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

Effect of combined motion on force transmission of a flexible instrument

The force transmission of a flexible instrument through an endoscope is deteriorated due to friction between the contacting surfaces. Friction force along the axial direction can be reduced by combining the translation motion input with rotational motion input at the proximal end of the instrument. The effect of the combined motion on the force transmission is studied for a flexible instrument through a curved rigid tube. A mathematical formula is derived for the reduction in friction force along the axial direction due to the combined motion input. The force transmission of a flexible instrument through a curved rigid tube is analysed using the capstan equation. The ratio of the input and output forces is compared for the combined motion with that of the translation motion only. A ratio ζ is defined to measure the reduction in the friction force along the axial direction due to the combined motion input. The analytical result shows the reduction in the friction force for the combined motion input. A flexible multibody model is set up and various simulations are performed with different motion inputs. The simulation result showed a reduction in the value of ζ in accordance with the analytical result for the given velocity ratio. The results are further validated with the experimental results. The simulation and experimental results show an agreement with the analytical solutions. The knowledge of force transmission with a combination of motions can be used to increase the force fidelity of a flexible instrument in applications like robotic surgery with a flexible 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

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