Finding Pitch Circle & Teeth for Amplitude Movement

[Jones1987]

How would I work out the pitch circle and number of teeth required to move the mechanism a certain amplitude? Looked over 4-5 sources for pitch circle, but cannot make sense of it..

 

[tvavanasd]

In the animation, if the pinion had all its teeth, there would be 12. 7 of those teeth have been removed (5 remaining). Not absolutely sure, but based on the model, it may only work with an even number of pinion teeth (prior to removal). 1 more than half of the original number of teeth likely have to be removed.
The rack shifts a total (from left to right say, before returning) of:
(pitch diameter) x (pi) / 2
or
(rack tooth pitch) x (number of original pinion teeth) / 2

This mechanism is really not very nice. Although it appears to be simple, its motion is quite violent. At the end of each stroke there is infinite acceleration. In the animation, it looks smooth, but that's only because the rack has no mass.

 

[Jones1987]

In the animation, if the pinion had all its teeth, there would be 12. 7 of those teeth have been removed (5 remaining). Not absolutely sure, but based on the model, it may only work with an even number of pinion teeth (prior to removal). 1 more than half of the original number of teeth likely have to be removed.
The rack shifts a total (from left to right say, before returning) of:
(pitch diameter) x (pi) / 2
or
(rack tooth pitch) x (number of original pinion teeth) / 2

This mechanism is really not very nice. Although it appears to be simple, its motion is quite violent. At the end of each stroke there is infinite acceleration. In the animation, it looks smooth, but that's only because the rack has no mass.

So if I had a pitch diameter of (0.1m) x (pi) / 2 = 0.1571 m/s? Is this correct?

 

[tvavanasd]

So if I had a pitch diameter of (0.1m) x (pi) / 2 = 0.1571 m/s? Is this correct?

I expect that travel should be 0.157 m.
Why are you suggesting the answer is in m/s?

 

[Jones1987]

So does it mean the pitch circle is 0.157m or the distance the rack moves is 0.157m per revolution?