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Find the velocity of the Piston , E.
A
C
DE
B
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Well start by considering the motion
of the mechanism:
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A
C
DE
B
The velocity diagram will follow the same
process as that of the mechanism.
1.Start at B, (which pivots about A),
2.move to D (which pivots about C),
3.and then to E (which moves in the slide).
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A
C
DE
B
The velocity of B relative to ground is known in
magnitude and direction.
o
( V B= x AB )
b
We need to select an appropriate scale for the velocity diagram.
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A
C
DE
B
We now consider velocities relative to the ground where
we know the direction but not the magnitude of the
velocity
The velocity at point D must be perpendicular to the line
connecting C to D.
o
b
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A
C
DE
B
The direction of the velocity of D relative to ground
is known:
o
b
(It is normal to C-D since it is constrained tomove about the fixed point C.)
The magnitude of the velocity of D relative to
ground is not known.
d line
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We now consider velocities relative to the ground where
we know the direction but not the magnitude of the
velocity
The velocity at point E relative to the ground must be in the
vertical direction
o
bA
C
DE
B
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A
C
DE
B
The direction of the velocity
of E relative to ground is
known:
(It is constrained by the
guide.)
The magnitude is unknown.
o
b
e line
d line
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A
C
DE
B
o
b
e line
d line
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To find the relative velocities, recall that the mechanism is made
up of rigid members.
The relative velocity that we find will have a direction which isperpendicular to a line linking each link on a member.
The velocity of A relative to Bmust also be perpendicular to
the line AB.
A
B
Direction of relative velocity
Velocity DiagramsAn Example: The slider crank mechanism
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A
C
DE
B
As we know both the
magnitude and the direction
of the vector b, we should
use this information.
We will therefore find the
relative velocity of D with
respect to B.
o
b
e line
d line
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Now we can graphically
determine the velocity of D
with respect to the ground.
(We measure it from our
velocity diagram with a ruler.)
A
C
DE
B
o
b
e line
d
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A
C
DE
B
o
b
e line
d
As we know both the
magnitude and the direction
of the vector d, we should
use this information.
We will therefore find the
relative velocity of E with
respect to D.
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A
C
DE
B
o
b
e line
d
We find that it is
perpendicular to a line drawn
between the points D and E.
Otherwise the member
would buckle or stretch.
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A
C
E
B
o
b
e line
d
Note we dont know the
magnitude of the velocity of
D with respect to B, only the
direction.
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o
b
e
d
Now we can graphically
determine the velocity of D
with respect to the ground.
(We measure it from our
velocity diagram with a ruler.)
A
C
DE
B
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o
b
e
d
We now have the velocities
of each point with respect to
the ground.
A
C
DE
B
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o
b
e
d
What does this vector
represent:
The velocity of D with respectto B or
The velocity of B with respect
to D?
A
C
DE
B
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o
b
e
d
A
C
DE
B
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o
b
e
d
What does this vector
represent:
The velocity of D with respectto E or
The velocity of E with respect
to D?
A
C
DE
B
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o
b
e
d
A
C
DE
B
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o
b
e
d
A
C
DE
B
What does this vector
represent:
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o
b
e
d
A
C
DE
B
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o
b
e
d
A
C
DE
B
(This may NOT beperpendicular to B-E)
WHY ?
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o
b
e
d
A
C
DE
B
It is clearly notperpendicular to the
line BE
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Faculty of Engineering
ENG1040 Engineering Dynamics
ENG1040
Engineering Dynamics
A Final Example of Velocity Diagrams
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Consider the basic 4-
bar linkage where one
of the members is
extended to give point
F. Find the velocity of
point F.
The velocity of point F is governedentirely by the velocities at points B and
D, and by the position of F with respect
to these two points.
A
C
D
B
F
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Well start by considering the motion
of the mechanism:
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A
C
D
B
F
Remember, we commence by defining
ground and by considering velocities
where we know both the magnitude and
direction.
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A
C
D
B
F
We know both the magnitude and
direction of the point B with respect to
the ground (O)
o
b
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A
C
D
B
F
There are no other velocities where we
know both the magnitude and the
direction.
o
b
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A
C
DB
F
We then consider velocity vectors where we know
the direction but not the magnitude with respect to
ground.
We know the direction of D with respect to the
ground (why?)
o
b
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A
C
DB
F
We then consider velocity vectors where we know
the direction but not the magnitude with respect to
ground.
We know the direction of D with respect to the
ground (why?)
o
b
d line
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A
C
D
B
F
Finally, we consider the relative velocities with
respect to our known velocity values.
We know the direction (but not the magnitude) of
the velocity of D with respect to B. It is
perpendicular to the line connecting B to D.
o
b
d line
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A
C
D
B
F
Finally, we consider the relative velocities with
respect to our known velocity values.
We know the direction (but not the magnitude) of
the velocity of D with respect to B. It is
perpendicular to the line connecting B to D.
o
b
d
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A
C
D
B
F
This is the velocity diagram so far.
We now consider the velocity of F.
We know the direction of the velocity of F with
respect to B.
o
b
d
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A
C
D
B
F
This is the velocity diagram so far.
We now consider the velocity of F.
We know the direction of the velocity of F with
respect to B.
o
b
d
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A
C
D
B
F
This is the velocity diagram so far.
We now consider the velocity of F.
We ALSO know the direction of the velocity of F
with respect to D.
o
b
d
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A
C
D
B
F
This is the velocity diagram so far.
We now consider the velocity of F.
We ALSO know the direction of the velocity of F
with respect to D.
o
b
d
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A
C
D
B
F
This is the velocity diagram so far.
We now consider the velocity of F.
We ALSO know the direction of the velocity of F
with respect to D.
o
b
d
f
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d
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A
C
D
B
F
We can now graphically find both the direction and
the magnitude of the F with respect to the ground.
(we can measure both direction and magnitude with
a ruler)
o
b
d
f
A 2nd Velocity Diagram example
A 2 d V l i Di l
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A
C
D
B
F
o
b
d
f
Note that the triangle bfd on the velocity diagramis SIMILAR to the triangle BFD on the mechanism
diagram - (although it has been rotated through
90 degrees).
A 2nd Velocity Diagram example
A 2 d V l i Di l
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A
C
D
B
F
o
b
d
f
The triangles also have the same sense.
The direction BFD is same as bfd both
anticlockwise.
A 2nd Velocity Diagram example
Summary
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Summary
50
What can you do now ?
You can now use velocity diagrams to determine
the velocity of all members of a mechanism.
Using similar techniques you will soon be able to
also determine the acceleration of all members of
a mechanism
We will consider acceleration diagrams next
week.
You need to practice using velocity diagrams.
See the prescribed text for examples.