A torque-transmitting, torque-sensing system has a first rotatable shaft which can be shifted radially in two orthogonally-displaced directions to be precisely concentric with a second rotatable shaft, has a first coupling element which is rotatable with but which is movable axially relative to one of those rotatable shafts, has a biasing means which urges the first coupling element for movement axially in one direction relative to the one rotatable shaft, has a second coupling element which is rotatable with the other rotatable shaft, and has a surface on one of those coupling elements which coacts with a complementary surface on the other of those coupling elements to enable those coupling elements to transmit torque from that rotatable shaft which is the driving shaft to that rotatable shaft which is the driven shaft while permitting the first coupling element to respond to a predetermined increase in rotation resistance of the driven shaft to move axially in the opposite direction relative to the one rotatable shaft.