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Modeling forces applied to scissors during cutting of biological materials is useful for surgical simulation. Previous approaches to haptic display of scissor cutting are based on recording and replaying measured data. This paper presents an analytical model based on the concepts of contact mechanics and fracture mechanics to calculate forces applied to scissors during cutting of a slab of material. The model considers the process of cutting as a sequence of deformation and fracture phases.

During deformation phases, forces applied to the scissors are calculated from a torque-angle response model synthesized from measurement data multiplied by a ratio that depends on the position of the cutting crack edge and the curve of the blades. Using the principle of conservation of energy, the forces of fracture are related to the fracture toughness of the material and the geometry of the blades of the scissors.

The forces applied to scissors generally include high-frequency fluctuations. We show that the analytical model accurately predicts the average applied force. The cutting model is computationally efficient, so it can be used for real-time computations such as haptic rendering. Experimental results from cutting samples of paper, plastic, cloth, and chicken skin confirm the model, and the model is rendered in a haptic virtual environment.

INTRODUCTION Modeling forces applied to surgical instruments is useful for surgical simulations and surgical planning []. Surgical simulators can provide a safe effective training environment, potentially reducing the use of human cadavers and animals []. Haptic technology is enabling the development of training simulators that allow users to feel tissue through virtual instruments. Realistic haptic feedback is expected to increase the training effectiveness of surgical simulators [], [].