Worm Gear Maths

Sun, 24 Oct 2010

I'm working on a worm gear for my next model. The plan is that I'll use it to make a simple mechanism and as the heart of a model. In a worm gear, for each complete turn of the worm advances the gear wheel by one tooth. This makes worm gears perfect for dramatically gearing down movement.

I've tried making them before but with only limited success. I had originally opened up a few washers and glued them to a drive shaft in a spiral. The problem I was that I ended up with a kink in the card like in the picture above. Looking at the parts it looked like the centre of the worm section where it glued to the shaft shouldn't be a square at all.

Time to crack open the maths. I had a spiral line (red on the shaft above) going round the 10mm shaft advancing 2.5mm across each face. Pythagoras – he say 10.3mm.

Working out the distance across the diagonal of the tube is another application of Pythagoras. The result this time is root 225 or exactly 15mm.



So, each corner of the centre of the worm part is a isosceles triangle with base 15mm, and sides 10.3mm. To make the parts I used the red construction lines to create the black line.


…and here is the resulting part, complete with orange square so you can see the difference.


The result works well with no kinks! Members can download the parts below and have a go.

Next step, gear wheel and box.