A robotically-controlled drive unit includes a torque sensing mechanism to measure the torque applied to a rotatable body that is configured to tension an actuation tendon to operate robotic surgical tools and catheters. The drive unit includes a motor unit that generates an output torque in response to a robotic control signal. A beam element generates a reactive torque in response to the output torque generated by the rotor, and a force sensor detects the reactive torque and communicates the magnitude of the reactive torque to a robotic controller. The drive unit may further include a mechanism to perform bi-directional torque sensing, examples of which include additional force sensors and compression springs.