Measuring Torque Through Resistance

I know there are other, possibly easier ways to measure torque applied to/by a motor, but I came up with an idea today. I lack the tools or knowledge to know if it’s possible so I figured I would post it here. It’s a bunch of individual questions.

Here is the situation
An arm on a robot is connected to the motor and I want to know what it takes for the motor to hold it up parallel to the ground.

  1. Could I unplug the motor from the cortex and hook a variable resistor (potentiometer, but not a VEX one) to the leads and adjust it to the point that the resistor prevents that arm from falling due to gravity (it is suspended in air parallel to the ground)?

  2. Would this heat up any/all components in the circuit, and if so, which?

  3. Then, by measuring the resistance of the resistor, could I in some way calculate torque? I don’t know enough about electricity to do this (I got my basic V=IR) but it seems like some kind of limit would be required to calculate it.

  4. What is the voltage and current of this circuit?

  5. Could you possible just measure the voltage before/after the motor and bypass any calculations involving the resistor?

Just an idea

I think the way it works is like this:

  • shorting the motor leads together will slow down a spinning motor.
  • using a variable resistor to short the leads together is like a variable dynamic brake.

But if the motor isn’t spinning, then there is no braking force, so the torque will force the motor to spin, then the brake will keep it from spinning fast.

Does this “dynamic braking effect” have a linear relationship to the speed the motor spins? (The torque on the arm directly affects the amount of voltage, right?)

If so, couldn’t you set the resistor the the right resistance so that these two are equal and the motor would not spin?

Yes the “dynamic braking effect” is linearish with the speed of the motor,
because when using the motor as a generator, the speed determines the voltage,
and the voltage through your resistor affects the current,
and the (back-)torque of the motor is linear with current.
Therefore, when the motor speed is zero, there is no voltage, no current, and no torque, so no braking effect.

(No, the torque on the arm does not directly affect the amount of voltage.
The torque on the arm (minus the back torque from the dynamic brake) is the net torque, and that affects the motor speed, which is linearish with the voltage.)

No, changing the resistor doesn’t make the dynamic brake effect into a static brake effect. Changing the resistor may change the max speed of the falling arm, but it can’t keep it from falling, because at zero speed, there is no brake effect.

If you know the torque vs current line of your motor,
then when you find the current (supplied by battery through cortex) that keeps the arm from falling, you can calculate the arm torque. Or vice versa.

What is your goal?

  • If your goal is to measure the torque, using a balancing weight x arm works pretty well: Put a large sprocket on the arm axle, and add weight to the hanging chain over the sprocket until the arm stays up. Then measure weight * radius of sprocket to get torque.

Yes, that was the goal. I had the idea about the counterbalancing weight but the resistance idea crossed my mind too and I didn’t know enough about the subject to really know if it would work or not. I understand now what you mean by the dynamic effect since the motor (dc generator) outputs a varying level of power as the arm moved. Sounds like a bunch of calculus… Thanks tho!

Would there be any other methods of measuring torque in this situation? I know a spring balance setup should work but I can’t think of any other ways.

The counterbalance idea would work, but to get a fairly precise measurement you would need a kind of “bucket of sand” setup where you fill the counterweight with a substance till the entire system is in equilibrium. The two substances that first come to mind are water and sand, neither of which would I like to bring near a robot. Any other ideas?

Nickels are 5 grams each, and usually have a 100% cash refund rate when you are through with them.

WOW! I didn’t know that! Checked the U.S. mint and found pennies are a rice round figure of 2.5g. Now all I need is a coin counter and a jar of nickels, haha.