Table - Sprocket Max/Min tooth counts, for various Wheel and Shaft Diameters

[kmcclary]

A complete "sprocket range" table would be a great boon for working out gear ratio "limits" during the design phase of a project.
Has anyone here ever made up a nice, simple table for the Min and Max tooth counts on sprockets, for the various common wheels and drive shaft diameters?

IOW... For example - What would be the max and min tooth counts, for: 4", 6", 8", 10", and 12" wheels, given these assumptions:
...A) #35 roller chain
...B) The AndyMark standard six hole mounting standard (a 1.875" bolt hole circle)
(...also... the minimum tooth count for a solid keyway hub), and
...C) Standard AndyMark wheels.

Note this is not a simple problem. You can get CLOSE, but there are some "experience factors" involved here (carpet sink in, tools hitting chains in the pits forcing a wheel dismount because you didn't allow clearance for the socket's diameter to fit onto the sprocket mount nut with the chain installed, etc...)

On the max count, you can't just compare the pitch diameter vs the wheel diameter. The chain links actually form a lumpy polygon as it goes over the sprocket, and the tread and load may make a difference when interacting with FIRST standard carpeting (fuzzy pile, compression surrounding the wheel as it sinks in, etc.) Since we MUST maintain clearance between the metal chain and the top of the carpeting pile, your experience is a better guide.

On the min count - It first depends on the hub mounting style. If you are using a bolt hole circle, you not only need that diameter, you also need to consider both the size & type of the mounting nuts and bolt heads colliding with the chain, AND possibly the tools (eg nut socket OUTER diameter), so it won't collide with the chain's edge when working on a bot in the pit with the chain installed. You also have to consider the wrap around on very small sprockets, at our common chain speeds. IOW, you may need to TRY it.

Examples -
--- Given a #35 chain, I'm seeing that the minimum practical tooth count on 1/2" keyed shaft hubs seems to be about 12T (I haven't tried anything smaller yet. Will anything smaller work???)
--- The small size limit on an #35 AM style 1.875" bolt hole circle sprocket seems to be roughly 22T, but I also haven't yet verified that it won't require removing the chain to work on it.

I also wish find the largest practical tooth count, that won't catch the carpeting, without having to buy a sample of every tooth count NEAR the "theoretical" max size just to test it!

So I guess what I'm really asking is for your experience "in practice", on FIRST fields, to build up this Basic Knowledge table / matrix.

What have you found to be the the largest and smallest PRACTICAL tooth counts, both for each common FIRST wheel sizes (eg 4/6/8/10/12"), and for common power drive shaft diameters (eg 1/2", 3/8", etc), so you won't hit the carpet, or not be able to use a tool on it without first dismounting the wheel from the robot?

Have you found any tooth count limit differences when using a Mechanum or Omniwheel, vs a "normal" tread wheel? Have any tricks? (Ex: Selecting certain types of screws may make a difference, etc.) Please share that experience, too!

Assume #35 roller chain to start. We can LATER consider other close sizes of common roller chain (20, 25, 40, etc).

Does anyone here have this already worked out?
If not, what's your max/min tooth count experience, given whatever wheels and shafts you HAVE used? We can piece this together that way.

In the end, I wish to end up with a nice one-page "Min/Max Tooth" table, for everyone's use! Can you help?

Thanks!
- Keith Mc.