[Physics] Arduino Servo Torque Calculation for a Automated Telescope

Question

I have a class project where I am using several servos to control a telescope. I'm trying to figure out the torque needed to rotate the tilt of the telescope with a servo from 0 to 90 degrees. I haven't come across any similar problems online that have examples. I know that the one I am currently using is close, but just isn't enough to lift the telescope up by itself.

I currently have an HS-311 (51oz-in) that isn't working. The servo I would potentially purchase in place is the HS-645MG (133oz-in).

From the experiments I've done, I've been able to rotate a ~6oz object almost perfectly, but the ~12oz telescope is too much. I assume that if I get the 133oz-in servo, it will be able to rotate 2.6 times the mass or 15.6oz in this case.

Here is a modified diagram of the original setup. The circular disc on the servo tip is 1" in diameter.

And here is what it looks like assembled (without telescope attached yet).

Answer 1

counterweights only help the servo in one direction if the telescope is already mounted on its cg. also, telescope completely vertical is when torque required to turn it is maximum.

you can either bring the scope closer to the axis of rotation by shortening the armature (it already looks as short as it can be), add gears to decrease the gear ratio (telescope slows down by this ratio, but torque increases by this ratio).

starting from scope being completely vertical, activate the servo so it wants to go anticlockwise. it shouldnt have the torque to accomplish this. now manually raise the scope until the servo does has torque to move the scope on its own. the angle where this happens is the critical angle. Do $51\over\cos\theta$ to calculate what torque you need for a new servo that can do this on its own.

my advice would be to use gears. specifically worm gear for the driver (servo). which will protect the system from failing like above (if the critical angle is reached it wont fall over, just stall in position). worm gears have the advantage that they can only be driven from the worm, and for example, cannot be forced to turn by pushing on the telescope, bumping into it etc. the disadvantage is the very low gear ratio (slow but high torque). and you would need a motor not servo..