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Research Papers

Flexible Multibody Modeling of a Surgical Instrument Inside an Endoscope

[+] Author and Article Information
Jitendra P. Khatait

Mechanical Automation and Mechatronics,
Faculty of Engineering Technology,
University of Twente,
AE Enschede 7500, The Netherlands
e-mail: j.p.khatait@utwente.nl

Dannis M. Brouwer

Mechanical Automation and Mechatronics,
Faculty of Engineering Technology,
University of Twente,
AE Enschede 7500, The Netherlands;
Demcon Advanced Mechatronics,
PH Enschede 7521, The Netherlands

J. P. Meijaard

Mechanical Automation and Mechatronics,
Faculty of Engineering Technology,
University of Twente,
AE Enschede 7500, The Netherlands;
Olton Engineering Consultancy,
BC Enschede 7514, The Netherlands

Just L. Herder

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

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the Journal of Computational and Nonlinear Dynamics. Manuscript received November 20, 2012; final manuscript received November 13, 2013; published online December 9, 2013. Assoc. Editor: Aki Mikkola.

J. Comput. Nonlinear Dynam 9(1), 011018 (Dec 09, 2013) (11 pages) Paper No: CND-12-1209; doi: 10.1115/1.4026059 History: Received November 20, 2012; Revised November 13, 2013

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 instrument.

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References

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Khatait, J. P., Brouwer, D. M., Aarts, R. G. K. M., and Herder, J. L., 2013, “Modeling of a Flexible Instrument to Study Its Sliding Behavior Inside a Curved Endoscope,” ASME J. Comput. Nonlinear Dyn., 8(3), p. 031002. [CrossRef]
Jonker, J. B. and Meijaard, J. P., 1990, “SPACAR—Computer Program for Dynamic Analysis of Flexible Spatial Mechanisms and Manipulators,” Multibody Systems Handbook, Springer-Verlag, Berlin, pp. 123–143.
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Figures

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Fig. 1

Model of the instrument with the curved tube

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Fig. 2

The spatial flexible beam element

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Fig. 3

Contact triad at the interacting node Po of the beam when in contact with the Bézier tube

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Fig. 4

Contact triad at the interacting node Po of the beam when in contact with the circular tube. The unit vector eb is normal to the plane containing the arc and is pointing downwards and into the paper.

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Fig. 5

Velocity and force components acting on the instrument at the point of contact P

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Fig. 6

Cross-sections of the tube and the instrument at the point of contact

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Fig. 7

Configuration of the planar tube with the instrument

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Fig. 8

Motion hysteresis for different values of μ

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Fig. 9

The velocity of the distal end vout is compared for different values of μ

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Fig. 10

Motion hysteresis with and without axial load for (μ = 0.2)

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Fig. 11

The velocity of the distal end vout with and without axial load for (μ = 0.2)

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Fig. 12

Comparison of the forces at the proximal end Fin and at the distal end Fout. The force Fcap, based on the capstan equation, is also shown.

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Fig. 13

Comparison of the logarithm of the force ratio at the ends ln(Fin/Fout) with the capstan equation (μ = 0.2,θ = π/2)

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Fig. 14

Difference in angular displacement for different values of (μ = 0.0,0.2,0.5,1.0)

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Fig. 15

Moment at the proximal end along the x-axis Mx for different values of (μ = 0.0,0.2,0.5,1.0)

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Fig. 16

Lag in the angular displacement (θin-θout) for different values of (p = 0.0,0.1,0.2,0.3)

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Fig. 17

Lag in the angular displacement (θin-θout) for different values of precurvature with a radius of (Rc1 = 0.3 m,Rc2 = 1.2 m) and μ, (--) for μ = 0.0, and (—) for μ = 0.5

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Fig. 18

Experimental setup showing the key modules

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Fig. 19

Experimental setup with the extension spring attached to the distal end of the wire

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Fig. 20

Forces and moments in the xyz-directions measured by the FSM

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Fig. 21

Comparison of the input force Fin and the output force Fout with respect to xin

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Fig. 22

Motion hysteresis in translation

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Fig. 23

The logarithm of the ratio of the input force and output force ln(Fin/Fout) with respect to the input displacement

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Fig. 24

Comparison of the logarithm of the force ratio ln(Fin/Fout) with the simulation result

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Fig. 25

Comparison of the rotation of the distal end θout,exp with the simulation result θout,sim for the given input rotation at the proximal end θin

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Fig. 26

Comparison of the rotation of the distal end θout with the simulation result for the given input rotation at the proximal end θin

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