Constant torque with stepper motors

I am trying to find a way to apply constant torque to a system so I thought maybe a stepper motor will do it. I have used these things a lot in systems but never got to directly talked to them. I know the principle. So if I exceed the maximal torque, the rotor, which is held in position, will slip. Say if I let the motor run as fast as it can and try to turn something with resistive torque applied, would it turn with a more or less constant torque like a wrench with torque setting?

Along this line, if I vary the current through the coils, will I be able to adjust this amount of torque? Is this project doable? Thanks.

A stepping motor produces most torque when it is stationary. As it speeds up the torque drops off until it reaches a point where it can no longer turn, then it skips steps and finally stalls.
The problem with trying to get more current down it is that as you go faster there is less time for the current to rise. An inductor is like a capacitor in this respect as it adds a delay. It takes time for the current to build up and the faster you go the less time you have. One trick is to up the voltage and use a chopping regulator driver to get a better top speed but you still end up with a doping torque.
You might be better off using a geared stepping motor.

A plain permanent magnet commutated DC electric motor would serve better - torque is dependent on current, so feeding the motor a constant current should produce a pretty constant torque (until you exceed the available supply voltage.) Feeding constant current would typically done via a software feedback loop that reads the current value and adjusts a PWM drive (often done to limit current anyway)

Stepper motor torque depends upon the precise position within the step cycle, and is not easily measured electronically.

Thanks Mike. My understanding of stepper motor is apparently lacking:)
The DC motor start to sound better now. Thanks Mark.