In post #14, the force required to turn the stepper motor shaft against the load will be translated to the rotatable base which is prevented from turning by the attached arm pressing against the load cell. The force measured by the load cell will be proportional to rotational torque by the length of the moment arm measured from the contact point of the arm to the load cell to the center of the stepper motor shaft.
And the OP can easily build and test that sensor!
Exactly. Load cells of various sensitivity are available from the usual suspects and the motor mount can be cobbled together from a stepper motor mount from suppliers like Servo City. The signal conditioning has been beat to death in this forum.
If you yourself are generating the torque with a stepper motor you can probably get by with measuring the current through the motor coils since current is proportional to torque. You'll have to calibrate it somehow, but that's probably the simplest method.
Calibration would be the hard part. Is it linear?
Good question! Will definitely be periodic. I suspect the inductance of the coils will make the torque shape like a sawtooth. Slow rise then quick drop.
I guess you could measure instantaneous torque and then also integrate it over time if you sensed the current.
Thank you Paul. I am trying to measure the torque output from a motor that will be applied through a shaft to precisely turn a bolt. I used the picture to show that there are torque measuring devices that are are not expensive (20 dollars), for example. I want to duplicate this form factor in an arduino environment.
Thank you cedarlakeinstruments. that is a good idea.
Thank you EmilyJane, this is a clever solution, probably the easiest. Yes I will need to have a lever arm to achieve the torque and prevent the stepper motor from turning in the opposite direction. That is where I could measure the torque. I think it would be nicer to have a torque sensor on the shaft, but to deform the shaft enough to cause enough current might be tricky. I am looking to generate 25 Nm...
That might be a cleaner mechanical arrangement but introduces the problem of how to get the electrical signals off the rotating shaft.
That actually may not be much of a problem. The OP wants to use a stepper motor. Each step will have the same torque. I have seen posts that state the stall torque is a bit different than the rotating torque, but may not be significant. The torque measurement only needs a single step of the stepper motor, since they all will have identical torque.
So, lock the output of the test shaft with the strain sensor properly mounted and tell the stepper to attempt one step and measure.
You lost me. Isn't the rotating torque dependent on the load placed on the shaft? in this case, the varying load of a tightening fastener. The stall torque would be when the shaft stopped turning due to the amount of load necessary to stop it.
A stepper motor is designed to have the same torque for each full step taken. You are thinking of a rotating regular DC motor. Do not include inertia with torque!
But, I am still not clear on whet the OP is really after, but seems to be just theoretical, anyway. I doubt is ANYTHING will ever be constructed.
Maybe the same maximum torque available per step but the actual torque produced to turn the shaft will depend on the load.
Maybe. Interesting project nonetheless. 
I do think i'd need a slip ring here. I was thinking that i might get a more accurate reading from the two 45 degree strain gauges on a piece of aluminum, which has more ability to twist and would give more of a readable signal 
Why do you think nothing will ever be constructed? It is constructed with the exception of the shaft torque sensor.
That was @Paul_KD7HB's conclusion, not mine. I was responding to him, not you.
Something has to have force applied to it for torque to exist. What is the range of torque that will be applied to your bolt and will the bolt ever stop from turning? I think you are designing a an electric drill with a slip clutch, or similar electric tool. If the bolt bottoms out and stops turning, and you have a stepper motor, you have found the torque that is the rated torque of the stepper.
The slip rings will make the reading noisier and will require periodic cleaning. Maybe something you can live with though. It's been a few years since I've constructed such a sensor but you used to be able to get premade assemblies with both gauges accurately etched onto the same substrate which will insure better linearity. Unless you are skilled at bonding strain gauges, you might want to get a few spares to practice on. You'll have to find an aluminum shaft with uniform properties although you can probably calibrate almost anything.