velocity diagrams 2

8/13/2019 Velocity Diagrams 2

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Find the velocity of the Piston , E.

A

C

DE

B

A Velocity Diagram example


2/47

Well start by considering the motion

of the mechanism:



3/47

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).



4/47

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.



5/47

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



7/47

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


11/47

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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15/47

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.



18/47

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



20/47

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



22/47

o

b

e

d


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



24/47

o

b

e

d

A

C

DE

B


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 ?



27/47

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

A 2nd Velocity Diagram example


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Well start by considering the motion

of the mechanism:



31/47

A

C

D

B

F

Remember, we commence by defining

ground and by considering velocities

where we know both the magnitude and

direction.



32/47

A

C

D

B

F

We know both the magnitude and

direction of the point B with respect to

the ground (O)

o

b



33/47

A

C

D

B

F

There are no other velocities where we

know both the magnitude and the

direction.

o

b



34/47

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



35/47

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



36/47

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



37/47

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



38/47

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



We know the direction of the velocity of F with

respect to B.

o

b

d



40/47

A

C

D

B

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




with respect to D.

o

b

d



42/47

A

C

D

B

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 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 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.


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.

velocity diagrams 2

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