Browsing by Subject "Mechanics"
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Item Open Access Control of underactuated planar pronking through an embedded spring-mass Hopper template(2011) Ankaralı, M.M.; Saranlı, U.Autonomous use of legged robots in unstructured, outdoor settings requires dynamically dexterous behaviors to achieve sufficient speed and agility without overly complex and fragile mechanics and actuation. Among such behaviors is the relatively under-studied pronking (aka. stotting), a dynamic gait in which all legs are used in synchrony, usually resulting in relatively slow speeds but long flight phases and large jumping heights. Instantiations of this gait for robotic systems have been mostly limited to open-loop strategies, suffering from severe pitch instability for underactuated designs due to the lack of active feedback. However, both the kinematic simplicity of this gait and its dynamic nature suggest that the Spring-Loaded Inverted Pendulum model (SLIP) would be a good basis for the implementation of a more robust feedback controller for pronking. In this paper, we describe how template-based control, a controller structure based on the embedding of a simple dynamical "template" within a more complex "anchor" system, can be used to achieve very stable pronking for a planar, underactuated hexapod robot. In this context, high-level control of the gait is regulated through speed and height commands to the SLIP template, while the embedding controller ensures the stability of the remaining degrees of freedom. We use simulation studies to show that unlike existing open-loop alternatives, the resulting control structure provides explicit gait control authority and significant robustness against sensor and actuator noise. © 2010 Springer Science+Business Media, LLC.Item Open Access Degrees of freedom of optical systems and signals with applications to sampling and system simulation(Optical Society of America, 2013) Oktem F.S.; Özaktaş, Haldun M.We study the degrees of freedom of optical systems and signals based on space-frequency (phase space) analysis. At the heart of this study is the relationship of the linear canonical transform domains to the space-frequency plane. Based on this relationship, we discuss how to explicitly quantify the degrees of freedom of first-order optical systems with multiple apertures, and give conditions for lossless transfer. Moreover, we focus on the degrees of freedom of signals in relation to the space-frequency support and provide a sub-Nyquist sampling approach to represent signals with arbitrary space-frequency support. Implications for simulating optical systems are also discussed. © 2013 Optical Society of America.Item Open Access Equivalence of linear canonical transform domains to fractional Fourier domains and the bicanonical width product: a generalization of the space-bandwidth product(Optical Society of America, 2010-07-30) Oktem, F. S.; Özaktaş, Haldun M.Linear canonical transforms (LCTs) form a three-parameter family of integral transforms with wide application in optics. We show that LCT domains correspond to scaled fractional Fourier domains and thus to scaled oblique axes in the space-frequency plane. This allows LCT domains to be labeled and ordered by the corresponding fractional order parameter and provides insight into the evolution of light through an optical system modeled by LCTs. If a set of signals is highly confined to finite intervals in two arbitrary LCT domains, the space-frequency (phase space) support is a parallelogram. The number of degrees of freedom of this set of signals is given by the area of this parallelogram, which is equal to the bicanonical width product but usually smaller than the conventional space-bandwidth product. The bicanonical width product, which is a generalization of the space-bandwidth product, can provide a tighter measure of the actual number of degrees of freedom, and allows us to represent and process signals with fewer samples.Item Open Access Lattice dynamics and elastic properties of lanthanum monopnictides(2008) Gökoǧlu G.; Erkişi, A.In this study, first principles calculation results of the second order elastic constants and lattice dynamics of two lanthanum monopnictides, LaN and LaBi, which crystallize in rock-salt structure (B1 phase), are presented. Calculations were based on plane wave basis sets and pseudopotential methods in the framework of Density Functional Theory (DFT) with generalized gradient approximation. Elastic constants are calculated by tetragonal and orthorhombic distortions on cubic structure. Phonon dispersion spectra was constructed in the linear response approach of the Density Functional Perturbation Theory (DFPT). The complete phonon softening with negative frequencies and large elastic anisotropy were observed for LaN single crystal as a sign of the structural instability. The phonon dispersion curve for LaBi is typical for lanthanum monopnictides and does not show any anomalous physical property. The calculated structural quantities for both LaN and LaBi systems agree well with the available experimental and theoretical data. © 2008 Elsevier Ltd. All rights reserved.Item Open Access Linear canonical transforms, degrees of freedom, and sampling in optical signals and systems(IEEE, 2014) Özaktaş, Haldun M.; Öktem, F. S.We study the degrees of freedom of optical systems and signals based on space-frequency (phase-space) analysis. At the heart of this study is the relationship of the linear canonical transform domains to the space-frequency plane. Based on this relationship, we discuss how to explicitly quantify the degrees of freedom of first-order optical systems with multiple apertures, and give conditions for lossless transfer. Moreover, we focus on the degrees of freedom of signals in relation to the space-frequency support and provide a sub-Nyquist sampling approach to represent signals with arbitrary space-frequency support. Implications for simulating optical systems are also discussed.Item Open Access Motion control for realistic walking behavior using inverse kinematics(IEEE, 2007-05) Memişoǧlu, Aydemir; Güdükbay,Uğur; Özgüç, BülentThis study presents an interactive hierarchical motion control system for the animation of human figure locomotion. The articulated figure animation system creates movements using motion control techniques at different levels, like goal-directed motion and walking. Inverse Kinematics using Analytical Methods (IKAN) software, developed at the University of Pennsylvania, is utilized for controlling the motion of the articulated body. © 2007 IEEE.Item Open Access Nanomechanical motion transducers for miniaturized mechanical systems(MDPI AG, 2017) Kouh, T.; Hanay, M. S.; Ekinci, K. L.Reliable operation of a miniaturized mechanical system requires that nanomechanical motion be transduced into electrical signals (and vice versa) with high fidelity and in a robust manner. Progress in transducer technologies is expected to impact numerous emerging and future applications of micro- and, especially, nanoelectromechanical systems (MEMS and NEMS); furthermore, high-precision measurements of nanomechanical motion are broadly used to study fundamental phenomena in physics and biology. Therefore, development of nanomechanical motion transducers with high sensitivity and bandwidth has been a central research thrust in the fields of MEMS and NEMS. Here, we will review recent progress in this rapidly-advancing area.Item Open Access Phase-space window and degrees of freedom of optical systems with multiple apertures(Optical Society of America., 2013) Özaktaş, Haldun M.; Oktem, F. S.We show how to explicitly determine the space-frequency window (phase-space window) for optical systems consisting of an arbitrary sequence of lenses and apertures separated by arbitrary lengths of free space. If the space-frequency support of a signal lies completely within this window, the signal passes without information loss. When it does not, the parts that lie within the window pass and the parts that lie outside of the window are blocked, a result that is valid to a good degree of approximation for many systems of practical interest. Also, the maximum number of degrees of freedom that can pass through the system is given by the area of its space-frequency window. These intuitive results provide insight and guidance into the behavior and design of systems involving multiple apertures and can help minimize information loss.