MIME 3300
Velocity analysis: review
Objective: Learn how to compute velocities
of the links of a mechanism
Why velocity analysis:
a) compute kinetic energy
b) compute acceleration  forces
Velocity analysis
Graphical
Analytical
1
Definition of linear velocity:

R

R


R  R



R dR
V  linear vel ocity  lim t 0

t dt
Velocity of pivoted rotating link

VPA

P

RPA
A
Velocity of A is zero
2


VPA  RPA  j
Velocity of rotating link, pinned at point A
is perpendicular to the radius of rotation and
tangent to the path of motion. The
magnitude of the velocity is equal to the
length of the radius of rotation multiplied by
the angular velocity 
Velocity of link – general motion

VPA

P

RPA
A

Velocity of A is V A
3


VPA  RPA  j



VP  V A  VPA
Graphical velocity analysis
Given angular velocity of link 2 find angular
velocities of other links

VBA

VB
A b

VA
a
O2
p
2
d
q
B
q
p
c
4
O4
4

VA
q

VBA
p

VB
p
q
Steps:
a)
b)
c)
d)
Compute VA



Solve graphically: VB  V A  VBA
Find angular speed of coupler
Find angular speed of link 4
Analytical method for velocity analysis
3
2
b
O2
2
R4
c
3
A
R2 a
4
B
R3
R1
d
4
O4
5
Steps:
a) Write loop equation in which vectors are
represented as complex numbers
b) Differentiate equation w.r.t. time
c) Solve equations w.r.t. unknown
velocities
Final results:
angular velocity of coupler:
a 2 sin( 4   2 )
3 
b sin(3   4 )
angular velocity of rocker:
4 
a 2 sin( 2  3 )
c sin( 4  3 )
6
Velocity analysis of crank-slider
mechanism
Link 3, connecting
rod, b=4
A
Link 2, Crank, length a
3
2 =600
3
C
B
link 4, slider
link 1, ground , d
Problem definition: Given the
position of the mechanism and the
angular velocity of the crank, find
the angular velocity of the
connecting rod and the velocity of
the slider.
Solution:
3 
a 2 cos( 2 )
b cos( 3 )
d  a2 sin(  2 )  b3 sin(  3 )
7