3-D Multibody Modeling of a Flexible Surgical Instrument Inside an Endoscope

Modern surgical procedures involve flexible instruments for\ud both diagnostic and therapeutic purposes. The implementation\ud of flexible instruments in surgery necessitates high motion and\ud force fidelity, and good controllability of the tip. However,\ud the positional accuracy and the force transmission of these\ud instruments are jeopardized by the friction and clearance inside\ud the endoscope, and the compliance of the instrument.\ud The objective of this paper is to set up a 3-D flexible\ud multibody model for a surgical instrument inside an endoscope\ud to study its translational and rotational behavior. The 3-D model\ud incorporates all the deformations—axial, torsion, and bending—\ud due to its interaction with the surroundings. The interaction\ud due to the contact is defined along the normal and tangential\ud direction at the contact point. The wall stiffness and damping\ud are defined in the normal direction. Friction is defined along the\ud tangential direction. The calculation of the interaction force and\ud moment is explained with an example.\ud Various simulations were performed to study the behavior of\ud the instrument inside a curved rigid tube. The simulations for the\ud insertion into a 3-D tube defined in a plane were compared for\ud both 2-D and 3-D model. The simulation results from the 3-D\ud ∗Address all correspondence to this author. Tel.: +31 53 489 5442. Fax: +31\ud 53 489 3631. Email: [email protected]\ud model give the same results as the 2-D model. A simulation was\ud carried out for the insertion in a 3-D tube using the 3-D model\ud and the total interaction force on the instrument was analyzed.\ud A 3-D multibody model was set up for the simulation of fine\ud rotation. A motion hysteresis of 5◦ was observed for the chosen\ud configuration.\ud The 3-D multibody model is able to demonstrate the characteristic\ud behavior of the flexible instrument under different\ud scenarios. Both translational and rotational behavior of the\ud instrument can be characterized for the given set of parameters.\ud The developed model will help us to study the effect of various\ud parameters on the motion and force transmission of the instrument

A two-node superelement description for modelling of flexible complex-shared beam-like components

In this paper, a two-node superelement description is proposed for use in multibody models which is capable of modelling flexible complex-shaped beam-like components. Assuming that the deformations with respect to a co-rotational frame remain small, substructuring methods may be used to obtain a dynamical model with reduced mass and stiffness matrices from a linear finite element model. The development of a two-node superelement is established by linking a reduced linear finite element model with a non-linear finite beam element capable of describing large rigid body motion and small elastic deformations. This is achieved by equating their potential and kinetic energies. Two examples are included. A simulation of the spin-up motion of a flexible beam with uniform cross-section and a similar simulation in which the beam is simultaneously excited in the out-of-plane direction. Both examples show good\ud agreement with simulations obtained using non-linear finite beam elements