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NASA NTRS2005

The Application of Infrared Thermographic Inspection Techniques to the Space Shuttle Thermal Protection System

The Nondestructive Evaluation Sciences Branch at NASA s Langley Research Center has been actively involved in the development of thermographic inspection techniques for more than 15 years. Since the Space Shuttle Columbia accident, NASA has focused on the improvement of advanced NDE techniques for the Reinforced Carbon-Carbon (RCC) panels that comprise the orbiter s wing leading edge. Various nondestructive inspection techniques have been used in the examination of the RCC, but thermography has emerged as an effective inspection alternative to more traditional methods. Thermography is a non-contact inspection method as compared to ultrasonic techniques which typically require the use of a coupling medium between the transducer and material. Like radiographic techniques, thermography can be used to inspect large areas, but has the advantage of minimal safety concerns and the ability for single-sided measurements. Principal Component Analysis (PCA) has been shown effective for reducing thermographic NDE data. A typical implementation of PCA is when the eigenvectors are generated from the data set being analyzed. Although it is a powerful tool for enhancing the visibility of defects in thermal data, PCA can be computationally intense and time consuming when applied to the large data sets typical in thermography. Additionally, PCA can experience problems when very large defects are present (defects that dominate the field-of-view), since the calculation of the eigenvectors is now governed by the presence of the defect, not the "good" material. To increase the processing speed and to minimize the negative effects of large defects, an alternative method of PCA is being pursued where a fixed set of eigenvectors, generated from an analytic model of the thermal response of the material under examination, is used to process the thermal data from the RCC materials. Details of a one-dimensional analytic model and a two-dimensional finite-element model will be presented. An overview of the PCA process as well as a quantitative signal-to-noise comparison of the results of performing both embodiments of PCA on thermographic data from various RCC specimens will be shown. Finally, a number of different applications of this technology to various RCC components will be presented.

Cramer, K. E.↗

NASA NTRS2006

Imperfection and Thickness Measurement of Panels Using a Coordinate Measurement Machine

This paper summarizes the methodology used to measure imperfection and thickness variation for flat and curved panels using a Coordinate Measurement Machine (CMM) and the software program MeasPanel. The objective is to provide a reference document so that someone with a basic understanding of CMM operation can measure a panel with minimal training. Detailed information about both the measurement system setup and computer software is provided. Information is also provided about the format of the raw data, as well as how it is post-processed for use in finite-element analysis.

Thornburgh, Robert P.↗

NASA NTRS2005

Forecasting of Storm Surge Floods Using ADCIRC and Optimized DEMs

Increasing the accuracy of storm surge flood forecasts is essential for improving preparedness for hurricanes and other severe storms and, in particular, for optimizing evacuation scenarios. An interactive database, developed by WorldWinds, Inc., contains atlases of storm surge flood levels for the Louisiana/Mississippi gulf coast region. These atlases were developed to improve forecasting of flooding along the coastline and estuaries and in adjacent inland areas. Storm surge heights depend on a complex interaction of several factors, including: storm size, central minimum pressure, forward speed of motion, bottom topography near the point of landfall, astronomical tides, and most importantly, maximum wind speed. The information in the atlases was generated in over 100 computational simulations, partly by use of a parallel-processing version of the ADvanced CIRCulation (ADCIRC) model. ADCIRC is a nonlinear computational model of hydrodynamics, developed by the U.S. Army Corps of Engineers and the US Navy, as a family of two- and three-dimensional finite element based codes. It affords a capability for simulating tidal circulation and storm surge propagation over very large computational domains, while simultaneously providing high-resolution output in areas of complex shoreline and bathymetry. The ADCIRC finite-element grid for this project covered the Gulf of Mexico and contiguous basins, extending into the deep Atlantic Ocean with progressively higher resolution approaching the study area. The advantage of using ADCIRC over other storm surge models, such as SLOSH, is that input conditions can include all or part of wind stress, tides, wave stress, and river discharge, which serve to make the model output more accurate.

