Flexible instruments are increasingly used to carry out complex procedures in many surgical interventions. The instrument tip is remotely controlled by the surgeon. The inherent flexibility of the instrument, coupled with the friction inside the endoscope access channel and the convoluted shape of the endoscope inside the body, makes the control of the instrument tip difficult and complicated. The objective of this paper is to model and to simulate a flexible endoscopic surgical instrument inside a tube and characterize its behaviour. The surgical instrument is modelled as a series of interconnected beam elements. The endoscope channel is modelled as a rigid tube of uniform circular cross-section. A planar model of the flexible instrument with friction is considered in this paper. Normal reaction and friction forces are calculated at the nodes. A Stribeck based continuous friction model with increased friction at low velocity is implemented in the model. Simulations are carried out both for the insertion of the flexible instrument and for fine manipulation. SPACAR, an analysis tool for flexible multibody dynamic systems, has been used for the modelling and simulation. The nodal displacement and force acting at the various nodes have been obtained depending on position and time. The simulation for the fine tip manipulation shows the stick-slip behaviour and hysteresis. The simulation results show the effect of bending rigidity and friction on motion hysteresis.
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