Remote center-of-motion (RCM) manipulators are a key issue in minimally invasive surgeries (MIS). The existing RCM parallel mechanisms (PMs) can only generate RCM motion based on the invariant RCM. To provide mobility for RCM, this paper designed a new family of RCM PMs with movable RCM that features a double-stage topological structure. Drawing mainly on configuration evolution and Lie-group, a general approach is proposed to design double-stage PMs with movable RCM. Feasible limbs for 2R1T RCM motion are enumerated and used to construct the secondary PM. Type synthesis of the primary PMs that realize movable RCM is accomplished based on the method presented. Different connection styles between the two stages that ensure the geometrical conditions of RCM motion are designed. Using different connection styles, double-stage PMs with movable RCM are constructed. These new RCM PMs can realize precise positioning of RCM by taking advantage of the primary PMs, which indicates their potential application prospects in MIS.
