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

Freedom and constraint analysis and optimization

Many mathematical and intuitive methods for constraint analysis of mechanisms have been proposed. In this article we compare three methods. Method one is based on Grüblers equation. Method two uses an intuitive analysis method based on opening kinematic loops and evaluating the constraints at the intersection. Method three uses a flexible multibody modeling approach which facilitates the analysis of complex systems. We demonstrate a visualization method using generalized von Mises stress to show overconstraint modes. A four bar mechanism and a two-degree-of- freedom (DOF) flexure-based mechanism serve as a case study. Briefly the optimization of the location and orientation of releases is discussed. The implementation of the releases in the flexure-based two DOF mechanism is presented.\u