Presentation for Velocity and Acceleration analysis of simple mechanisms by Graphical Method.

1. Velocity and Acceleration analysis of
Simple Mechanisms: Graphical Methods-I
© Dr.V.R Deulgaonkar Janaury
2018

2. Absolute & Relative Motions
• Motion of train in particular direction:
• Motion of man inside train: Motion of man
relative to train.
• Motion of man/absolute motion of
man/motion of man relative to earth =
motion of man relative to train+ Motion of
train relative to earth
© Dr.V.R Deulgaonkar Janaury
2018

3. © Dr.V.R Deulgaonkar Janaury
2018

4. Vector Characteristics
1. Length of vector drawn to a suitable scale
represents the magnitude of the quantity.
2. Direction of the line is parallel to the line
in which the quantity acts.
3. An arrow head on the line indicates the
direction-sense of the quantity that is
always from tail to head.(ab)
© Dr.V.R Deulgaonkar Janaury
2018

5. © Dr.V.R Deulgaonkar Janaury
2018

6. 4 If the sense is as shown in fig 1, the vector
is read as “ab” & if the sense is opposite
(fig 2) the vector is read as “ba”. {ab = -ba}
5 Vector ab also represent a vector quantity
of a body B relative to A as velocity of B
relative to A (fig 3)
© Dr.V.R Deulgaonkar Janaury
2018

7. Motion of a Link
• Consider a rigid link OA, of length r, rotate
about fixed point O with uniform angular
velocity ω rad/s in CCW.
• Link OA turns through a small angle δθ in
a small interval of time δt. Then A will
travel along AA’.
• Velocity of A relative to O = Arc AA’/δt
V = r(δθ/δt)
© Dr.V.R Deulgaonkar Janaury
2018

8. • In the limits, when
• Vao = r
Vao = rω, the direction of Vao is along the
displacement of A. As δt approaches to
zero, AA’ will be perpendicular to OA
Hence velocity of A is rω and is
perpendicular to OA.
© Dr.V.R Deulgaonkar Janaury
2018

9. • Assume a point B on the link OA, then
velocity of B = ω.(OB) ┴ to OB.
If ob represents the velocity of B, it can be
observed that = =
Here we see that b divides the velocity
vector in the same ratio as B divides the
link
© Dr.V.R Deulgaonkar Janaury
2018

10. Relative Velocity Method
• Steps in velocity analysis
• Consider all fixed points at a single point.
• Using suitable scale construct velocity
vector for the link whose length and
angular velocity is known. Then proceed to
other links by constructing perpendiculars
and complete the velocity polygon.
© Dr.V.R Deulgaonkar Janaury
2018

11. Velocities in Slider Crank
Mechanism
© Dr.V.R Deulgaonkar Janaury
2018

12. Rubbing Velocity at a Pin
Joint
© Dr.V.R Deulgaonkar Janaury
2018

13. Velocity Polygons for simple
mechanisms
© Dr.V.R Deulgaonkar Janaury
2018

14. Velocity analysis of crank and
slotted lever mechanism
© Dr.V.R Deulgaonkar Janaury
2018

15. Acceleration analysis by relative
acceleration method
• Before constructing acceleration polygon
velocity analysis needs of given
mechanism should be carried out.
• Velocity analysis is a pre-requisite for
acceleration analysis.
• Two component of acceleration are
– Tangential Component: rα
– Radial/centripetal component : V2 / R
© Dr.V.R Deulgaonkar Janaury
2018

16. Acceleration analysis of 4-bar
mechanism
© Dr.V.R Deulgaonkar Janaury
2018

17. Procedure for construction of
acceleration polygon
Name
of
link
Link
Length
Velocity from
velocity
polygon
Acceleration
Centripetal
Component
Direction Tange
ntial
comp
onent
Direct
ion
Known or
Given
All values of
velocity are
computed from
velocity polygon
and hence are
used for
calculating
centripetal
component
AB
BC
© Dr.V.R Deulgaonkar Janaury
2018