Modern surgical procedures involve flexible instruments for both diagnostic and therapeutic purposes. 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 and clearance inside the endoscope, and the compliance of the instrument.
The objective of this paper is to set up a 3-D flexible multibody model for a surgical instrument inside an endoscope to study its translational and rotational behavior. The 3-D model incorporates all the deformations—axial, torsion, and bending—due to its interaction with the surroundings. The interaction due to the contact is defined along the normal and tangential direction at the contact point. The wall stiffness and damping are defined in the normal direction. Friction is defined along the tangential direction. The calculation of the interaction force and moment is explained with an example.
Various simulations were performed to study the behavior of the instrument inside a curved rigid tube. The simulations for the insertion into a 3-D tube defined in a plane were compared for both 2-D and 3-D model. The simulation results from the 3-D model give the same results as the 2-D model. A simulation was carried out for the insertion in a 3-D tube using the 3-D model and the total interaction force on the instrument was analyzed. A 3-D multibody model was set up for the simulation offline rotation. A motion hysteresis of 5° was observed for the chosen configuration.
The 3-D multibody model is able to demonstrate the characteristic behavior of the flexible instrument under different scenarios. Both translational and rotational behavior of the instrument can be characterized for the given set of parameters. The developed model will help us to study the effect of various parameters on the motion and force transmission of the instrument.