, the following points should be kept in mind:
1. The velocity image of a link is a scaled reproduction of the shape of the link in the
velocity diagram from the configuration diagram, rotated bodily through 90° in the
direction of the angular velocity.
2. The order of the letters in the velocity image is the same as in the configuration
diagram.
3. In general, the ratio of the sizes of different images to the sizes of their respective
links is different in the same mechanism.

10. ANGULAR VELOCITY OF LINKS

11. VELOCITY OF RUBBING
The velocity of rubbing of the two surfaces
will depend upon the angular velocity of a
link relative to the other.

12. SLIDER CRANK MECHANISM

13. CRANK & SLOTTED LEVER MECHANISM
While analyzing the motions of
various links of a mechanism,
sometimes describing the motion
of a movable point on a link which
has some angular velocity becomes
difficult.
P & Q coincident points