Dynamic Simulations of Elastic Rods for Medical Applications

This study deals with a detailed development of a computational model based on the Cosserat rod theory to describe the motion of elastic filaments such as threads and hair. The need for a simulation software for the act of suturing has motivated this study. The dynamic equations governing the motion of elastic rods have been solved using a finite difference scheme. The scheme is central difference in space and forward difference in time and is conditionally stable. The simulations are carried out for a cantilever beam for various force and moment inputs at its free end. The results have been validated using known analytical results. The scheme has proven to be fast enough to be used in real-time simulations

Dynamic Simulations of Elastic Rods for Medical Applications

This study deals with a detailed development of a computational model based on the Cosserat rod theory to describe the motion of elastic filaments such as threads and hair. The need for a simulation software for the act of suturing has motivated this study. The dynamic equations governing the motion of elastic rods have been solved using a finite difference scheme. The scheme is central difference in space and forward difference in time and is conditionally stable. The simulations are carried out for a cantilever beam for various force and moment inputs at its free end. The results have been validated using known analytical results. The scheme has proven to be fast enough to be used in real-time simulations

Dynamic Characteristics of Biologically Inspired Hair Receptors for Unmanned Aerial Vehicles

The highly optimized performance of nature’s creations and biological assemblies has inspired the development of their engineered counter parts that can potentially outperform conventional systems. In particular, bat wings are populated with air flow hair receptors which feedback the information about airflow over their surfaces for enhanced stability and maneuverability during their flight. The hairs in the bat wing membrane play a role in the maneuverability tasks, especially during low-speed flight. The developments of artificial hair sensors (AHS) are inspired by biological hair cells in aerodynamic feedback control designs. Current mathematical models for hair receptors are limited by strict simplifying assumptions of creeping flow hair Reynolds number on AHS fluid-structure interaction (FSI), which may be violated for hair structures integrated on small-scaled Unmanned Aerial Vehicles (UAVs). This study motivates by an outstanding need to understand the dynamic response of hair receptors in flow regimes relevant to bat-scaled UAVs. The dynamic response of the hair receptor within the creeping flow environment is investigated at distinct freestream velocities to extend the applicability of AHS to a wider range of low Reynolds number platforms. Therefore, a threedimensional FSI model coupled with a finite element model using the computational fluid dynamics (CFD) is developed for a hair-structure and multiple hair-structures in the airflow. The Navier-Stokes equations including continuity equation are solved numerically for the CFD model. The grid independence of the FSI solution is studied from the simulations of the hairstructure mesh and flow mesh around the hair sensor. To describe the dynamic response of the hair receptors, the natural frequencies and mode shapes of the hair receptors, computed from the finite element model, are compared with the excitation frequencies in vacuum. This model is described with both the boundary layer effects and effects of inertial forces due to fluid-structure xiv interaction of the hair receptors. For supporting the FSI model, the dynamic response of the hair receptor is also validated considering the Euler-Bernoulli beam theory including the steady and unsteady airflow

On the Statics, Dynamics, and Stability of Continuum Robots: Model Formulations and Efficient Computational Schemes

This dissertation presents advances in continuum-robotic mathematical-modeling techniques. Specifically, problems of statics, dynamics, and stability are studied for robots with slender elastic links. The general procedure within each topic is to develop a continuous theory describing robot behavior, develop a discretization strategy to enable simulation and control, and to validate simulation predictions against experimental results.Chapter 1 introduces the basic concept of continuum robotics and reviews progress in the field. It also introduces the mathematical modeling used to describe continuum robots and explains some notation used throughout the dissertation.The derivation of Cosserat rod statics, the coupling of rods to form a parallel continuum robot (PCR), and solution of the kinematics problem are reviewed in Chapter 2. With this foundation, soft real-time teleoperation of a PCR is demonstrated and a miniature prototype robot with a grasper is controlled.Chapter 3 reviews the derivation of Cosserat rod dynamics and presents a discretization strategy having several desirable features, such as generality, accuracy, and potential for good computational efficiency. The discretized rod model is validated experimentally using high speed camera footage of a cantilevered rod. The discretization strategy is then applied to simulate continuum robot dynamics for several classes of robot, including PCRs, tendon-driven robots, fluidic actuators, and concentric tube robots.In Chapter 4, the stability of a PCR is analyzed using optimal control theory. Conditions of stability are gradually developed starting from a single planar rod and finally arriving at a stability test for parallel continuum robots. The approach is experimentally validated using a camera tracking system.Chapter 5 provides closing discussion and proposes potential future work

