Robot-assisted minimally invasive surgery (MIS) has shown tremendous advances over the traditional technique. The remote center-of-motion (RCM) mechanism is one of the main components of a MIS robot. However, the widely used planar RCM mechanism, with double parallelogram structure, requires an active prismatic joint to drive the surgical tool move in–out of the patient’s body cavity, which restricts the dexterity and the back-drivability of the robot to some extent. To solve this problem, a two degree-of-freedom (DOF) planar RCM mechanism type synthesis method is proposed. The basic principle is to construct virtual double parallelogram structure at any instant during the mechanism movements. Different with the existing ones, both of the actuated joints of the obtained RCM mechanism are revolute joints. Combining the proposed mechanism with a revolute joint whose axis passes through the RCM point to drive the whole mechanism out of the plane, the spatial RCM mechanisms to manipulate surgical tool in three-dimension (3D) space can be obtained; and the 3D RCM mechanism can be used for manipulating multi-DOF instruments in a robot-assisted MIS or can be used as an external positioner in robotic single-port surgeries.