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

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

Flexible multibody modeling of a surgical instrument inside an endoscope

The implementation of flexible instruments in surgery necessitates high motion and force fidelity and good controllability of the tip. However, the positional accuracy and the force transmission of these instruments are jeopardized by the friction, the clearance, and the inherent compliance of the instrument. The surgical instrument is modeled as a series of interconnected spatial beam elements. The endoscope is modeled as a rigid curved tube. The stiffness, damping, and friction are defined in order to calculate the interaction between the instrument and the tube. The effects of various parameters on the motion and force transmission behavior were studied for the axially-loaded and no-load cases. The simulation results showed a deviation of 1.8% in the estimation of input force compared with the analytical capstan equation. The experimental results showed a deviation on the order of 1.0%. The developed flexible multibody model is able to demonstrate the characteristic behavior of the flexible instrument for both the translational and rotational input motion for a given set of parameters. The developed model will help us to study the effects of various parameters on the motion and force transmission of the instrumen