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Astronomy Calculations


Mount Gearbox Ratio Calculator

Exotic mounts has the RA and DEC axis as a part of the motor and then there is no need of gearboxes. But what is normal is to use a worm gear, gear box or belt drive, often in combination. There are also friction wheels that act as a gearbox. Harmonic drive is very interesting because of its lack of backlash.

More to read about worm drive, gearbox and belt drive at Wikipedia:

With this calculator you find your total gear ratios from different setup of gear boxes. You also find the angular resolution per micro step of stepper motor or tick from your DC motor encounter.

As usual when I write something new I do it online. Click your web browser update button to see the latest. It's in early stage and still in progress, there can be something wrong in the calculations! Don't buy expensive gears until you have double check everything!

Messier 51, Whirlpool galaxy

Type in your data

It start to calculate as soon you change or write new figures in the white or dark red boxes. Do not exceed the maximum number of characters, delete characters if necessary.

You use the information on your own risk! There can always be a mistake in my equations behind the calculations, check that the result is correct. Let me know if you find something wrong and I try to correct it. Some calculations are very simple done and not correct in the small details.


1, Your mounts worm gear ratio ?

Common worm drives are 130:1, 135:1, 144:1, 180:1, 435:1.

Worm wheel teeth Worm number of threads    
= Ratio Worm gear
10 to 9999 1 to 4   ratio

2, Gearbox or belt drive ratio?

Common ratios are from 1:1 to 75:1, the last one with multiple gear drives.

Primary gearbox 1

Big wheel teeth numbers Small wheel teeth numbers
= Gearbox 1 Ratio
10 to 999 teeth 6 to 50 teeth   ratio

Secondary gearbox 2
If not in use, set 10:10

Big wheel teeth numbers Small wheel teeth numbers
= Gearbox 2 Ratio
10 to 999 teeth 6 to 50 teeth   ratio

Total ratio.

  Gearbox 1+2 = Gearbox 1+2 Ratio
  Worm drive + gearbox 1+2 = Total Ratio

    total ratio

3, Motor steps or ticks per revolution ?

Angle resolution of motor:
Normal values for stepper motors are 200, 400 or 1000 steps per revolution and above that micro stepping.
Normal for DC motor's angular sensors (encounter) are 4096 (12-bits), 16384 (14-bits) per revolution.

Steps / ticks per revolution of motor     Arc seconds
  = Resolution arc seconds
1 to 999999     per step

4, Micro steps ?

Common micro stepping is 2, 32 and 64, only stepper motors!
If DC motor set = 1.

Normally you need a resolution of every step / tick the motor do from 1" (wide angle) to 0.05" (long focal length) or 5 to 10 times the pixel scale. EQ6 mount has about 0.14" per micro step.

Micro steps     Arc seconds
  = Resolution arc seconds
1, 2, 4, 8, 16, 32, 64     per micro step


In my dream mount I have a worm gear of 435:1 and then a direct connected DC motor with a high resolution position sensor (encounter). But it will not be an easy project, my experience from the industry is that direct drive DC motors are sensitive and easily come into oscillation.

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