Modeling and Design of a Spherical Remote Center-of-Motion Surgical Robot ^†

Remote center-of-motion mechanisms are essential in minimally invasive surgery because they allow surgical instruments or an endoscopic camera to pivot around a trocar entry point while eliminating lateral motion at the incision. This paper presents the design, kinematic modeling, prototype implementation and preliminary evaluation under laboratory conditions of a compact, spherical, remote center-of-motion robot for minimally invasive surgical orientation tasks. The proposed mechanism uses a spherical kinematic architecture actuated by a contra-rotating differential gearbox. This gearbox generates two coaxial output rotations of equal magnitude and opposite direction from a single input, mechanically synchronizing the opposed motion of the two base links and eliminating the need for cable-pulley transmission or dual electronically synchronized motors. A second actuator chain rotates the gearbox assembly around the base axis, thereby decoupling the extension–retraction motion from base-axis rotation. Forward and inverse kinematic formulations were derived for teleoperation of the robot using a 7 degrees of freedom haptic device and for remote center-of-motion orientation control using a 3-axis joystick. A proof-of-concept prototype was developed and integrated with a custom embedded controller, closed-loop motor control, a master-console interface and video feedback loop. The system was evaluated in a phantom-torso setup using a custom endoscopic camera, internal visual markers and an OptiTrack-based measurement of the remote center-of-motion accuracy. The qualitative experiment confirmed functional integration of the mechanical, electronic and software subsystems, while the optical-tracking measurement showed that the pivot constraint was maintained with a mean deviation of 1.69 mm and a root-mean-square deviation of 2.13 mm over the analyzed orientation sweep. The main limitations remain the 1:1 gearbox ratio, limited actuator torque, additively manufactured gearing and the absence of repeated-trial repeatability and full workspace characterization.