I am aware of golf-teaching aids, which are supposed to guide you through the correct swing.

I would like to see a sort of robot, which you would strap yourself into, and it would have servo-motors or something so as to guide you through the correct movement. It would be general-purpose, not confined to one sport. The teacher would get into a similar rig, and record the movement; the student's rig would be a play-back.

Has anyone invented such a thing?

To minimize the amount of specialized hardware, consider this: The student would stick on some electrodes that could give a shock, or buzzers that could give a palpable signal. A digital camera (or two) would observe the student, figure out the 3-D movement, and compare it to the model. Deviations would result in a signal. For example, if your hand is too high, you'd get a signal on the back of your wrist.