Sensitivity analysis of a double-parallelogram based RCM mechanism used for MIS robots

Parallelogram-based remote center-of-motion (RCM) mechanisms are extensively used to design robots for minimally invasive surgery (MIS). For their kinematic modeling, classically, it is assumed that link parameters of the opposite sides of constituting parallelograms are equal which made the RCM an invariant point and simplified the prescribed modeling process. However, link parameter equality does not exist in actual practice due to the inevitable constraints of manufacturing, assembly and testing/measurement, etc. Consequently, the RCM and surgical end-effector deviate from their theoretically designed positions. This paper introduces a novel approach to model the kinematics of parallelogram-based mechanisms by accounting for the error in manufactured link parameters. Additionally, it works out the types, possible ways, order, and nature of the said deviation. Further, a double-parallelogram-based RCM mechanism is adopted to demonstrate the proposed concept, and a prototype of the same is manufactured using laser micromachining and rapid prototyping techniques. Thereafter, the developed kinematic models are validated both analytically and physically. In contrast to the results given by the conventional kinematic modeling approach, the results obtained through the proposed approach and performed experiment showed better agreement with each other. The sensitivity of RCM and surgical end-effector to the inequalities, involved in the manufactured prototype, is revealed through several plots in the Matlab environment. A significant improvement in positional accuracy of the RCM and surgical end-effector have been achieved. It proves the efficacy of the presented method and it is believed that it applies to other parallelogram-based mechanisms as well.