making a pinion to match an existing rack

[davidh]

being an unknown rack configuration, tooth detail and all, I would like to attempt to make a 12 or 13 tooth pinion to fit the rack. im going to use the assembly as a slotter so there's not much travel, and it does not need to last a lifetime, as im old anyway.
sooo, if I were to make a "dam" around the rack to hold modeling silicon, encompassing 12 or 13 teeth at a given depth, and pour silicone (sp) to make an inverted model of the teeth, and then took that model and attached it end to end so it forms a pinion, would that suffice as a pattern for making the actual steel pinion ?

I have guessed at what I think I need mathematically but not certain of it working and cutting teeth is not going to be easy with my machines, I don't think.

I could just try it but I thought I would ask the group of wizards here first.

 

[Tony Wells]

No, not really. Racks have a straight sided tooth, and pinions are involute. With some dimensions, you should be able to figure out what the proper pitch and pressure angle you need on the pinion.

 

[British Steel]

As Tony says, some (fairly precise) measurements will determine what gear you need:

First, measure the rack pitch (best to measure over plenty of teeth and divide for accuracy), divide this by Pi (3.1416 is close enough) and see whether the result in inches is the decimal equivalent of a fraction (use the 1/x key on your calculator and see whether you get a whole number, the imperial DP, or very close) - if this doesn't give a sensible result, repeat for metric module pitches by dividing the pitch in mm by Pi and if you get a sensible decimal (e.g 0.8, 1.0, 1.5 etc) that's the metric module pitch of the rack.

So, by now you should know the gear pitch you need, next comes the pressure angle - this will either be 14.5 or 20 degrees and can be measured fairly easily, take your school protractor and draw 29 and 40 degree angles and compare to the included angle.between rack teeth, which is twice the pressure angle.

Hope.this helps,

Dave H. (the other one)

 

[benmychree]

I would try to borrow as set of gear tooth gages; they are stamped steel replicas of rack teeth, and are generally made two sided with both 14 1/2 deg and 20 deg pressure angle; these are the most common in the USA, but there are also metric module and circular pitch to contend with. Measureing say, 10 pitches accuratly and dividing by ten should give you the spacing of the teeth as has been pointed out, and a protractor will give the pressure angle. The gages are the easy way.