How Can You Measure Torque in a Servo-Controlled System?

[madgorillaz15]

Homework Statement

Hi guys, I am attempting to experimentally measure torque from two rods connected to a servo. Let's say rod A stays fixed, and the servo, mounted at the end of rod A (at joint J) moves rod B to a certain angle θ with a velocity v. In addition to velocity and angle, I also know that the servo is powered with a constant 5 volts, and in my measurement circuit I'm also measuring the current. Therefore I should know the instantaneous current (I) resulting from any force that opposes the movement of rod A. Also, let's say I can measure the mass and length of rod A, but I would prefer if I didn't have to do that. I hand-drew a picture to try and make this a bit more clear, but please let me know if I need to elaborate at all (I'm not very familiar with servos really, and physics isn't quite my thing).

Homework Equations

I'm thinking I may need power, but a friend told me I may also need moment of inertia (let's call it IA). So I'm not quite sure, but I think these are important:

P=IV
IA=∑mr²
τ=rFsin(θ)

The Attempt at a Solution

I was thinking that if I could obtain a profile for power, I could integrate to get the work, and somehow get torque from that. This is where I'm stuck though. I would really appreciate any help someone could provide me, even if it's just some direction. Is there something I'm not taking into account? What's the easiest way of doing this? Are there multiple ways?

 

[CWatters]

It's not clear why you have two rods that are both moving? Is this a model aircraft servo? They are usually mounted on a fixed plate and have a light weight rotating arm. You could measure the stall torque using a spring scale connected to the moving arm or by attaching a string, pulley and variable weights. However the stall torqur might not be of interest. The speed of the servo is likely to reduce as the load torque increases so you might care to plot speed vs torque. Model servos are quite fast so to measure the speed over say 45 degrees you might need to rig up some micro switches to start/stop an electronic timer. You can calculate output power from speed (angular velocity) and torque data. The input power can be calculated from the voltage and current but the current may not be constant - you might need something like a storage scope or data logger and do some integration/averaging.

If the arm has significant mass and velocity then yes the moment of inertia might be significant.

 

[madgorillaz15]

It's not clear why you have two rods that are both moving? Is this a model aircraft servo? They are usually mounted on a fixed plate and have a light weight rotating arm. You could measure the stall torque using a spring scale connected to the moving arm or by attaching a string, pulley and variable weights. However the stall torqur might not be of interest. The speed of the servo is likely to reduce as the load torque increases so you might care to plot speed vs torque. Model servos are quite fast so to measure the speed over say 45 degrees you might need to rig up some micro switches to start/stop an electronic timer. You can calculate output power from speed (angular velocity) and torque data. The input power can be calculated from the voltage and current but the current may not be constant - you might need something like a storage scope or data logger and do some integration/averaging.

If the arm has significant mass and velocity then yes the moment of inertia might be significant.

Hi CWatters, thanks for sparing your time with a response-I'm still struggling with this problem.

I don't think I explained this well. Both rods will not be moving. You can pretty much imagine rod A being some fixed wall or surface. Only rod B will be moving. In reality, rod A is connected to rod B and via a mechanism I won't get in to; however rod A stays stationary throughout. In the final design, there will be a force that will actually resist the motion of rod B (basically resisting the servo), which is why I'm interested in calculating torque via the parameters I listed. And, yes I am very interested in speed vs torque. Although I'm using a pretty strong servo, I do think the arm will have "significant" mass (around or over 4-5 kg). Let me know if you think I'm not being clear about anything. For reference, I'm currently using an Arduino to control the servo.

Would there be any way to calculate torque from these variables? Are there multiple ways, perhaps? Thanks.

Edit: Thinking about it again, using the length shouldn't be a big deal. Perhaps not the mass either.

 

[CWatters]

If you just have a rod the basic equation is..

Torque = moment of inertia * Angular acceleration.

You can work out the moment of inertia for a rod...

http://en.wikipedia.org/wiki/List_of_moments_of_inertia#Moments_of_inertia

Can you measure the instantaneous acceleration?

I'm afraid I'm away from my PC for several days now so may not be able to follow up.

 

[madgorillaz15]

If you just have a rod the basic equation is..

Torque = moment of inertia * Angular acceleration.

You can work out the moment of inertia for a rod...

http://en.wikipedia.org/wiki/List_of_moments_of_inertia#Moments_of_inertia

Can you measure the instantaneous acceleration?

I'm afraid I'm away from my PC for several days now so may not be able to follow up.

I think I can track the instantaneous acceleration by taking the derivative of velocity.

If the mass wasn't a significant factor, would there be a way to do this just by using velocity/Power/angle etc..? Or another way? I may need an alternative.

 

[CWatters]

If the mass of the rod is very small the torque will also be very small unless there is another load? eg the rod is pulling something?

Another way to estimate torque would be to measure the current..

PowerOut = Efficiency * PowerIn

PowerOut = TorqueOut * AngularVelocityOut
PowerIn = Current * Voltage

So..

TorqueOut * AngularVelocityOut = Efficiency * Current * Voltage

rearrange..

TorqueOut = Efficiency * Current * Voltage / AngularVelocityOut

The big unknown is the Efficiency. However you could try applying a known torque (eg a load) and measure everything else to calculate the efficiency.