Certain aspects relate to systems and techniques for docking medical instruments. For example, a medical system can include an instrument drive mechanism having a drive output that rotates and engages a corresponding drive input on a robotic medical instrument, a motor configured to rotate the drive output, and a torque sensor configured to measure torque imparted on the drive output. The robotic medical instrument can include a pre-tensioned pull wire actuated by the drive input. The system can activate the motor associated with the drive output to rotate the drive output in response to a torque signal from the torque sensor associated with the drive output in order to align the drive output with the drive input.