A robotic surgical system includes a sterile surgical instrument, a robotic surgical manipulator, and a sterile drape covering at least a portion of the robotic surgical manipulator. The surgical instrument has a proximal interface and a distal end effector. The proximal interface includes a gimbal assembly with two intersecting rotational axes coupled to the distal end effector. The robotic surgical manipulator has a drive plate that bears against the gimbal assembly. The drive plate has two degrees of rotational freedom about a center of motion that is coincident with an intersection of the axes of the gimbal assembly. The sterile drape includes a sterile sheet covers at least a portion of the robotic surgical manipulator, a frame bonded to the sterile sheet, an instrument interface that covers the drive plate of the robotic surgical manipulator, and a diaphragm that connects the instrument interface to the frame.