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.