Gear tooth geometry

[henrycasson]

Usually I do clock gears using epicycloidal gears, which are the tradition. Now I need a train which runs the opposite way to usual, from the seconds hand driving back down to the slower hands, which ,of course, is exactly what quartz clocks do. The theoreticians tell me to use involute gears for this. I do involute gears using Wellmans odontograph, which approximates the involute function with two arcs, and is exceedingly accurate. The trouble is that it does not do low number pinions.  I tried to spreadsheet  the Wellman radii, and fit a curve to extrapolate  down, but the results are unconvincing. There are any number of gear drawing apps, including one resident in Fusion. They all  appear to do single arc approximations. I am sure that is OK. Could any of you real engineers out there point me to the literature which describes the geometry of the curves that are used. 

[Anonymous]

Dudleys gear handbook is my go to for gear design.

[Anonymous]

There's also geargenerator.com

If you do wood clocks I'm going to assume you already know if gear2motion (formerly gearotic)

[etfrench]

Perhaps this video will be of some use.

p.s. This link uses the same method as the video.

[Anonymous]

Oh, this is a big one!

I wrote a whole bunch of Python code (1500 lines + tooltip images) to do this for F360 - I should put it up somewhere to share it maybe. I wanted internal gears as well as external, with numbers for backlash as well as the use of parameters to take information from (like centre holes) and put information into (like the pitch diameter). I store the gear information in body properties so that you can just click on the body to retrieve all the information. I probably went overboard but I was discovering the Fusion 360 object model along the way.

(I also have a script to pull all the user and model parameters out into a file. To answer the question - where is this parameter being used?)

However, I started with these excellent answers on stackexchange:

https://engineering.stackexchange.com/questions/13852/involute-gear-curve-when-root-diameter-falls-b...

https://engineering.stackexchange.com/questions/13633/internal-teeth-involute-gear-pitch-circles

I used an involute curve for the main part of the gear - I plotted points along the curve and then used a spline to connect them. For the base, I then drew a trochoid from the root circle, but only if I considered it worth while (for large teeth really). The intersection between the curves was discovered using Newton Raphson style brute force - if it's within 0.001mm that'll do. I'm an engineer, not a mathematician - I wasn't going to solve that equation!

I wanted to do twisted gears next but I was figuring out sweeps along helixes first. The last update to F360 has added a guide plane which makes that a lot easier.

Conor.

[henrycasson]

We may have some similar mental processes. A long time ago, not wishing to pollute my mind with any actual knowledge about how it was done, I set out to design an involute gear. I made a spreadsheet of 1000 values, manipulated some text so that I could copy the whole megilla into the command line of autocad R 14, and drew a curve from 1000 line segments . CNC at that time did  not take kindly to this approach, so I started reading and found Wellman, approximating the curve with two arcs. Still playing around I spreadsheeted to show that at any size I wanted it was within 0.001 inches, so I was more forgiving than you. My point in the question was that the popular gear generators seem to do a single arc, but I was wrong, they do similar line segments or splines, although with fewer segments. I'll stop fussing and start laser cutting.