A robotic surgical system incorporating a surgical robot attached to a patient's bone by an attachment member, such that motion of the bone induces corresponding motion of the robot, maintaining the robot/bone positional relationship. The robot is supported on a mechanical mounting member attached through a controlled joint to a bed-mounted base element. The controlled joint can alternatively enable the mechanical mounting member to move freely relative to the base element, or its position can be controlled by signal inputs adapted to prevent excessive force being applied in the system. Two modes of operation are available (i) free motion in which the control system is decoupled from the mounting member, which rides freely with patient bone motion, and (ii) servo-controlled motion, in which drive mechanisms control the joint motion to prevent application of excessive force on the patient bone or attachment member.