Section 4
Velocity Analysis
 Determine “how fast” parts of a machine
are moving.
 Important when concerned with the timing
of a mechanism.
 First step in acceleration analysis.
Velocity
 Linear
– Straight line, instantaneous speed of a point.
vA = 30 in/s 300
 Rotational
– Instantaneous speed of the rotation of a link.
w2 = 72 rad/s, ccw
2
Linear and Angular Velocity
 For points on the same link
vB
B
v=rw
vA
A
2
rA
 Points have linear velocity (v)
 Links have rotational velocity (w)
rB
w2
Relative Velocity
 Two points on a rigid body can only have a
relative velocity:
Perpendicular to the line that
connects them.
B
B
A
A
The motion of B
relative to A (vB/A)
Relative Velocity Method
 Relative velocity equation is used to form
vector polygons, and determine velocities of
key points.
vi = vj +> vi/j
vi/j
vj
vi
Problem 4-1
Determine the velocity of the piston, as the
crank rotates at 600 rpm, cw.
650
8 in
2 in
Problem 4-7
Determine the rotational velocity of the
crushing ram, as the crank rotates clockwise
at 60 rpm.
360 mm
60 mm
180 mm
400 mm
Point on a Floating Link
X
i
j
 Must use simultaneous velocity equations
vi
vx = vi +> vx/i
vX/i
v
j/i
vx = vj +> vx/j
vX
 Use the Velocity Image
vj
vX/j
Acceleration Analysis
 Determines the amount that parts of a
machine are “speeding-up” or “slowing
down”.
 Important because a force is required to
produce accelerations.
Acceleration of a Point
Acceleration of a point, a, is caused by a
change in velocity. Velocity can change its:
Magnitude
 tangential acceleration
dv v
a 

dt t
t
• In direction of velocity if part is accelerating.
• Opposite direction of velocity if part is decelerating.
Acceleration of a Point
Velocity can also change its:
Direction
 normal acceleration
2
v
an 
 w 2r
r
• directed towards center of rotation (or relative rotation).
Angular Acceleration
 Angular acceleration of a link, a, is
influenced by the tangential acceleration.
a t  ra
atB
B
vB
anB
2
a2
A
w2
Relative Acceleration
 Two points on a rigid body can only have a
relative tangential acceleration:
Perpendicular to the line that
connects them.
 Therefore, the relative normal acceleration
is:
Parallel to the line that connects
them.
Relative Acceleration Method
 Relative acceleration equation is used to
form vector polygons, and determine the
acceleration of key points.
ai = aj +> ai/j
 Breaking each component into normal and
tangential components gives:
ain +> ait = ajn +> ajt +> ai/jn +> ai/jt
Acceleration Analysis Reminders
 Points on translating links have no normal
acceleration.
 Points on links that rotate at constant speed
have no tangential acceleration.
Problem 4-31
Determine the acceleration of the piston, as
the crank rotates clockwise, at a constant rate
of 600 rpm.
650
8 in
2 in
Problem 4-37
Determine the angular acceleration of the
crushing ram, as the crank rotates clockwise
at a constant rate of 60 rpm.
360 mm
60 mm
180 mm
400 mm
Point on a Floating Link
X
 Must use simultaneous
i
j
acceleration equations
ax = ain +> ait +> ax/in +> ax/it
ax = ajn +> ajt +> ax/jn +> ax/jt
vj
anX/j
ani
vi
vX
a tj
atX/j
aX
atj/i
vX/i
vX/j
vj/i
a ti
atX/i
anX/i
anj/i
Problem 4-72
For the windshield wiper linkage shown,
determine the acceleration of the cg of the
connecting link. The motor is running at 30
rpm clockwise.
7.25 in
2 in
13 in
450
6.7 in
14 in
3.5 in
Acceleration Image
 Must use total acceleration
an
a tj
aX/j
aX
i
anX/j
atX/j
ai
aX/i
a ti
atj/i
atX/i
anj/i
anX/i
aj/i