First I can mention that english is not my native language, just in case you would think that some words or phrases below look awkward.
I am a programmer with some (but not too much) experience of Arduino programming some years ago (and including some Bluetooth communication).
Now I would like to learn 3d printing with a construction that includes a motor.
But I do not know how to figure out how strong motor I would need, nor how to figure out the needed size of the gears.
The specific project I am thinking about to create is a motor to be mounted on my door on top of an existing thumb lock, to eventually be able to unlock it from the outside through bluetooth.
I think it might be done with a rectangle pocket/hole that can be cut out from a gear, and the other gear would be controlled with a motor.
See the pictures below (screenshots from my FreeCAD drawing), with the big left gear with a rectangular hole that would fit the the thumb lock, and the smaller right gear would be the motor driven gear.
So when a motor is attached to the small square hole in the small right gear, it would make the larger gear spin around and thus make the thumb lock in the recatangle to become switched and unlock the door.


Of course the drawing is not finished yet, since the gears will need to be attached to not only a thumb lock and a motor, but also some kind of surrounding box to be attached on the door.
But now my question is not about completing the box construction for the 3d printing, but my focus now is about how to figure out the needed strength of the motor and the needed sizes of the gears.
I am not sure about if a servo would be needed (and if so, why?) or if it would be okay to use a stepper motor.
But if a stepper is okay then I could consider the following motor (swedish web page selling an Arduino motor):
If you then would click into the PDF (in english) manual:
Then you can see the following torque specifications:
in-traction torque: > 34.3 mN.m (120 Hz)
self-positioning torque: > 34.3 mN.m
friction torque: 600-1200 gf.cm
pull-in torque: 300 gf.cm
But I do not know which of these numbers are most relevant and how to use them.
I suppose "mN.m" means milli-Newton-Meter i.e. 34.3 mN.m is 0.0343 Nm.
And I have used an online calculator to find out that 300 gf·cm (gram-force centimeter) is 0.0294 Nm, and 600 gf·cm = 0.0588 Nm, amd 1200 gf·cm = 0.1177 Nm
Let us say that the width of the rectangular thumb lock would be 4 cm (i.e corresponding to the long side of the rectangle in my above FreeCAD drawing) and I would push upwards at the left (or right) edge with my finger with the force 5 Newton, then the torque would be 0.1 Nm (5 * 0.04/2)
But first of all I do not know if 5 Newton is the needed force, but that is just a rough guess of mine.
Are there any appropriate tools for measuring how much force you need for switching a thumb lock?
Secondly, if I would be able to figure out the needed torque (Nm) e.g if 0.1 Nm would be the needed torque, then how can I figure out the needed motor strength?
Which of the above four quoted torque values in the above specification would be applicable for my gear construction?
And can you only look at those values, without considering the sizes of the gears?
I mean a weak motor could maybe be compensated (i.e. made stronger) by choosing different gear sizes?