Valenti, Elizabeth↗

NASA NTRS2006

Time-dependent strains and stresses in a pumpkin balloon

This paper presents a study of pumpkin-shaped superpressure balloons, consisting of gores made from a thin polymeric film attached to high stiffness, meridional tendons. This type of design is being used for the NASA ULDB balloons. The gore film shows considerable time-dependent stress relaxation, whereas the behaviour of the tendons is essentially time-independent. Upon inflation and pressurization, the "instantaneous", i.e. linear-elastic strain and stress distribution in the film show significantly higher values in the meridional direction. However, over time, and due to the biaxial visco-elastic stress relaxation of the the material, the hoop strains increase and the meridional stresses decrease, whereas the remaining strain and stress components remain substantially unchanged. These results are important for a correct assessment of the structural integrity of a pumpkin balloon in a long-duration mission, both in terms of the material performance and the overall stability of the shape of the balloon. An experimental investigation of the time dependence of the biaxial strain distribution in the film of a 4 m diameter, 48 gore pumpkin balloon is presented. The inflated shape of selected gores has been measured using photogrammetry and the time variation in strain components at some particular points of these gores has been measured under constant pressure and temperature. The results show good correlation with a numerical study, using the ABAQUS finite-element package, that includes a widely used model of the visco-elastic response of the gore material:

Gerngross, T.↗

NASA NTRS1998

Ice-shelf Dynamics Near the Front of Filchner-Ronne Ice Shelf, Antarctica, Revealed by SAR Interferometry: Model/Interferogram Comparison

We compare Earth Remote Sensing (ERS) satellite synthetic-aperture radar (SAR) interferograms with artificial interferograms constructed using output of a finite-element ice-shelf flow model to study the dynamics of Filchner-Ronne Ice Shelf (FRIS) near Hemmen Ice Rise (HIR) where the iceberg-calving front itersects Berkener Island (BI).

Ice-shelf Filchner-Ronne Antarctica SAR Interferom↗

NASA NTRS2006

Three-Dimensional Field Solutions for Multi-Pole Cylindrical Halbach Arrays in an Axial Orientation

This article presents three-dimensional B field solutions for the cylindrical Halbach array in an axial orientation. This arrangement has applications in the design of axial motors and passive axial magnetic bearings and couplers. The analytical model described here assumes ideal magnets with fixed and uniform magnetization. The field component functions are expressed as sums of 2-D definite integrals that are easily computed by a number of mathematical analysis software packages. The analysis is verified with sample calculations and the results are compared to equivalent results from traditional finite-element analysis (FEA). The field solutions are then approximated for use in flux linkage and induced EMF calculations in nearby stator windings by expressing the field variance with angular displacement as pure sinusoidal function whose amplitude depends on radial and axial position. The primary advantage of numerical implementation of the analytical approach presented in the article is that it lends itself more readily to parametric analysis and design tradeoffs than traditional FEA models.

Thompson, William K.↗

NASA NTRS2005

Distributed-feedback Terahertz Quantum-cascade Lasers with Laterally Corrugated Metal Waveguides

We report the demonstration of distributed-feedback terahertz quantum-cascade lasers based on a first-order grating fabricated via a lateral corrugation in a double-sided metal ridge waveguide. The phase of the facet reflection was precisely set by lithographically defined facets by dry etching. Single-mode emission was observed at low to moderate injection currents, although multimode emission was observed far beyond threshold owing to spatial hole burning. Finite-element simulations were used to calculate the modal and threshold characteristics for these devices, with results in good agreement with experiments.

Williams, Benjamin S.↗

NASA NTRS2004

Mid-frequency Band Dynamics of Large Space Structures

High and low intensity dynamic environments experienced by a spacecraft during launch and on-orbit operations, respectively, induce structural loads and motions, which are difficult to reliably predict. Structural dynamics in low- and mid-frequency bands are sensitive to component interface uncertainty and non-linearity as evidenced in laboratory testing and flight operations. Analytical tools for prediction of linear system response are not necessarily adequate for reliable prediction of mid-frequency band dynamics and analysis of measured laboratory and flight data. A new MATLAB toolbox, designed to address the key challenges of mid-frequency band dynamics, is introduced in this paper. Finite-element models of major subassemblies are defined following rational frequency-wavelength guidelines. For computational efficiency, these subassemblies are described as linear, component mode models. The complete structural system model is composed of component mode subassemblies and linear or non-linear joint descriptions. Computation and display of structural dynamic responses are accomplished employing well-established, stable numerical methods, modern signal processing procedures and descriptive graphical tools. Parametric sensitivity and Monte-Carlo based system identification tools are used to reconcile models with experimental data and investigate the effects of uncertainties. Models and dynamic responses are exported for employment in applications, such as detailed structural integrity and mechanical-optical-control performance analyses.

