Can you make a dynamometer from a partciular kind of motor/generator?

You can make an adequate dynamometer with a loaded generator, estimating the torque from the current, although "real" ones use a torque sensor.

yeah, that could be done.

you won't get a direct engine power reading from the generator's output though as efficiency will likely change dependant on RPM and load,

so you still have to measure torque and RPM then calculate to get the engine's power.

Can't you measure watts from the generator, make necessary corrections for losses, and get the power of the motor?

Well, I'm thinking that you can measure watts consumed in a load from the generator. But you would need to know a lot about the generator characteristics and be able to measure the rotation in rpm. Do you absolutly have to measure torque?

No, efficiency will vary dependant upon operating parameters, for an extreme example consider the case when the generator's output is short-circuited.

for

for a DC motor/generator: voltage =3D speed/speed_constant ( in rpm/V), current =3D current * torque_constant ( in Nm/A)

why shouldn't it still work if shorted?, torque will be determined by the current through the DC resistance of the motor. the voltage across the DC resistance will be determined by the speed.

lots of dynamometers are a simple drum or disc with a know moment of inertia, with speed being sampled and acceleration thus torque calculated from that

-Lasse

Typo: torque = current * torque_constant

For speed, I'd be inclined to measure frequency rather than voltage, with a tacho sensor if necessary (e.g. if the load is a DC generator and the AC component's fundamental can't be reliably separated from its harmonics).

The main issue is that the constants only provide an approximation. Depending upon the precision, that may be enough. Or beyond that, it may suffice to perform a one-time calibration step to measure torque as a function of current and speed (and temperature if that can be measured easily) and use the results to interpret subsequent electrical measurements.

There are two components to the voltage drop: back-EMF and current through the winding resistance. The former increases with speed, the latter with current (and thus torque). The speed constant only determines the former.

When free-running (high speed, low torque), back-EMF dominates; near stall (low speed, high torque), winding resistance dominates.

If voltage = speed/speed_constant was an absolute, any given voltage would produce a fixed speed regardless of load (up to and including welding the axle to the body).

That only works if it's desired (or acceptable) for the speed to vary as the integral of the applied torque (e.g. rolling road scenario). It won't work if you want to measure behaviour under varying loads, or stall torque (although for the latter, a passive load won't work either).