Design of a wrist and operator interface for an agricultural manipulator : a thesis presented in partial fulfilment of the requirements for the degree of Master of Technology in Engineering and Automation at Massey University

Roadside mowing and tree pruning has always been a job that most people would consider as unpleasant. This project is concerned with the development of a system to make these tasks simpler, safer and more pleasant for the operator. 1.1 Software This project is involved with the design of a complex mechanical system, which could be done using a modern CAD package. To achieve this, research into what modelling package was best was necessary. Several contenders were considered. These include SolidWorks [1], Mechanical Desktop [2] and CADKEY [3]. CADKHY was disregarded early as it is not as expandable as the other two. Both SolidWorks and Mechanical Desktop have additional software packages that allow for motion, force and stress analysis. The major difference between SolidWorks and Mechanical Desktop, is that SolidWorks is a true three dimensional modelling package, whereas Mechanical Desktop is based on the two dimensional AutoCAD system with a three dimensional toolbox. The choice was finalised to SolidWorks as it handles three dimensional modelling more efficiently. Massey University also uses SolidWorks. This allowed the project to continue while studying at the Turitea campus. 1.2 Overview This project is involved with the development of a wrist mechanism and hydraulic control system for an agricultural manipulator. The manipulator is called the Hydra Trim and was developed by Pivot Engineering Ltd. Napier [4]. The wrist mechanism is an integral part of making the Hydra Trim a success. The hydraulic control requires not only the valves but also an interface between the operator and the valves

Lattice Polarized K3 Surfaces and Siegel Modular Forms

The goal of the present paper is two-fold. First, we present a classification of algebraic K3 surfaces polarized by the lattice H+E_8+E_7. Key ingredients for this classification are: a normal form for these lattice polarized K3 surfaces, a coarse moduli space and an explicit description of the inverse period map in terms of Siegel modular forms. Second, we give explicit formulas for a Hodge correspondence that relates these K3 surfaces to principally polarized abelian surfaces. The Hodge correspondence in question underlies a geometric two-isogeny of K3 surfaces

Modular Invariants for Lattice Polarized K3 Surfaces

We study the class of complex algebraic K3 surfaces admitting an embedding of H+E8+E8 inside the Neron-Severi lattice. These special K3 surfaces are classified by a pair of modular invariants, in the same manner that elliptic curves over the field of complex numbers are classified by the J-invariant. Via the canonical Shioda-Inose structure we construct a geometric correspondence relating K3 surfaces of the above type with abelian surfaces realized as cartesian products of two elliptic curves. We then use this correspondence to determine explicit formulas for the modular invariants.Comment: 29 pages, LaTe

Valuing Medieval Annuities: Were Corrodies Underpriced?

Medieval bishops condemned and restricted the sale of corrodies (a type of annuity), partly on the grounds of their perceived unprofitability. The available data on the profitability of corrodies is limited and little analysed, and the episcopal condemnation of corrodies has been adopted by modern researchers. After recognising the difficulties, this paper applies an annuity pricing model to study corrody pricing. Given various assumptions, contrary to the established view, it is argued that the sale of corrodies was financially profitable for institutions. Finally, some reasons are considered for the negative attitude of contemporary and historical opinion towards the sale of corrodies.Corrodies, pensions, annuities, monasteries, pricing models

Special function identities from superelliptic Kummer varieties

We prove that the factorization of Appell's generalized hypergeometric series satisfying the so-called quadric property into a product of two Gauss' hypergeometric functions has a geometric origin: we first construct a generalized Kummer variety as minimal nonsingular model for a product-quotient surface with only rational double points from a pair of superelliptic curves of genus $2r-1$ with $r \in \mathbb{N}$. We then show that this generalized Kummer variety is equipped with two fibrations with fibers of genus $2r-1$. When periods of a holomorphic two-form over carefully crafted transcendental two-cycles on the generalized Kummer variety are evaluated using either of the two fibrations, the answer must be independent of the fibration and the aforementioned family of special function identities is obtained. This family of identities can be seen as a multivariate generalization of Clausen's Formula. Interestingly, this paper's finding bridges Ernst Kummer's two independent lines of research, algebraic transformations for the Gauss' hypergeometric function and nodal surfaces of degree four in $\mathbb{P}^3$.Comment: 46 pages, 2 figure