dynamics↗

NASA NTRS2006

Predicting Tail Buffet Loads of a Fighter Airplane

Buffet loads on aft aerodynamic surfaces pose a recurring problem on most twin-tailed fighter airplanes: During maneuvers at high angles of attack, vortices emanating from various surfaces on the forward parts of such an airplane (engine inlets, wings, or other fuselage appendages) often burst, immersing the tails in their wakes. Although these vortices increase lift, the frequency contents of the burst vortices become so low as to cause the aft surfaces to vibrate destructively. Now, there exists a new analysis capability for predicting buffet loads during the earliest design phase of a fighter-aircraft program. In effect, buffet pressures are applied to mathematical models in the framework of a finite-element code, complete with aeroelastic properties and working knowledge of the spatiality of the buffet pressures for all flight conditions. The results of analysis performed by use of this capability illustrate those vibratory modes of a tail fin that are most likely to be affected by buffet loads. Hence, the results help in identifying the flight conditions during which to expect problems. Using this capability, an aircraft designer can make adjustments to the airframe and possibly the aerodynamics, leading to a more robust design.

Moses, Robert W.↗

NASA NTRS2006

NASA Tech Briefs, May 2006

T-Shaped Emitter Metal Structures for HBTs Rigorous Estimation of SNR of a PSK Communication Link Advanced Ka-Band Transceiver With Monopulse Tracking EMI Filters for Low-Temperature Applications Lightweight Electronic Camera for Research on Clouds Pilot Weather Advisor System Waveguide Power-Amplifier Module for 80 to 150 GHz Better Back Contacts for Solar Cells on Flexible Substrates Topics covered include:Tunable, Highly Stable Lasers for Coherent Lidar; Improved Photon-Emission-Microscope System; Program Synthesizes UML Sequence Diagrams; Aspect-Oriented Subprogram Synthesizes UML Sequence Diagrams; Updated Computational Model of Cosmic Rays Near Earth; Software for Alignment of Segments of a Telescope Mirror; Simulation of Dropping of Cargo With Parachutes; DAVE-ML Utility Program; Robust Control for the Mercury Laser Altimeter; Thermally Stable Piezoelectric and Pyroelectric Polymers; Combustion Synthesis of Ca3(PO4)2 Net-Shape Surgical Implants; Stochastic Representation of Chaos Using Terminal Attractors; Two High-Temperature Foil Journal Bearings; Using Plates To Represent Fillets in Finite-Element Modeling; Repairing Chipped Silicide Coatings on Refractory Metal Substrates; Simplified Fabrication of Helical Copper Antennas; Graded-Index "Whispering-Gallery" Optical Microresonators; Optical Profilometers Using Adaptive Signal Processing; Manufacture of Sparse-Spectrum Optical Microresonators; Exact Tuning of High-Q Optical Microresonators by Use of UV; Automation for "Direct-to" Clearances in Air-Traffic Control; Improved Traps for Removing Gases From Coolant Liquids; and Lunar Constellation of Frozen Elliptical Inclined Orbits.

