PREDICATION FOR RELATIVE MOTION OF THE COLONOSCOPE IN COLONOSCOPY

2013 ◽  
Vol 13 (03) ◽  
pp. 1350023 ◽  
Author(s):  
WU BIN CHENG ◽  
MICHAEL A. J. MOSER ◽  
SIVARUBAN KANAGARATNAM ◽  
WEN JUN ZHANG
Keyword(s):  
Frictional Force ◽  
Frictional Contact ◽  
Linear Complementarity ◽  
Intestinal Wall ◽  
Deformable Objects ◽  
Dynamic Friction ◽  
Unilateral Constraints ◽  
Common Procedure ◽  
Mechanical Compliance ◽  
Signorini's Problem

Colonoscopy is common procedure frequently carried out. It is not without its problems, which include looping formation. Looping formation prevents the tip of the colonoscope itself from advancing, thus further probing induces a risk of perforation, significant patient discomfort, and failure of colonoscopy. During colonoscopy, the manipulated colonoscope for intubation in the colon goes through the friction between the colonoscope and the colon. Due to major frictional force, the sigmoidal colon forms looping with the scope during intubation. The interactive frictional force between the colon and the colonoscope is highly complex because of frictional contact between two deformable objects. In this paper, contact force computation was formulated into a linear complementarity problem (LCP) by linearizing Signorini's problem, which was adapted into non-interpenetration with unilateral constraints. Frictional force was computed by the mechanical compliance of finite element method (FEM) models with the consideration of dynamic friction between the colonoscope and the intestinal wall. Furthermore, we presented a mathematical model of the elongation of the colon that predicts the motion of scope relative to the intestinal wall in colonoscopy.

Coefficients of Friction: Static Versus Dynamic

2020 ◽  
Author(s):  
Jack Youqin Huang
Keyword(s):  
Coefficient Of Friction ◽  
Frictional Force ◽  
Inertial Force ◽  
Static Friction ◽  
Theory And Practice ◽  
Dynamic Friction ◽  
Kinetic Friction ◽  
The Coefficient Of Friction ◽  
Static Versus Dynamic ◽  
New Discovery

Abstract This paper deals with the problem of static and dynamic (or kinetic) friction, namely the coefficients of friction for the two states. The coefficient of static friction is well known, and its theory and practice are commonly accepted by the academia and the industry. The coefficient of kinetic friction, however, has not fully been understood. The popular theory for the kinetic friction is that the coefficient of dynamic friction is smaller than the coefficient of static friction, by comparison of the forces applied in the two states. After studying the characteristics of the coefficient of friction, it is found that the comparison is not appropriate, because the inertial force was excluded. The new discovery in the paper is that coefficients of static friction and dynamic friction are identical. Wheel “locked” in wheel braking is further used to prove the conclusion. The key to cause confusions between the two coefficients of friction is the inertial force. In the measurement of the coefficient of static friction, the inertial force is initiated as soon as the testing object starts to move. Therefore, there are two forces acting against the movement of the object, the frictional force and the inertial force. But in the measurement of the coefficient of kinetic friction, no inertial force is involved because velocity must be kept constant.

Modeling and simulation of dynamics of a planar-motion rigid body with friction and surface contact

2017 ◽  
Vol 31 (16-19) ◽  
pp. 1744021 ◽  
Author(s):  
Xiaojun Wang ◽  
Jing Lv
Keyword(s):  
Rigid Body ◽  
Frictional Contact ◽  
Lagrange Equation ◽  
Linear Complementarity ◽  
Friction Model ◽  
Contact Forces ◽  
Planar Motion ◽  
Stick Slip ◽  
Normal Contact ◽  
Friction Law

The modeling and numerical method for the dynamics of a planar-motion rigid body with frictional contact between plane surfaces were presented based on the theory of contact mechanics and the algorithm of linear complementarity problem (LCP). The Coulomb’s dry friction model is adopted as the friction law, and the normal contact forces are expressed as functions of the local deformations and their speeds in contact bodies. The dynamic equations of the rigid body are obtained by the Lagrange equation. The transition problem of stick-slip motions between contact surfaces is formulated and solved as LCP through establishing the complementary conditions of the friction law. Finally, a numerical example is presented as an example to show the application.

Complementarity Problem Formulation of Three-Dimensional Frictional Contact

1991 ◽  
Vol 58 (1) ◽  
pp. 134-140 ◽  
Author(s):  
B. M. Kwak
Keyword(s):  
Complementarity Problem ◽  
Frictional Contact ◽  
Nonlinear Complementarity Problem ◽  
Three Dimensional ◽  
Linear Complementarity Problems ◽  
Problem Formulation ◽  
Linear Complementarity ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Special Case

A general three-dimensional frictional contact problem has been formulated in the form of a complementarity problem in an incremental analysis setting. The derivation is straight forward and very natural. It is shown that the complementarity problem for a three-dimensional case is inherently nonlinear, not like the two-dimensional problem where a linear complementarity problem formulation is possible. The two-dimensional case is a special case of the three-dimensional formulation. Approximate linear complementarity problems of the nonlinear complementarity problem by a Newton approach, or by introducing polyhedral law of friction, have been proposed for efficient numerical implementations.

Hemivariational inequalities modeling electro-elastic unilateral frictional contact problem

2017 ◽  
Vol 23 (3) ◽  
pp. 329-347 ◽  
Author(s):  
Piotr Gamorski ◽  
Stanisław Migórski
Keyword(s):  
Contact Problem ◽  
Frictional Contact ◽  
Coupled System ◽  
Contact Friction ◽  
Hemivariational Inequalities ◽  
Unilateral Constraints ◽  
Frictional Contact Problem ◽  
Uniqueness Of The Solution ◽  
Pseudomonotone Mappings ◽  
Weak Solvability

We study a class of abstract hemivariational inequalities in a reflexive Banach space. For this class, using the theory of multivalued pseudomonotone mappings and a fixed-point argument, we provide a result on the existence and uniqueness of the solution. Next, we investigate a static frictional contact problem with unilateral constraints between a piezoelastic body and a conductive foundation. The contact, friction and electrical conductivity condition on the contact surface are described with the Clarke generalized subgradient multivalued boundary relations. We derive the variational formulation of the contact problem which is a coupled system of two hemivariational inequalities. Finally, for such system we apply our abstract result and prove its unique weak solvability.

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