Modern surgical procedures involve flexible instruments forudboth diagnostic and therapeutic purposes. The implementationudof flexible instruments in surgery necessitates high motion andudforce fidelity, and good controllability of the tip. However,udthe positional accuracy and the force transmission of theseudinstruments are jeopardized by the friction and clearance insideudthe endoscope, and the compliance of the instrument.udThe objective of this paper is to set up a 3-D flexibleudmultibody model for a surgical instrument inside an endoscopeudto study its translational and rotational behavior. The 3-D modeludincorporates all the deformations—axial, torsion, and bending—uddue to its interaction with the surroundings. The interactionuddue to the contact is defined along the normal and tangentialuddirection at the contact point. The wall stiffness and dampingudare defined in the normal direction. Friction is defined along theudtangential direction. The calculation of the interaction force andudmoment is explained with an example.udVarious simulations were performed to study the behavior ofudthe instrument inside a curved rigid tube. The simulations for theudinsertion into a 3-D tube defined in a plane were compared forudboth 2-D and 3-D model. The simulation results from the 3-Dud∗Address all correspondence to this author. Tel.: +31 53 489 5442. Fax: +31ud53 489 3631. Email: j.p.khatait@utwente.nludmodel give the same results as the 2-D model. A simulation wasudcarried out for the insertion in a 3-D tube using the 3-D modeludand the total interaction force on the instrument was analyzed.udA 3-D multibody model was set up for the simulation of fineudrotation. A motion hysteresis of 5◦ was observed for the chosenudconfiguration.udThe 3-D multibody model is able to demonstrate the characteristicudbehavior of the flexible instrument under differentudscenarios. Both translational and rotational behavior of theudinstrument can be characterized for the given set of parameters.udThe developed model will help us to study the effect of variousudparameters on the motion and force transmission of the instrument.
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