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NASA NTRS1995

NASA Tech Briefs, November 1995

The contents include: 1) Mission Accomplished; 2) Resource Report: Marshall Space Flight Center; 3) NASA 1995 Software of the Year Award; 4) Microbolometers Based on Epitaxial YBa2Cu3O(sub 7-x) Thin Films; 5) Garnet Random-Access Memory; 6) Fabrication of SNS Weak Links on SOS Substrates; 7) High-Voltage MOSFET Switching Circuit; 8) Asymmetric Switching for a PWM H-Bridge Power Circuit; 9) Better Ohmic Contacts for InP Semiconductor Devices; 10) Low-Bandgap Thermovoltaic Materials and Devices; 11) Digital Frequency-Differencing Circuit; 12) Imaging Magnetometer; 13) Computer-Assisted Monitoring of a Complex System; 14) Buffered Telemetry Demodulator; 15) Compact Multifunction Inspection Head; 16) Optical Detection of Fractures in Ceramic Diaphragms; 17) Eddy-Current Detection of Cracks in Reinforced Carbon/Carbon; 18) Apparent Thermal Conductivity of Multilayer Insulation; 19) Optimizing Misch-Metal Compositions in Metal Hydride Anodes; 20) Device for Sampling Surface Contamination; 21) Probabilistic Failure Assessment for Fatigue; 22) Probabilistic Fatigue and Flaw-Propagation Analysis; 23) Windows Program for Driving the TDU-850 Printer; 24) Subband/Transform MATLAB Functions for Processing Images; 25) Computing Equilibrium Chemical Compositions; 26) Program Processes Thermocouple Readings; 27) ICAN-Second-Generation Integrated Composite Analyzer; 28) Integrated Composite Analyzer with Damping Capabilities; 29) Computing Efficiency of Transfer of Microwave Power; 30) Program Calculates Power Demands of Electronic Designs; 31) Cost-Estimation Program; 32) Program Estimates Areas Required by Electronic Designs; 33) Program to Balance Mapped Turbopump Assemblies; 34) BiblioTech; 35) Controlling Mirror Tilt With a Bimorph Actuator; 36) Burst-Disk Device Simulates Effect of Pyrotechnic Device; 37) Bearing-Mounting Concept Accommodates Thermal Expansion; 38) Parallel-Plate Acoustic Absorbers for Hot Environments; 39) Adjustable-Length Strut Withstands Large Cyclic Loads; 40) Tool Indicates Contact Angles in Bearing Raceways; 41) Gravity Slides With Magnetic Braking; 42) High-Torque, Lightweight, Pneumatically Driven Wrench for Small Spaces; 43) Device for Testing Compatibility of an O-Ring; 44) Magnetic Heat Pump Containing Flow Diverters; 45) Variable-Tilt Helicopter Rotor Mast; 46) "Beach-Ball" Robotic Rovers; 47) Apparatus Would Measure Temperatures of Ball Bearings; 48) Flexible Borescope for Inspecting Ducts; 49) Texturing Copper To Reduce Secondary Emission of Electrons; 50) Automated Laser Cutting in Three Dimensions; 51) Algorithm Helps Monitor Engine Operation; 52) Flexible Revision of Data-Processing Communications; 53) Software for Managing the Use of Land; 54) Thermal Strap Increases Cryocooling Efficiency; 55) Reversible Nut With Engagement Indication; 56) Control Algorithms for Kinematically Redundant Manipulators; 57) Computed Hydrogen-Flow Splits in a Rocket Engine; 58) Pressure and Thermal Modeling of Rocket Launches; 59) Field of View of a Spacecraft Antenna: Analysis and Software; 60) Digital Controller for Laser-Beam-Steering Subsystem; 61) More About Beam-Steering Subsystem for Laser Communication; 62) Digital Controller for Laser-Beam-Steering Subsystem: Part 2; 63) Interface Circuit Board for Space-Shuttle Communications; 64) Automated Planning of Spacecraft Telecommunications; 65) Artifacts of Spectral Analysis of Instrument Readings; 66) Neural-Network Controller for Vibration Suppression; 67) Adaptive Finite-Element Computation in Fracture Mechanics; 68) Attitude Control for the Cassini Spacecraft; 69) Analytical Model for Fluid Dynamics in a Microgravity Environment; 70) Study of Rocket-Engine Joints Bonded by NVCU/NARloy-Z; 71) Improved Silicon Nitride for Advanced Heat Engines; 72) Parameters for Welding Aluminum/Lithium Alloys; 73) Lightweight Composite Intertank Structure; 74) Foil Patches Seal Small Vacuum Leaks; 75) Data Base on Cables and Connectors; 76) Effect of Clock Mode on Radiation Hardnessf an ADC; and 77) Fault-Tolerant Control for a Robotic Inspection System.

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NASA NTRS2006

Progress in Computational Simulation of Earthquakes

GeoFEST(P) is a computer program written for use in the QuakeSim project, which is devoted to development and improvement of means of computational simulation of earthquakes. GeoFEST(P) models interacting earthquake fault systems from the fault-nucleation to the tectonic scale. The development of GeoFEST( P) has involved coupling of two programs: GeoFEST and the Pyramid Adaptive Mesh Refinement Library. GeoFEST is a message-passing-interface-parallel code that utilizes a finite-element technique to simulate evolution of stress, fault slip, and plastic/elastic deformation in realistic materials like those of faulted regions of the crust of the Earth. The products of such simulations are synthetic observable time-dependent surface deformations on time scales from days to decades. Pyramid Adaptive Mesh Refinement Library is a software library that facilitates the generation of computational meshes for solving physical problems. In an application of GeoFEST(P), a computational grid can be dynamically adapted as stress grows on a fault. Simulations on workstations using a few tens of thousands of stress and displacement finite elements can now be expanded to multiple millions of elements with greater than 98-percent scaled efficiency on over many hundreds of parallel processors (see figure).

