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I'm trying to increase the torque on the output shaft of my robot's gearbox. I have a motor with a pinion attached to it with 8 teeth. I want to create a gear with 33 teeth that will mesh with the pinion that I currently have. I've got access to a 3D printer to make the gear, but I don't know how to design the second gear so that it will mesh properly.

What parameters do I need to know about the first gear (8 teeth) to ensure that the second gear (33 teeth) will mesh correctly? How do I translate these parameters into the design of the second gear?

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To make compatible gears, you need to match the pitch and shape of the teeth.

First, check out this wiki article about gears and especially the image about nomenclature, so you have a good idea of the names for things:

Gear Nomenclature

You first need to determine the pitch of the gear you want to match, the 8-tooth gear. If it has a diameter of say 10 mm, then take the circumference for your new gear (πd = 31.4 mm) and divide by the number of teeth (8) to get a pitch of 3.925 mm. Note that I am using the root circle to calculate diameter, rather than outside circle.

Knowing the pitch, multiply by 33 to get the circumference: 129.525 mm. We can now determine the diameter (d = c / π), 41.25 mm.

You'll need to use the same tooth shape, that is, the angles for the faces and flanks of the teeth, so that the gears mesh well.

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