A family of RCM mechanisms: Type synthesis and kinematics analysis

•Propose a novel family of 2-DOF remote center-of-motion parallel mechanism.•The RCM points can be located at variable positions by deforming linkages.•Propose a type synthesis method for RCM and 2T mechanisms.•Propose a combined Jacobian matrix to analyze the complex kinematics.•The non-constrained RCM points contribute to more adaptable MIS manipulators.