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I'm trying to build a kinetic machine that rotates socket ratchet tools (e.g. https://en.wikipedia.org/wiki/Socket_wrench) to make a bunch of ratchet 'clicking' sounds for an art project. I'm trying to determine the proper stepper motor to do the job so I'm mostly looking at how much torque will be required. I just wanted to go through my calculations to see if I'm estimating the required torque properly. NB: keep in mind I'm not taking into account the friction imposed by the socket clicking mechanism....

I'm modeling the ratchet as a lever with equally distributed weight (M=1.4 kg) and of Length=R=0.475m) to calculate the moment of inertia for a lever: I = (1/3)MR2 = 0.089 kg-m2

If I want to be able to rotate the ratchet, I have to apply acceleration to get it moving from rest. I want it be able to make one rotation per second. alpha = 1(rev/s)*2$\sf\pi$/1s = 2$\sf\pi$

Therefore, I'm estimating that the torque needed to get the ratchet to start moving would be T >= I*alpha = 0.56 N-m . Does this seem right?

Also, I'm wondering how I can reduce the torque constraint. For instance, if I attach an arm appendage to the shaft on the motor so that its pushing/rotating at the edge of the socket wrench, it seems like this would significantly reduce the required torque? How would I factor this into my calculation?

Any advice would be super appreciated! many thanks in advance!

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    $\begingroup$ Mount your ratchet in its intended orientation, tie a string to one end, and use a pulley to apply a force tangentially from a mass hanging downwards. Gradually add weight until the ratchet ‘clicks’. Calculate torque required from length of arm and mass used. Why guess? $\endgroup$ – Jonathan R Swift Jun 29 '20 at 7:25
  • $\begingroup$ Hey @JonathanRSwift thanks for the response! $\endgroup$ – melonhead Jun 29 '20 at 12:55
  • $\begingroup$ First, make sure your torque isn't dominated by the torque needed by the ratchet head. Second, it's unclear if you're rotating just the ratchet, or the handle -- if you're rotating the handle, then the torque required to lift that (and resist it dropping on the downward-traveling side) will dominate. $\endgroup$ – TimWescott Jul 1 '20 at 0:27
  • $\begingroup$ Yeah I figured that might be unclear. I’m just rotating the handle. So I’m trying to figure out what is the maximum mass(load?) of the ratchet as it turns as seen by the stepper (the ratchet will be upright like a hand on a clock and if turning counter clockwise, I assume the max load will be when it’s at 45 and 135 degrees. Any ideas on how to calculate required torque would be greatly appreciated! $\endgroup$ – melonhead Jul 2 '20 at 13:43
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The required torque is independent of the ratchet moment of inertia and its rotation speed. You are confusing speed with acceleration.

Lets say we have enough torque to give us (5 degrees)/s acceleration. In 2 mins it will be spinning at 2pi/s and in 10 minutes it will be at 10pi/s or a frequency of 5 turns/s. So a small acceleration could lead to very fast rotation in time.

It is dependent on the system's total rotattional friction. Any torque slightly bigger than your ratchet friction will turn it and will get it to 1 rotation/s. Then your stepper motor will keep steady the motion.

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  • $\begingroup$ Hey @kamran thanks for the response! Yes, I see what you're saying - I think I was under the impression that you need an acceleration to get the mass to rotate from rest and that this relates to the stall torque of the prospective motor. I'm just trying to find a suitable stepper that provides enough torque to rotate the ratchet $\endgroup$ – melonhead Jun 29 '20 at 12:58
  • $\begingroup$ The acceleration does matter if you care about how quickly you bring the thing up to speed. "Good" steppers will have an inertia vs. acceleration vs. initial speed table in their data sheets -- but I'm going to use that as a definition of "good", so it's circular. $\endgroup$ – TimWescott Jul 1 '20 at 0:26

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