Donnellan, Andrea↗

NASA NTRS2005

Program Calculates Forces in Bolted Structural Joints

FORTRAN 77 computer program calculates forces in bolts in the joints of structures. This program is used in conjunction with the NASTRAN finite-element structural-analysis program. A mathematical model of a structure is first created by approximating its load-bearing members with representative finite elements, then NASTRAN calculates the forces and moments that each finite element contributes to grid points located throughout the structure. The user selects the finite elements that correspond to structural members that contribute loads to the joints of interest, and identifies the grid point nearest to each such joint. This program reads the pertinent NASTRAN output, combines the forces and moments from the contributing elements to determine the resultant force and moment acting at each proximate grid point, then transforms the forces and moments from these grid points to the centroids of the affected joints. Then the program uses these joint loads to obtain the axial and shear forces in the individual bolts. The program identifies which bolts bear the greatest axial and/or shear loads. The program also performs a fail-safe analysis in which the foregoing calculations are repeated for a sequence of cases in which each fastener, in turn, is assumed not to transmit an axial force.

Buder, Daniel A.↗

NASA NTRS2005

High-Aperture-Efficiency Horn Antenna

A horn antenna (see Figure 1) has been developed to satisfy requirements specific to its use as an essential component of a high-efficiency Ka-band amplifier: The combination of the horn antenna and an associated microstrip-patch antenna array is required to function as a spatial power divider that feeds 25 monolithic microwave integrated-circuit (MMIC) power amplifiers. The foregoing requirement translates to, among other things, a further requirement that the horn produce a uniform, vertically polarized electromagnetic field in its patches identically so that the MMICs can operate at maximum efficiency. The horn is fed from a square waveguide of 5.9436-mm-square cross section via a transition piece. The horn features cosine-tapered, dielectric-filled longitudinal corrugations in its vertical walls to create a hard boundary condition: This aspect of the horn design causes the field in the horn aperture to be substantially vertically polarized and to be nearly uniform in amplitude and phase. As used here, cosine-tapered signifies that the depth of the corrugations is a cosine function of distance along the horn. Preliminary results of finite-element simulations of performance have shown that by virtue of the cosine taper the impedance response of this horn can be expected to be better than has been achieved previously in a similar horn having linearly tapered dielectric- filled longitudinal corrugations. It is possible to create a hard boundary condition by use of a single dielectric-filled corrugation in each affected wall, but better results can be obtained with more corrugations. Simulations were performed for a one- and a three-corrugation cosine-taper design. For comparison, a simulation was also performed for a linear- taper design (see Figure 2). The three-corrugation design was chosen to minimize the cost of fabrication while still affording acceptably high performance. Future designs using more corrugations per wavelength are expected to provide better field responses and, hence, greater aperture efficiencies.

Pickens, Wesley↗

NASA NTRS2004

Dynamics and Controls of a Conceptual Jovian Moon Tour Spacecraft

The dynamics and control challenges presented by a conceptual Jovian Moon Tour spacecraft are summarized in this paper. Attitude and orbital dynamics interactions are present due to the designed low-thrust trajectory, and controls structure interactions are also present due to the non-collocated sensor-actuator pairs on board the flexible spacecraft. A finite-element based simulation model is described which is capable of handling the complex orbital and attitude dynamics arising during the low-thrust spiraling maneuvers of the spacecraft. A few numerical simulations demonstrate that some of the challenges hitherto identified can be faced via integrated dynamics and control analysis, and that reasonable assessments of the pointing performance can be made.

dynamics↗

NASA NTRS2003

Explicit Pore Pressure Material Model in Carbon-Cloth Phenolic

An explicit material model that uses predicted pressure in the pores of a carbon-cloth phenolic (CCP) composite has been developed. This model is intended to be used within a finite-element model to predict phenomena specific to CCP components of solid-fuel-rocket nozzles subjected to high operating temperatures and to mechanical stresses that can be great enough to cause structural failures. Phenomena that can be predicted with the help of this model include failures of specimens in restrained-thermal-growth (RTG) tests, pocketing erosion, and ply lifting

