Students’ Evolving Meaning About Tangent Line with the Mediation of a Dynamic Geometry Environment and an Instructional Example Space

In this paper I report a lengthy episode from a teaching experiment in which fifteen Year 12 Greek students negotiated their definitions of tangent line to a function graph. The experiment was designed for the purpose of introducing students to the notion of derivative and to the general case of tangent to a function graph. Its design was based on previous research results on students’ perspectives on tangency, especially in their transition from Geometry to Analysis. In this experiment an instructional example space of functions was used in an electronic environment utilising Dynamic Geometry software with Function Grapher tools. Following the Vygotskian approach according to which students’ knowledge develops in specific social and cultural contexts, students’ construction of the meaning of tangent line was observed in the classroom throughout the experiment. The analysis of the classroom data collected during the experiment focused on the evolution of students’ personal meanings about tangent line of function graph in relation to: the electronic environment; the pre-prepared as well as spontaneous examples; students’ engagement in classroom discussion; and, the role of researcher as a teacher. The analysis indicated that the evolution of students’ meanings towards a more sophisticated understanding of tangency was not linear. Also it was interrelated with the evolution of the meaning they had about the inscriptions in the electronic environment; the instructional example space; the classroom discussion; and, the role of the teacher

A novel haptic model and environment for maxillofacial surgical operation planning and manipulation

This paper presents a practical method and a new haptic model to support manipulations of bones and their segments during the planning of a surgical operation in a virtual environment using a haptic interface. To perform an effective dental surgery it is important to have all the operation related information of the patient available beforehand in order to plan the operation and avoid any complications. A haptic interface with a virtual and accurate patient model to support the planning of bone cuts is therefore critical, useful and necessary for the surgeons. The system proposed uses DICOM images taken from a digital tomography scanner and creates a mesh model of the filtered skull, from which the jaw bone can be isolated for further use. A novel solution for cutting the bones has been developed and it uses the haptic tool to determine and define the bone-cutting plane in the bone, and this new approach creates three new meshes of the original model. Using this approach the computational power is optimized and a real time feedback can be achieved during all bone manipulations. During the movement of the mesh cutting, a novel friction profile is predefined in the haptical system to simulate the force feedback feel of different densities in the bone

Study of orifice fabrication technologies for the liquid droplet radiator

Eleven orifice fabrication technologies potentially applicable for a liquid droplet radiator are discussed. The evaluation is focused on technologies capable of yielding 25-150 microns diameter orifices with trajectory accuracies below 5 milliradians, ultimately in arrays of up to 4000 orifices. An initial analytical screening considering factors such as trajectory accuracy, manufacturability, and hydrodynamics of orifice flow is presented. Based on this screening, four technologies were selected for experimental evaluation. A jet straightness system used to test 50-orifice arrays made by electro-discharge machining (EDM), Fotoceram, and mechanical drilling is discussed. Measurements on orifice diameter control and jet trajectory accuracy are presented and discussed. Trajectory standard deviations are in the 4.6-10.0 milliradian range. Electroforming and EDM appear to have the greatest potential for Liquid Droplet Radiator applications. The direction of a future development effort is discussed

A holistic integrated dynamic design and modelling approach applied to the development of ultraprecision micro-milling machines

Ultraprecision machines with small footprints or micro-machines are highly desirable for micro-manufacturing high-precision micro-mechanical components. However, the development of the machines is still at the nascent stage by working on an individual machine basis and hence lacks generic scientific approach and design guidelines. Using computer models to predict the dynamic performance of ultraprecision machine tools can help manufacturers substantially reduce the lead time and cost of developing new machines. Furthermore, the machine dynamic performance depends not only upon the mechanical structure and components but also the control system and electronic drives. This paper proposed a holistic integrated dynamic design and modelling approach, which supports analysis and optimization of the overall machine dynamic performance at the early design stage. Based on the proposed approach the modelling and simulation process on a novel 5-axis bench-top ultraprecision micro-milling machine tool – UltraMill – is presented. The modelling and simulation cover the dynamics of the machine structure, moving components, control system and the machining process, and are used to predict the overall machine performance of two typical configurations. Preliminary machining trials have been carried out and provided the evidence of the approach being helpful to assure the machine performing right at the first setup

Steel Compression Members with Partial-length Reinforcement

Steel wide-flange columns in existing truss bridges may be built-up with flange cover plate reinforcement to increase compressive capacity. This thesis investigates the use of partial-length steel cover plates about column mid-height to improve the weak-axis buckling resistance. The present research first reviews literature concerning the Euler buckling of members with partial-length reinforcement. Inelastic buckling is simulated by 3-D finite element analysis accounting for cover plate length, cover plate area, bolt hole perforations, yield stresses, residual and locked-in dead load stresses, and initial out-of-straightness. The model is validated by a load test of a full-scale column with bolted reinforcement plates. A parametric sensitivity study shows that reinforced capacity is characterized by the transition between failure initiating either in the original column at the unreinforced end segments, or at column mid-height in the reinforced segment. An equation developed through multiple linear regression is proposed for a simplified procedure for preliminary design

