A surgical system includes a surgical instrument that is sensitive to backlash that would adversely affect the transmission of controlled torque and position to the surgical instrument. The surgical instrument is coupled to motors in a surgical instrument manipulator assembly via a mechanical interface. The combination of the mechanical interface and surgical instrument manipulator assembly have low backlash, e.g., less than 0.7 degrees. The backlash is controlled in the surgical instrument manipulator assembly. From the drive output disk in the surgical instrument manipulator assembly to the driven disk of the surgical instrument, the mechanical interface has zero backlash for torque levels used in surgical procedures.