Gutierrez-Lemini, Danton↗

NASA NTRS2003

NASA Tech Briefs, October 2003

Topics covered include: Cryogenic Temperature-Gradient Foam/Substrate Tensile Tester; Flight Test of an Intelligent Flight-Control System; Slat Heater Boxes for Thermal Vacuum Testing; System for Testing Thermal Insulation of Pipes; Electrical-Impedance-Based Ice-Thickness Gauges; Simulation System for Training in Laparoscopic Surgery; Flasher Powered by Photovoltaic Cells and Ultracapacitors; Improved Autoassociative Neural Networks; Toroidal-Core Microinductors Biased by Permanent Magnets; Using Correlated Photons to Suppress Background Noise; Atmospheric-Fade-Tolerant Tracking and Pointing in Wireless Optical Communication; Curved Focal-Plane Arrays Using Back-Illuminated High-Purity Photodetectors; Software for Displaying Data from Planetary Rovers; Software for Refining or Coarsening Computational Grids; Software for Diagnosis of Multiple Coordinated Spacecraft; Software Helps Retrieve Information Relevant to the User; Software for Simulating a Complex Robot; Software for Planning Scientific Activities on Mars; Software for Training in Pre-College Mathematics; Switching and Rectification in Carbon-Nanotube Junctions; Scandia-and-Yttria-Stabilized Zirconia for Thermal Barriers; Environmentally Safer, Less Toxic Fire-Extinguishing Agents; Multiaxial Temperature- and Time-Dependent Failure Model; Cloverleaf Vibratory Microgyroscope with Integrated Post; Single-Vector Calibration of Wind-Tunnel Force Balances; Microgyroscope with Vibrating Post as Rotation Transducer; Continuous Tuning and Calibration of Vibratory Gyroscopes; Compact, Pneumatically Actuated Filter Shuttle; Improved Bearingless Switched-Reluctance Motor; Fluorescent Quantum Dots for Biological Labeling; Growing Three-Dimensional Corneal Tissue in a Bioreactor; Scanning Tunneling Optical Resonance Microscopy; The Micro-Arcsecond Metrology Testbed; Detecting Moving Targets by Use of Soliton Resonances; and Finite-Element Methods for Real-Time Simulation of Surgery.

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NASA NTRS2003

Simulation System for Training in Laparoscopic Surgery

A computer-based simulation system creates a visual and haptic virtual environment for training a medical practitioner in laparoscopic surgery. Heretofore, it has been common practice to perform training in partial laparoscopic surgical procedures by use of a laparoscopic training box that encloses a pair of laparoscopic tools, objects to be manipulated by the tools, and an endoscopic video camera. However, the surgical procedures simulated by use of a training box are usually poor imitations of the actual ones. The present computer-based system improves training by presenting a more realistic simulated environment to the trainee. The system includes a computer monitor that displays a real-time image of the affected interior region of the patient, showing laparoscopic instruments interacting with organs and tissues, as would be viewed by use of an endoscopic video camera and displayed to a surgeon during a laparoscopic operation. The system also includes laparoscopic tools that the trainee manipulates while observing the image on the computer monitor (see figure). The instrumentation on the tools consists of (1) position and orientation sensors that provide input data for the simulation and (2) actuators that provide force feedback to simulate the contact forces between the tools and tissues. The simulation software includes components that model the geometries of surgical tools, components that model the geometries and physical behaviors of soft tissues, and components that detect collisions between them. Using the measured positions and orientations of the tools, the software detects whether they are in contact with tissues. In the event of contact, the deformations of the tissues and contact forces are computed by use of the geometric and physical models. The image on the computer screen shows tissues deformed accordingly, while the actuators apply the corresponding forces to the distal ends of the tools. For the purpose of demonstration, the system has been set up to simulate the insertion of a flexible catheter in a bile duct. [As thus configured, the system can also be used to simulate other endoscopic procedures (e.g., bronchoscopy and colonoscopy) that include the insertion of flexible tubes into flexible ducts.] A hybrid approach has been followed in developing the software for real-time simulation of the visual and haptic interactions (1) between forceps and the catheter, (2) between the forceps and the duct, and (3) between the catheter and the duct. The deformations of the duct are simulated by finite-element and modalanalysis procedures, using only the most significant vibration modes of the duct for computing deformations and interaction forces. The catheter is modeled as a set of virtual particles uniformly distributed along the center line of the catheter and connected to each other via linear and torsional springs and damping elements. The interactions between the forceps and the duct as well as the catheter are simulated by use of a ray-based haptic-interaction- simulating technique in which the forceps are modeled as connected line segments.

Basdogan, Cagatay↗