2R: The earliest proposed 2R parallel RCM mechanism was the PantoScope for force reflection in 1997 with two limbs—an RPaR-RRRRR (one limb consisting of a revolute joint, a parallelogram joint and a revolute joint in serial; the other limb consists of five revolute joints in serial), with the RCM point located at the intersection of the two revolute joint axes fixed on the base [
53]. The PantoScope had a simple structure, and along with a parallelogram mechanism, it inspired the design of other parallel RCM mechanisms with two limbs. Li et al. [
54] designed a URR-UPR (one limb consisting of a universal joint and two revolute joints; the other limb consisting of a universal joint, a prismatic joint, and a revolute joint) RCM mechanism, which could be developed into a 4-DOF compact hybrid robotics wrist by adding serial joints to meet various MIS demands. Realpe et al. [
55] proposed an RPaRRC-RPaR (C: column joint) RCM tensegrity mechanism, which could be reconfigured and perform decoupled stiffness modulation. Wang et al. [
56] designed a metamorphic RCM mechanism with UPaR‒UPa limbs and analyzed it using a constrained screw multiset, which had three motion branches with 2-, 1-, and 1-DOF RCMs. The actuations of these 2-DOF RCM mechanisms with two limbs were always the two revolute joints fixed on a base, and their workspace was almost symmetrical. Their RCM points were always located at the intersection of axes of revolute joints fixed on the base. Not only 2-DOF RCM mechanisms but most RCM mechanisms, both serial and parallel, must locate the RCM point at the intersection of revolute joint axes fixed on a base or as actuations. The constraint must consider specific robot design and deployment for practical applications to avoid collision, especially for complex MIS. To overcome the RCM point position constraint, Wang et al. [
57] analyzed basic planar parallelogram mechanism using screw theory to clarify the RCM principle and proposed a 2-DOF RCM mechanism by mapping the structure of a planar parallelogram to spatial mechanism based on a 3-UU parallel mechanism (Fig.8). The RCM point could be located at any position by reshaping the linkages without constraints. On the basis of this principle, Wang et al. [
58] proposed a family of 2-DOF RCM mechanisms, and a new type of synthesis method by coupling two 2-DOF translation parallel mechanisms with a spherical workspace and redundant linkages by multiple 2-DOF RCM mechanisms with RCM points being able to be located at any position could be generated. As for the 2-DOF parallel RCM mechanisms with the simplest structure, another famous type of 2-DOF RCM mechanism has been developed, namely, the 5R spherical mechanism, which was initially designed for a force-reflecting manipulator with spherical rotation motion, not as an RCM [
59,
60]. It rotated on a spherical surface and around the center of a sphere, which satisfied the RCM definition. Many studies have been conducted on 5R spherical mechanisms regarding workspace, singularity, decoupled actuation, and motion/force transmission to obtain better performance [
61–
65]. However, a common 5R spherical RCM mechanism issue is that the workspace is limited by the revolute joint angle and the RCM points must be located at the intersection of all revolute joints inside the mechanism. A new parallel RCM mechanism for an ear and facial surgical application was proposed, coupling a parallelogram RCM mechanism and a spherical mechanism [
66]. The decoupled RCM mechanism could deploy the actuation on the base and locate the RCM point outside the mechanism, which gave it a lower inertia and more flexibility for the application. For the compliant parallel 2R RCM mechanism, a 2-DOF large-range compliant RCM stage with input/output decoupling was presented based on an
n pseudo-rigid-body-model method and compliance matrix method, as shown in Fig.8 [
67].