The discussion revolves around determining the pitch circle and the number of teeth required for a mechanism to achieve a specific amplitude of movement. Participants explore the mechanics of a pinion and rack system, including the implications of tooth removal and the resulting motion characteristics.
Participants express uncertainty regarding the calculations and interpretations of the pitch circle and movement distances, indicating that multiple competing views remain without consensus.
There are unresolved assumptions regarding the definitions of pitch circle and the implications of tooth removal on the mechanism's operation. The calculations presented are not universally agreed upon, and the context of motion characteristics remains ambiguous.
This discussion may be of interest to those involved in mechanical engineering, particularly in the design and analysis of gear systems and mechanisms.
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.
Jones1987 said:So if I had a pitch diameter of (0.1m) x (pi) / 2 = 0.1571 m/s? Is this correct?