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Research Papers

Modeling of a Flexible Instrument to Study its Sliding Behavior Inside a Curved Endoscope

[+] Author and Article Information
Jitendra P. Khatait

e-mail: j.p.khatait@utwente.nl

Just L. Herder

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

1Address all correspondence to this author.

Contributed by the Design Engineering Division of ASME for publication in the Journal of Computational and Nonlinear Dynamics. Manuscript received September 1, 2011; final manuscript received March 7, 2012; published online October 30, 2012. Assoc. Editor: Aki Mikkola.

J. Comput. Nonlinear Dynam 8(3), 031002 (Oct 30, 2012) (10 pages) Paper No: CND-11-1146; doi: 10.1115/1.4007539 History: Received September 01, 2011; Revised March 07, 2012

Flexible instruments are increasingly used to carry out surgical procedures. The instrument tip is remotely controlled by the surgeon. The flexibility of the instrument and the friction inside the curved endoscope jeopardize the control of the instrument tip. Characterization of the surgical instrument behavior enables the control of the tip motion. A flexible multibody modeling approach was used to study the sliding behavior of the instrument inside a curved endoscope. The surgical instrument was modeled as a series of interconnected planar beam elements. The curved endoscope was modeled as a rigid curved tube. A static friction-based contact model was implemented. The simulations were carried out both for the insertion of the flexible instrument and for fine manipulation. A computer program (SPACAR) was used for the modeling and simulation. The simulation result shows the stick-slip behavior and the motion hysteresis because of the friction. The coefficient of friction has a large influence on the motion hysteresis, whereas the bending rigidity of the instrument has little influence.

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Figures

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Fig. 1

Model of the instrument with the curved tube at the beginning of insertion

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Fig. 2

Cubic Bézier curve defined by four points

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Fig. 3

Normal distance between a point Po and a Bézier curve. Orthogonal vectors are also shown at the contact node.

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Fig. 4

Three regions of contact

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Fig. 5

Modeling of the contact between the beam and inner wall of the tube

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Fig. 6

Comparison of the continuous friction model based on the Coulomb model for various values of the velocity coefficient cv

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Fig. 7

Normal and tangential directions defined at the point of contact

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Fig. 8

Input motion profile for the insertion

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Fig. 9

Time history of the forces exerted at nodes 1 and 2 while inserting in the circular tube (μ = 0.0). Here, F1 and F2 are the total interaction forces acting at different time instances at nodes 1 and 2, respectively.

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Fig. 10

Time history of the forces exerted at first four distal nodes while inserting in circular tube (μ = 0.0)

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Fig. 11

Time history of the forces exerted at nodes 1 and 2 while inserting in a Bézier tube (μ = 0.0). Here, F1 and F2 are the total interaction forces acting at different time instances at nodes 1 and 2, respectively.

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Fig. 12

Time history of the forces exerted at the first four distal nodes while inserting in a Bézier tube (μ = 0.0)

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Fig. 13

Total force exerted on the instrument while inserting in a circular tube (μ = 0.5). The total force is compared for different numbers of elements.

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Fig. 14

Motion hysteresis in the case of a circular tube (μ = 0.2)

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Fig. 15

Comparison of the translation velocity at input and output (μ = 0.2)

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Fig. 16

Effect of the friction on the motion hysteresis in a Bézier tube

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Fig. 17

Effect of the bending rigidity on the motion hysteresis in a Bézier tube (μ = 0.5)

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Fig. 18

The planar flexible beam element

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