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Research Papers

# Improved Force Transmission of a Flexible Surgical Instrument by Combining Input Motion

[+] Author and Article Information
Jitendra P. Khatait

Department of Mechanical Engineering,
Indian Institute of Technology Delhi,
New Delhi 110016, India;
Mechanical Automation and Mechatronics,
Faculty of Engineering Technology,
University of Twente,
Enschede 7500 AE, The Netherlands
e-mail: jpkhatait@mech.iitd.ac.in

Dannis M. Brouwer, Ronald G. K. M. Aarts, Just L. Herder

Mechanical Automation and Mechatronics,
Faculty of Engineering Technology,
University of Twente,
Enschede 7500 AE, The Netherlands

1Corresponding author.

Manuscript received December 6, 2013; final manuscript received December 5, 2014; published online January 12, 2015. Assoc. Editor: Carl Nelson.

J. Med. Devices 9(1), 011009 (Mar 01, 2015) (11 pages) Paper No: MED-13-1289; doi: 10.1115/1.4029418 History: Received December 06, 2013; Revised December 05, 2014; Online January 12, 2015

## Abstract

The force transmission of a flexible instrument through an endoscope is considerably deteriorated due to friction between the contacting surfaces. Friction force along the axial direction can be reduced by combining the translational motion input with rotation. A ratio ζ is defined to measure the reduction in the friction force along the axial direction due to the combined motion input at the proximal end of the instrument. An analytical formula is derived that shows the reduction in the friction force for the combined motion input. A flexible multibody model was setup and various simulations were performed with different motion inputs. The simulation result showed a reduction of 80% in the value of ζ in accordance with the analytical result for the given velocity ratio. Several experiments were performed with constant translational motion input combined with constant and sinusoidal rotational motion input. A maximum reduction of 84% is obtained in the value of ζ against a reduction of 89% calculated analytically. 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.

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## References

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## Figures

Fig. 1

A flexible wire inside a curved rigid tube. The distal end is attached to a spring ksp. The input motion is applied at the proximal end.

Fig. 2

Friction force at contact point P. The unit vectors along the axial direction ea and the circumferential direction ec constitute the tangent plane at the point of contact. The resultant tangential velocity vt makes an angle φ with the unit vector ea. The resultant friction force Ft acts in the opposite direction of vt.

Fig. 3

Velocity profile of the input motion in translation and rotation. The velocity along the axial direction va is combined with the velocity along the circumferential direction vc after t = 1.75 s. The velocities along the circumferential direction are shown for different amplitude A (rad) and frequency f = 1 Hz.

Fig. 4

The ratio ζ for the combined motion as the velocity ratio changes. The sinusoidal rotational motion is combined with the constant axial motion after t = 1.75 s. Several plots of the ratio ζ are shown for sinusoidal rotational motion of different amplitudes A (rad) and frequency f = 1 Hz.

Fig. 5

Configuration of the flexible multibody model of the instrument and of the curved rigid tube used for the simulation. The instrument is defined by interconnected spatial beam elements.

Fig. 6

Experimental setup with 2-DOFs AM, 6-DOFs FSM, and 2-DOFs tip motion measurement module (T3M). The AM provides actuation at the proximal end. The FSM measures all the six components of the interaction force between the instrument and the tube. The T3M performs contactless measurement of the distal end motion.

Fig. 7

Experimental setup with the spring attached to the distal end of the wire. One end of the spring is attached to the base through a string allowing loading in axial direction only.

Fig. 8

Comparison of the input and output forces with and without rotational motion combined with the translational motion. The sinusoidal rotational motion is combined with the constant axial motion after t = 1.75 s.

Fig. 9

Comparison of the value of the ratio ζ with and without rotational motion combined with the translational motion. The sinusoidal rotational motion is combined with the constant axial motion after t = 1.75 s. Analytical result is shown by the dashed line (––).

Fig. 10

Comparison of the value of the ratio ζ corresponding to constant axial velocity va = 5 mm/s combined with the sinusoidal rotational input of different amplitudes A (rad) and frequency f = 1 Hz

Fig. 11

Comparison of the ratio ζ for the combined motion—a rotational speed ωin with a translational motion input vin. The corresponding analytical values of the ratio ζ = cos φ for the combined motion are also shown. (a) Case 1: vin = 0.25 mm/s, (b) case 2: vin = 0.5 mm/s, and (c) case 3: vin = 1.0 mm/s.

Fig. 12

Comparison of the ratio ζ for the translational motion input vin = 0.25 mm/s combined with the sinusoidal rotational input of amplitude A = 2π rad and frequency f = 0.1 Hz. The corresponding analytical value of the ratio ζ is also shown.

Fig. 13

Comparison of the ratio ζ for a translational motion input vin = 0.25 mm/s combined with a sinusoidal rotational input of amplitude A = 2π rad and frequency f = 0.1 Hz. A Fourier fit to the experimental plot and the corresponding shifted analytical plot are also shown. (a) Forward and (b) reverse.

Fig. 14

Comparison of the ratio ζ for the translational motion input vin = 0.5 mm/s combined with the sinusoidal rotational input of amplitude A = 2π rad and frequency f = 0.1 Hz. The corresponding analytical value of the ratio ζ is also shown.

Fig. 15

Comparison of the ratio ζ for a translational motion input vin = 0.5 mm/s combined with a sinusoidal rotational input of amplitude A = 2π rad and frequency f = 0.1 Hz. A Fourier fit to the experimental plot and the corresponding shifted analytical plot are also shown.

Fig. 16

Comparison of the ratio ζ for the translational motion input vin = 0.5 mm/s combined with the sinusoidal rotational input of amplitude A = 3π rad and frequency f = 0.2 Hz. The corresponding analytical value of the ratio ζ is also shown.

Fig. 17

Comparison of the ratio ζ for a translational motion input vin = 0.5 mm/s combined with a sinusoidal rotational input of amplitude A = 3π rad and frequency f = 0.2 Hz. A Fourier fit to the experimental plot and the shifted analytical plot are also shown.

Fig. 18

Comparison of the ratio ζ for the translational motion input vin = 1.0 mm/s combined with the sinusoidal rotational input of amplitude A = 3π rad and frequency f = 0.2 Hz. The corresponding analytical value of the ratio ζ is also shown.

Fig. 19

Comparison of the ratio ζ for a translational motion input vin = 1.0 mm/s combined with a sinusoidal rotational input of amplitude A = 3π rad and frequency f = 0.2 Hz. A Fourier fit to the experimental plot and the corresponding analytical plot are also shown.

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