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# Velocity Diagrams

A new technique
Lecture Outline An Example Mechanism Velocity Diagrams why learn them? Velocity Diagrams A new technique An Example Analysis of a velocity diagram Conclusion

When we are dealing with a RIGID member, the velocity of one point on that member relative to another point on that member is very special, because:

## The distance between the points cannot change

Steel girders much more rigid

## Elastic bands deform easily

Velocity Diagrams
Motion of a Rigid Body
Lecture Outline An Example Mechanism Velocity Diagrams why learn them? Velocity Diagrams A new technique An Example Analysis of a velocity diagram Conclusion

## The velocity of B relative to A must be perpendicular to the line AB

A
Velocity of B relative to A If this were not so, there would be a component of the velocity of B relative to A along AB the length would thus change

Velocity Diagrams
Motion of a Rigid Body
Lecture Outline An Example Mechanism Velocity Diagrams why learn them? Velocity Diagrams A new technique An Example Analysis of a velocity diagram Conclusion

## The velocity of A relative to B must also be perpendicular to the line AB.

A
Direction of relative velocity

## The member AB is still of constant length

Velocity Diagrams
Motion of a Rigid Body
Lecture Outline An Example Mechanism Velocity Diagrams why learn them? Velocity Diagrams A new technique An Example Analysis of a velocity diagram Conclusion

The key point is: There can be no component of relative velocity (of one end with respect to the other end) in the direction of the line joining any two points on a rigid member

Velocity Diagrams
An Example: The slider crank mechanism
Lecture Outline An Example Mechanism Velocity Diagrams why learn them? Velocity Diagrams A new technique An Example Analysis of a velocity diagram Conclusion

Question: Find the velocity of the piston for the position shown We usually draw velocities relative to ground and relative to other points on the mechanism

B A O Z = 300 rpm

Velocity Diagrams
An Example: The slider crank mechanism
Lecture Outline An Example Mechanism Velocity Diagrams why learn them? Velocity Diagrams A new technique An Example Analysis of a velocity diagram Conclusion

First step: The velocity of B relative to ground is known (Make sure you convert Z to radians per second before you calculate this velocity)

B A O
Z = 300 rpm

Velocity Diagrams
An Example: The slider crank mechanism
Lecture Outline An Example Mechanism Velocity Diagrams why learn them? Velocity Diagrams A new technique An Example Analysis of a velocity diagram Conclusion

The direction of the velocity of A relative to ground is known - It must be horizontal Its magnitude is unknown at present

B A O
Z = 300 rpm

Velocity Diagrams
An Example: The slider crank mechanism
Lecture Outline An Example Mechanism Velocity Diagrams why learn them? Velocity Diagrams A new technique An Example Analysis of a velocity diagram Conclusion

We will now consider a simple velocity diagram based on the slider crank mechanism

## The velocity diagram proceeds as follows

Velocity Diagrams
An Example: The slider crank mechanism
Lecture Outline An Example Mechanism Velocity Diagrams why learn them? Velocity Diagrams A new technique An Example Analysis of a velocity diagram Conclusion

## The velocity of B relative to ground is drawn

B A O
Z = 300 rpm
Remember: Start with what you know We know the velocity at the point B from the question

Velocity Diagrams
An Example: The slider crank mechanism
Lecture Outline An Example Mechanism Velocity Diagrams why learn them? Velocity Diagrams A new technique An Example Analysis of a velocity diagram Conclusion

## The direction of A relative to the ground is known

B A O
Z = 300 rpm

o
We refer to this line as the a line

Velocity Diagrams
An Example: The slider crank mechanism
Lecture Outline An Example Mechanism Velocity Diagrams why learn them? Velocity Diagrams A new technique An Example Analysis of a velocity diagram Conclusion

## The direction of A relative to the ground is known

B A O
Z = 300 rpm

o
b

Velocity Diagrams
An Example: The slider crank mechanism
Lecture Outline An Example Mechanism Velocity Diagrams why learn them? Velocity Diagrams A new technique An Example Analysis of a velocity diagram Conclusion

## The direction of A relative to the ground is known

B A O
Z = 300 rpm

o
Because the velocity at A is with respect to ground, it starts at ground (the point O in the diagram)

Velocity Diagrams
An Example: The slider crank mechanism
Lecture Outline An Example Mechanism Velocity Diagrams why learn them? Velocity Diagrams A new technique An Example Analysis of a velocity diagram Conclusion

To complete the diagram we require the Velocity of A relative to B AB is a rigid member. Its length cannot change! What do we know therefore about the direction of the velocity of A relative to B?

## The velocity of A relative to B must also be perpendicular to the line AB.

A
Direction of relative velocity

Velocity Diagrams
An Example: The slider crank mechanism
Lecture Outline An Example Mechanism Velocity Diagrams why learn them? Velocity Diagrams A new technique An Example Analysis of a velocity diagram Conclusion

## The direction of A relative to the ground is known

B A O
Z = 300 rpm a The direction of the velocity of A relative to B is known The magnitude is unknown

o
b

Velocity Diagrams
An Example: The slider crank mechanism
Lecture Outline An Example Mechanism Velocity Diagrams why learn them? Velocity Diagrams A new technique An Example Analysis of a velocity diagram Conclusion

## The direction of A relative to the ground is known

B A O
Z = 300 rpm a Note that it connects to the point b Why is this? b

Velocity Diagrams
An Example: The slider crank mechanism
Lecture Outline An Example Mechanism Velocity Diagrams why learn them? Velocity Diagrams A new technique An Example Analysis of a velocity diagram Conclusion

## The direction of A relative to the ground is known

B A O
Z = 300 rpm a
Graphically, we can now determine the velocity of a relative to the ground. (we can measure its length with a ruler)

o
b

Velocity Diagrams
An Example: The slider crank mechanism
Lecture Outline An Example Mechanism Velocity Diagrams why learn them? Velocity Diagrams A new technique An Example Analysis of a velocity diagram Conclusion

## The direction of A relative to the ground is known

B A O
Z = 300 rpm a We now have the required velocity diagram!

o
b

## Note the following

Lecture Outline An Example Mechanism Velocity Diagrams why learn them? Velocity Diagrams A new technique An Example Analysis of a velocity diagram Conclusion

## ie. VA = VB+VA rel. to B

Capital letters are used in the mechanism. The mechanism must be drawn to scale. Lower case letters are used in the velocity diagram. A suitable scale must also be used for the velocity diagram.

Note Also:
Lecture Outline An Example Mechanism Velocity Diagrams why learn them? Velocity Diagrams A new technique An Example Analysis of a velocity diagram Conclusion

The velocity diagram is NOT the mechanism diagram. They are totally different diagrams although they are related. Note again that: An APPROPRIATE scale must be chosen for the velocity diagram simple to calculate, and a diagram of a reasonable size (postage stamp size is too small). You can select the scale.

Velocity Diagrams
An Example: The slider crank mechanism
Lecture Outline An Example Mechanism Velocity Diagrams why learn them? Velocity Diagrams A new technique An Example Analysis of a velocity diagram Conclusion

## The direction of A relative to the ground is known

B A O
Z = 300 rpm Therefore we can have a larger velocity diagram. In an exam, this would be easier to work with! b a

## Some features of the velocity diagram.

Lecture Outline An Example Mechanism Velocity Diagrams why learn them? Velocity Diagrams A new technique An Example Analysis of a velocity diagram Conclusion
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