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Full-Text Articles in Engineering
Trajectory Generation For Stair Ascent Walking Using Rayleigh Oscillator, T. Afzal, Andrew B. Wright, Kamran Iqbal
Trajectory Generation For Stair Ascent Walking Using Rayleigh Oscillator, T. Afzal, Andrew B. Wright, Kamran Iqbal
Journal of the Arkansas Academy of Science
This paper describes a trajectory generation technique for stair-ascent walking. The knee, hip and ankle joint trajectory during stair ascent are generated using mutually coupled, nonlinear oscillators. The parameters of the oscillators are tuned using the harmonic balance method, which converts the nonlinear differential equations to a set of algebraic equations. Fourier analysis of data generated by stair-ascent walking is performed to extract the amplitude and the phase of the dominant frequency components for each joint trajectory. The solution for the oscillator is assumed to be a sinusoidal wave and then by harmonic balance method the parameters of the oscillator …
Titanium-Oxygen Bond Length -Bond Valence Relationship, D. Dodd, F. D. Hardcastle, S. Laffoon
Titanium-Oxygen Bond Length -Bond Valence Relationship, D. Dodd, F. D. Hardcastle, S. Laffoon
Journal of the Arkansas Academy of Science
A bond length–bond valence correlation is a simple method of checking and evaluating molecular structures and is of great interest in chemistry, biology, geology, and material science. Recently, we used quantum-mechanical arguments to derive Pauling’s bond length-valence relationship and to define the adjustable fitting parameter b in terms of atomic-orbital exponents. Improved orbital exponents were generated for elements 1-103 using published atomic radii and single-bond covalent radii as well as a continuous function for effective principal quantum number. In this study, we use orbital exponents for titanium (Ti) and oxygen (O) to generate a bond length-valence relationship for Ti-O bonds. …
Valence-Length Correlations For Chemical Bonds From Atomic Orbital Exponents, F. D. Hardcastle
Valence-Length Correlations For Chemical Bonds From Atomic Orbital Exponents, F. D. Hardcastle
Journal of the Arkansas Academy of Science
Pauling’s empirical bond valence-length correlation has proven valuable because it offers a quick and convenient way of checking and evaluating molecular structures and determining oxidation states from measured bond lengths. In this study, a simplified quantum-mechanical approach was used to derive Pauling’s empirical bond valence-length relationship by considering overlap of hydrogen-like orbitals. An expression for the b “empirical” fitting parameter was derived in terms of atomic-orbital exponents. A new set of orbital exponents is presented using published atomic/covalent radii and a continuous function for the effective principal quantum. The b parameters calculated from the orbital exponents are consistent with bond …