Finding Pitch Circle & Teeth for Amplitude Movement

AI Thread Summary
To determine the pitch circle and number of teeth for a mechanism to achieve a specific amplitude, the calculations involve the pitch diameter and the number of original pinion teeth. The mechanism's design may require an even number of teeth before any are removed, with the suggestion that removing one more than half of the original teeth is necessary for proper function. The total shift of the rack can be calculated using the pitch diameter multiplied by pi divided by two or the rack tooth pitch times the number of original pinion teeth divided by two. Concerns are raised about the mechanism's violent motion and infinite acceleration at the end of each stroke, despite appearing smooth in animation. Clarification is sought regarding whether the calculated distance is in meters or meters per second, specifically questioning the interpretation of the pitch circle versus the distance the rack moves per revolution.
Jones1987
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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..
 
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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.
 
tvavanasd said:
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?
 
Last edited:
Jones1987 said:
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?
 
So does it mean the pitch circle is 0.157m or the distance the rack moves is 0.157m per revolution?
 

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