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Determining the proper spacing between two mating gears

At ServoCity, we field a high number of tech questions that deal with how to determine the proper spacing between the teeth of two mating gears. This spacing is a preset distance on the Actobotics Channel at 1.5” to allow 2 gears with the sum of 96 teeth to mesh properly; but what if you’re working on a project that the spacing is not determined by a piece of channel or a frame with predetermined holes? The formula is: 

(Spur + Pinion) / Pitch = N where 0.5N = the center to center distance

So let’s say we want to use a 108 tooth spur gear with a 48 tooth pinion gear to create a ratio of 2.25:1 (figured by dividing the big gear by the small gear). Both gears need to be the same pitch; for this example we’ll use 32 pitch gears. 

(108+48)/32 =4.875 which is equal to N so half of that number (2.4375”) would be the ideal center to center distance between the 108 tooth spur gear and the 48 tooth pinion gear. 

The same formula can be used if you have a preset center to center distance and wish to find the number of teeth that would properly fit in the space provided. Using the number we found above: 

2.4375*2 = N, therefore N = 4.875”
4.875 x 32 = 156 

This means that the sum of the 2 (32 pitch) gears must equal 156 to fit within the preset center to center distance of 2.4375”. You can then adjust the ratio as needed by adding teeth to one gear and subtracting from the other.

Hope this helps with your current or future projects!