Aesthetic-oriented classification of 2D free-form curves

Nowadays, it is commonly admitted that the aesthetic appearance of a product has an enhanced role in its commercial success. Therefore, understanding and manipulating the aesthetic properties of shapes in the early design phases has become a very important field of research. There exists an appropriate vocabulary for describing the aesthetic properties of 2D free-form curves that includes terms such as straightness, acceleration, convexity and tension, which are normally used by stylists when describing and modifying shapes. However, the relationships between this vocabulary and the geometric models are not well established. This work investigates the possibility of applying Machine Learning Techniques (MLT) to discover possible classification patterns of 2D free-form curves with respect to the so-called straightness of the curve. First, we verified that MLT can correctly (99.78%) reapply the classification to new curves. In addition, we verified the abilities of the Attribute Selection methods to identify the most important attributes for the considered classification, among a larger set of attributes. As a result, it was possible to recognize as the most characterizing parameters the same curve attributes previously used to compute the measure of straightness (S). Moreover, Linear Regression (LR) was able to extract automatically an exact mathematical model, which can correlate the geometric quantities with the class of the curve, congruent to one we previously specified. This work indeed demonstrates that MLT are very suitable and can be efficiently used in this context. The work is a first step towards the characterization and classification of free form surfaces giving the general directions on how MLT can be exploited to characterize free-form surfaces with respects to the aesthetic properties.This work has been partially supported by the VISIONAIR project funded by the European Commission under grant agreement 262044

Development of a Miniature Electrostatic Accelerometer /MESA/ for low g applications Summary report

Design, fabrication, and testing of miniature digital electrostatic accelerometer for low gravity measurements in spac

LOCAL BUCKLING IN CORRODED STEEL BRIDGE COMPRESSION MEMBERS

Corrosion in steel bridge members is common in Northern climates and can occur uniformly in the vehicle splash zone or locally near connections. The analysis of corroded compression members in steel bridges is often uncertain due to a lack of experimentally verified theoretical knowledge of their underlying mechanics. Code criteria for analyzing compression members with section loss may be overly conservative because the effect of localized deterioration on local and Euler buckling is not well understood. The research reported in this thesis clarifies the local buckling susceptibility of corroded steel bridge compression members. A finite element analysis model was developed to predict the critical load causing local buckling of a W-shape given a predetermined flange cross sectional loss. The finite element analysis model was validated experimentally with five full-scale column tests with idealized corrosive patterns. A robust sensitivity analysis was conducted to determine the sensitivity of the axial capacity to geometric variables that affect local buckling for a range of slenderness ratios. A simplified assessment method, based on data obtained in the sensitivity study, is presented that accounts for both localized and uniform deterioration in steel bridge compression members with corroded flanges. This method provides engineers with a means to quickly and conservatively assess the reduced capacity of such members

Superconducting bearings for application in cryogenic experiments in space

Linear superconducting magnetic bearings suitable for use in a proposed orbital equivalence principle experiment and for general application in space were developed and tested. Current flows in opposite directions in adjacent superconducting wires arranged parallel to the axis of a cylinder. This configuration provides maximum stiffness radially while allowing the test mass to move freely along the cylinder axis. In a space application, the wires are extended to cover the entire perimeter of the cylinder: for the earth-based tests it was desirable to use only the bottom half. Control of the axial position of the test mass is by small control coils which may be positioned inside or outside the main bearing. The design is suitable for application to other geometries where maximum stiffness is desired. A working model scaled to operate in a 1-g environment was perfected approximate solutions for the bearings were developed. A superconducting transformer method of charging the magnets for the bearing, and a position detector based on a SQUID magnetometer and associated superconducting circuit were also investigated

Magnetic Resonance Imaging of Optic Nerve Traction During Adduction in Primary Open-Angle Glaucoma With Normal Intraocular Pressure.

PurposeWe used magnetic resonance imaging (MRI) to ascertain effects of optic nerve (ON) traction in adduction, a phenomenon proposed as neuropathic in primary open-angle glaucoma (POAG).MethodsSeventeen patients with POAG and maximal IOP ≤ 20 mm Hg, and 31 controls underwent MRI in central gaze and 20° to 30° abduction and adduction. Optic nerve and sheath area centroids permitted computation of midorbital lengths versus minimum paths.ResultsAverage mean deviation (±SEM) was -8.2 ± 1.2 dB in the 15 patients with POAG having interpretable perimetry. In central gaze, ON path length in POAG was significantly more redundant (104.5 ± 0.4% of geometric minimum) than in controls (102.9 ± 0.4%, P = 2.96 × 10-4). In both groups the ON became significantly straighter in adduction (28.6 ± 0.8° in POAG, 26.8 ± 1.1° in controls) than central gaze and abduction. In adduction, the ON in POAG straightened to 102.0% ± 0.2% of minimum path length versus 104.5% ± 0.4% in central gaze (P = 5.7 × 10-7), compared with controls who straightened to 101.6% ± 0.1% from 102.9% ± 0.3% in central gaze (P = 8.7 × 10-6); and globes retracted 0.73 ± 0.09 mm in POAG, but only 0.07 ± 0.08 mm in controls (P = 8.8 × 10-7). Both effects were confirmed in age-matched controls, and remained significant after correction for significant effects of age and axial globe length (P = 0.005).ConclusionsAlthough tethering and elongation of ON and sheath are normal in adduction, adduction is associated with abnormally great globe retraction in POAG without elevated IOP. Traction in adduction may cause mechanical overloading of the ON head and peripapillary sclera, thus contributing to or resulting from the optic neuropathy of glaucoma independent of IOP