A surgical system includes a drive unit on a support. The drive unit includes motors or other actuators and a plurality of output elements arranged such that operation of each drive unit linearly translates a corresponding one of the output elements. A surgical device has an input subsystem carried at the proximal end of the shaft. The input subsystem includes linearly translatable input elements or pistons. The input and output elements are positioned such that operation of an actuator linearly translates an output element, causing linear translation of a corresponding input element. The input elements deliver linear motion to a rotary conversion system which converts the linear motion to rotary motion and delivers the rotary motion to a shaft of the surgical device, causing axial rolling of the surgical device or its distal end effector. A sterile drape is positionable between the input elements and the output elements.
