Calculating Extreme Criteria of Eigenvalue Problems of a Medical Robot for Soft Tissue Surgery Using the Multi-objective Optimization

Abstract

Medical robots with an instant center of rotation mechanism in a trocar are used for operating a human body or servicing artificial organs. The result of the work is the development of a multicriteria optimization model of a discussed medical robot, considering safety factor, first eigenfrequency and buckling coefficient as a criteria. The article also analyzes two issues of mechanics, the natural frequency and linear buckling. A discrete mesh model of a novel robot design with ten degrees of freedom and ended with a scalpel was developed based on finite element method. For the given loads and supports, a multi-criteria optimization model was evolved, which was solved by using the response surface method and the multi-objective genetic algorithm. The results section shows the Pareto fronts for the criteria and geometrical dimensions of the kinematic chain. The courses of resonant vibrations and buckling strains were also characterized. The solved optimization model gives correct values for the adopted criteria. The values of resonance were defined, which makes it possible to select mechatronic drive systems in terms of the input they generate. Variability of the resonant vibrations phenomena, as well as shapes and directions of buckling, provide information about the displacements taking place in the medical robot system.