Market impacts and the life cycle of investors orders

In this paper, we use a database of around 400,000 metaorders issued by investors and electronically traded on European markets in 2010 in order to study market impact at different scales. At the intraday scale we confirm a square root temporary impact in the daily participation, and we shed light on a duration factor in $1/T^{\gamma}$ with $\gamma \simeq 0.25$. Including this factor in the fits reinforces the square root shape of impact. We observe a power-law for the transient impact with an exponent between $0.5$ (for long metaorders) and $0.8$ (for shorter ones). Moreover we show that the market does not anticipate the size of the meta-orders. The intraday decay seems to exhibit two regimes (though hard to identify precisely): a "slow" regime right after the execution of the meta-order followed by a faster one. At the daily time scale, we show price moves after a metaorder can be split between realizations of expected returns that have triggered the investing decision and an idiosynchratic impact that slowly decays to zero. Moreover we propose a class of toy models based on Hawkes processes (the Hawkes Impact Models, HIM) to illustrate our reasoning. We show how the Impulsive-HIM model, despite its simplicity, embeds appealing features like transience and decay of impact. The latter is parametrized by a parameter $C$ having a macroscopic interpretation: the ratio of contrarian reaction (i.e. impact decay) and of the "herding" reaction (i.e. impact amplification).Comment: 30 pages, 12 figure

Development of a semi–empirical reaction kinetic model for PEM fuel cells

In the drive to more sustainable energy production, polymer electrolyte fuel cells (PEFC) have been at the pinnacle of global research. One of the major drawbacks of PEFCs is therequirement for expensive noble metal catalysts (platinum and ruthenium). Furthermore 75% of the overpotential losses at the cathode are due to the activation of the oxygen reduction reaction (ORR). To reduce the platinum content requirements and understand the cause of the large overpotential of the ORR, a fundamental understanding of the reaction mechanism and the manner in which it proceeds under different operatingconditions is required. Presently, there still remains a large debate in literature around the mechanism followed by the ORR.This study developed a kinetic model from conventional kinetic isotherms and it is proposed that an associative adsorption mechanism occurs at a low overpotential resulting in the dissociation of the hydroperoxyl species determining the rate of the ORR at the cathode of the PEFC. In order to explain the above phenomena a kinetic model was developed, based on the Eley-Rideal mechanism. Furthermore, experiments were conducted at different oxygen partial pressures and low potentials whereby the associative mechanism is believed to dominate. Under these conditions linear sweep voltammograms were recorded. Regression of the derived kinetic model, by using the values for oxygen partial pressure, applied overpotential and kinetic current allowed for the determination of the kinetic constant of a polycrystalline platinum catalyst for ORR

The development of a process for the treatment of a complex ore

The writer has carried out tests to determine the most feasible method of treating a complex ore from Tecolote, Sonoro [sic], Mexico. The ore contains gold, silver, copper and zinc -- Introductory, page 1

Crystal morphology and surface reactivity studies of calcium hydroxide

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.Calcium hydroxide samples, obtained as a precipitate from the mixing of solutions of sodium hydroxide with a variety of calcium salts in the optional presence of ethanol and a silylating agent, have been characterised by the techniques of nitrogen adsorption, water vapour adsorption , thermogravimetric analysis, Fourier-transform infra-red spectroscopy, ultra-violet spectroscopy and electron microscopy. The morphology of the samples varied from octahedral crystals to hexagonal prisms to sheets. The individual morphology depends on the conditions of precipitation, the nature and concentration of the calcium salt(s) and the nature of the precipitation medium. It has been shown that a large excess of sodium hydroxide results in octahedral forms, calcium salt(s) in approximate equimolar amount or in large excess to the sodium hydroxide results in hexagonal forms, and sheets are formed in the presence of ethanolic precipitation medium. A poisoning mechanism has been suggested in terms of the morphological properties of the samples. It has been found that the sheet forms of calcium hydroxide can be stabilised by reaction with a silylating agent, resulting in greater thermal stability and chemical stability of the surface. Silylation was found not to occur by direct contact between the precipitated calcium hydroxide samples and silylating agents. Silylation only occurred when precipitation was carried out in the presence of a solution of the silylating agent in absolute ethanol. The silylation of the surface of calcium hydroxide has been found to stabilise the material. Reaction of this with 3-aminopropyltriethoxysilane formed an intermediate which subsequently reacted with p-nitrobenzoyl chloride to form an inorganic - organic composite. The technique of thermogravimetric analysis has been employed to measure the thermal stability of the samples. It has been found that the samples exhibit major weight losses at around 688K for the non-silylated samples and around 918K for the silylated samples. The BETnitrogen and the BET-H20 surface areas of the samples range typically from --1 to 43 m2g-1 , and from 9 to 798 m2g-1 respectively. On the basis of this evidence, taken together with the isotherm shapes it has been shown that: the samples are non-porous; non-silylated calcium hydroxide samples are more hydrophobic than the silylated samples, but upon heat-treatment in air below the decomposition temperature the silylated samples became more hydrophobic, whereas the non-silylated samples became more hydrophilic; samples heated in air at above the decomposition temperature exhibit a dramatic increase in hydrophilicity, the H 20-BET surface areas becoming —800 m2g-1 for non silylated samples, compared to 368 - 600 m 2g-1 for silylated samples, indicative of chemisorption following decomposition of the calcium hydroxide to form calcium oxide