The use of robotics to enhance visualization and tissue manipulation capabilities is contributing to the advancement of minimally invasive surgery (MIS). For the development of surgical robot manipulators, the use of advanced dynamic control is an important aspect at the design stage to determine the driving forces and/or torques which must be exerted by the actuators in order to produce a desirable trajectory of the end effector. Therefore, this study focuses on the generation of inverse dynamic models for a spherical bevel-geared mechanism called CoBRASurge (Compact Bevel-geared Robot for Advanced Surgery), which is used as a surgical tool manipulator. For given typical trajectories of end effectors in clinical experiments, the motion of each element in the mechanism can be derived using the inverse kinematic equations. The driving torques exerted by actuators can be determined according to the presented inverse dynamic formulations. The simulation results of CoBRASurge reveal the nature of the driving torques in spherical bevel-geared mechanisms. Such models can be used for the design of advanced dynamic control systems, including gravity compensation and haptic interfaces for enhanced surgical functionality. In addition, sensitivity analysis of mass contribution has been performed to evaluate the effect of individual elements on the peak driving torques, which provides a solid guideline for the design of the next-generation CoBRASurge prototype. The present dynamic modeling methodology also presents a general dynamic analysis approach for other spherical articulated linkage mechanisms.