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Astronomy Calculations:
Gearbox ratio of focuser

When designing a stepper motor focuser there are a lot of parameters that you have to think about.

What is the needed step resolution from the stepper motor, how much do you need that one step move the focuser draw tube?

It has to be designed to use the full stroke (in most cases) of the focuser draw tube, that is the range of steps that shall cover the focuser from inward to outward position.

You need information about stepper motors and your telescope setup:

Here I try to sort it out:


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.

Focuser draw tube stroke length?

First we have to find out how many turns do we need from the focuser knob to go from inward to outward position. You shall normally use the direct connected knob, not the one over the normally built in 10:1 reducer. One goal of this design is to use most of the focus draw tube stroke as long it gives enough of movement per motor step.

Focuser stroke length
(0 to 200 mm)

The diameter of the friction axis to the focuser?

Most common is that the focuser has an axis that by force act on a steel plate, no gears. Then use the axis diameter. Some focuser has a rack and pinion system to get out of the problem that the friction focuser can slip. Then try to find the gear mounted on the axis and its mean diameter.

Axis diameter
(0.01 to 9.99 mm)

Calculated number of turns of focus knob to cover the draw tube stroke length:

= Calculated results number of turns

Stepper motor number of step per revolution?

We need some data of the stepper motor. How many steps per revolution.

Some motors have included a built in gearbox. Set the number of steps related to the output axis, the built in gearbox ratio can be difficult to find.

Most common is 200 steps per revolution (1.6 degree step) and no gearbox.

Number of steps
(0.0 to 999.9 steps)

Max step number?

We also need to know how big number of steps the stepper motor driver can count to. Most common is 16 bit or 2^16 = 65536 steps.

Number of steps full range
(0 to 9999999 max steps)

Number of micro steps per main step?

Some drivers can use micro steps, from 1/1 to 1/64. Normally 1/1 or 1/2, above that will not be good, the motor loss torque and can not hold the position without power.

Number of micro steps
(1, 2, 4, 8, 16, 32, 64 micro steps)

Needed gearbox ratio:

= Calculated results needed gearbox ratio to use the full focus stroke

If you get a calculated gear box ratio of 127.6, try to find a gearbox above that, not below, say 150:1.

Draw tube movement per step:

= Calculated results micro meter move per step (resolution)

You need a resolution about one fifth of your depth of focus or less, see the link above. Example, if your focus depth is 100 micro meter, then a move of 10 to 20 micro meter per step can be good values. Bad quality optics is less sensitive of the focus point.

If you get too high value in the calculations above you can limit the stroke of the draw tube, say that you have 100 mm focus stroke, then only use the first 50 mm. Type in that value and a new gear ratio will be calculated and then the resolution changes. Note you can only do this if you have your optics in focus in the range 0 to 50 mm. You can also try to find a driver that can handle higher values then 16 bit system can do or a stepper motor with different step size.

In my own case I use about 85 mm of my 100 mm focuser stroke. The move per step is about 2 micro meter.

Normally there is no problem to use a 100 mm focus stroke on a f/7 telescope and still have resolution enough with a correct designed gear ratio. But a f/3 telescope of high quality and calculated for the blue spectra are on the limit, that kind of telescopes are often of Newton design and have shorter focus stroke.

If you are not limited by 16 bit resolution in the driver you can use higher gear ratios and get better precision. As a bonus that system give more torque that can handle heavier cameras. A bit slower due the higher gear ratio.

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