Vibrations of beams and rods carrying a moving mass

We study the vibration of slender one-dimensional elastic structures (beams, cables, wires, rods) under the effect of a moving mass or load. We first consider the classical small- deflection (Euler-Bernoulli) beam case, where we look at tip vibrations of a cantilever as a model for a barreled launch system. Then we develop a theory for large deformations based on Cosserat rod theory. We illustrate the effect of moving loads on large-deformation structures with a few cable and arch problems. Large deformations are found to have a resonance detuning effect on the cable. For the arch we find different failure modes depending on its depth: a shallow arch fails by in-plane collapse, while a deep arch fails by sideways flopping. In both cases the speed of the traversing load is found to have a stabilising effect on the structure, with failure suppressed entirely at sufficiently high speed

A numerical method for fluid-structure interactions of slender rods in turbulent flow

This thesis presents a numerical method for the simulation of fluid-structure interaction (FSI) problems on high-performance computers. The proposed method is specifically tailored to interactions between Newtonian fluids and a large number of slender viscoelastic structures, the latter being modeled as Cosserat rods. From a numerical point of view, such kind of FSI requires special techniques to reach numerical stability. When using a partitioned fluid-structure coupling approach this is usually achieved by an iterative procedure, which drastically increases the computational effort. In the present work, an alternative coupling approach is developed based on an immersed boundary method (IBM). It is unconditionally stable and exempt from any global iteration between the fluid part and the structure part. The proposed FSI solver is employed to simulate the flow over a dense layer of vegetation elements, usually designated as canopy flow. The abstracted canopy model used in the simulation consists of 800 strip-shaped blades, which is the largest canopy-resolving simulation of this type done so far. To gain a deeper understanding of the physics of aquatic canopy flows the simulation data obtained are analyzed, e.g., concerning the existence and shape of coherent structures

Modelling and simulation of flexible instruments for minimally invasive surgical training in virtual reality

Improvements in quality and safety standards in surgical training, reduction in training hours and constant technological advances have challenged the traditional apprenticeship model to create a competent surgeon in a patient-safe way. As a result, pressure on training outside the operating room has increased. Interactive, computer based Virtual Reality (VR) simulators offer a safe, cost-effective, controllable and configurable training environment free from ethical and patient safety issues. Two prototype, yet fully-functional VR simulator systems for minimally invasive procedures relying on flexible instruments were developed and validated. NOViSE is the first force-feedback enabled VR simulator for Natural Orifice Transluminal Endoscopic Surgery (NOTES) training supporting a flexible endoscope. VCSim3 is a VR simulator for cardiovascular interventions using catheters and guidewires. The underlying mathematical model of flexible instruments in both simulator prototypes is based on an established theoretical framework – the Cosserat Theory of Elastic Rods. The efficient implementation of the Cosserat Rod model allows for an accurate, real-time simulation of instruments at haptic-interactive rates on an off-the-shelf computer. The behaviour of the virtual tools and its computational performance was evaluated using quantitative and qualitative measures. The instruments exhibited near sub-millimetre accuracy compared to their real counterparts. The proposed GPU implementation further accelerated their simulation performance by approximately an order of magnitude. The realism of the simulators was assessed by face, content and, in the case of NOViSE, construct validity studies. The results indicate good overall face and content validity of both simulators and of virtual instruments. NOViSE also demonstrated early signs of construct validity. VR simulation of flexible instruments in NOViSE and VCSim3 can contribute to surgical training and improve the educational experience without putting patients at risk, raising ethical issues or requiring expensive animal or cadaver facilities. Moreover, in the context of an innovative and experimental technique such as NOTES, NOViSE could potentially facilitate its development and contribute to its popularization by keeping practitioners up to date with this new minimally invasive technique.Open Acces