Robot-assisted minimally invasive surgery (MIS) has shown tremendous advances over the traditional technique. A crucial challenge for developing a MIS robot is the kinematic design of the remote center-of-motion (RCM) mechanism. In this paper, a class of spatial RCM mechanism is analyzed. They are obtained by generating virtual parallelograms. The main process is to construct a line that passes through a fixed point under the mechanical constraint. The axis of the surgical tool is then constrained to parallel with that line. Hence, due to the geometrical feature of the parallel lines, the axis of the surgical tool will always pass through a fixed point, i.e., the RCM point. Due to the specially designed structure, the fixed point does not need to be physically belonging to the mechanism. The geometrical analysis method is employed to obtain the closed-form solution of the forward kinematics of the proposed mechanisms. Due to the high load capacity of parallel mechanism, the robots based on the proposed RCM mechanisms have promising applications as an external positioner to be used in robotic single-port surgeries.
