Get high torque out of stepper motor

Question

I have a project where I need to lift about 2 kg about 15 cm above the ground with a stepper motor. I understand the holding torque can be calculated force times distance. So that would give me holding torque of:

2kg x 10N x 0.15 = 3 Nm

Is this correct?

These kind of steppers are however pretty expensive and since I need around 15 pcs of them I need to look for some cheaper options. Are there any other way increasing the torque? Ive read about worm gear but havnt find any that suits my project. Any recommendation would be apreciated.

Another option would be to lasercut some gears out if wood for making my own gearbox, not sure how to do it properly though. Is it enough to have a small cogwheel rotating a bigger for generate lower speed but higher torque and in that case how can I calculate how much?

Any tips of good approaches of increasing the torque?

UPDATE I found this calculator. Seems to be enough with a really big cogwheel :) https://www.omnicalculator.com/physics/gear-ratio

Answer 1

No, not correct. How high you lift the object does not influence the holding torque; the horizontal distance between the centre of gravity of the lifted object and the centre of the stepper motor's axle does.

Call it the horizontal distance between the rope you use and the centre of the motor's axle; that distance is the length of the "lever", and what you should use in calculating the holding torque.

Assuming the 4 cm distance from the comments, the holding torque would be 2 kg · 10 m/s² · 0.04 m = 0.8 Nm.

If that is still too much, you can try getting the rope closer to the axle, or use a gearbox.