This paper optimizes a GPS smoothing filter to minimize biases caused by ionosphere divergence du... more This paper optimizes a GPS smoothing filter to minimize biases caused by ionosphere divergence during anomalous storms. Ionospheric storms represent the most severe threat to high-integrity differential GPS systems, such as Ground-Based Augmentation Systems (GBAS). Substituting the optimized filter for the Hatch Filter typically used in GBAS reduces ionosphere divergence bias by over 10% for a fixed level of noise attenuation.
Aircraft use navigation guides to help pilots land especially in low visibility conditions. The c... more Aircraft use navigation guides to help pilots land especially in low visibility conditions. The commonly used Instrument Landing System is very effectively yet expensive and inflexible. The Global Positioning System (GPS) can be used to design potentially cheaper and more versatile navigation systems. The Local Area Augmented System (LAAS) is one of the proposed systems for navigation. However it is yet to be certified by the Federal Aviation Administration (FAA) owing to its susceptibility to certain rare events which can potentially cause a system failure in LAAS. LAAS implements the idea of using differential corrections from a nearby reference station to increase the accuracy of the position estimate of the user. One of the biggest threats to LAAS, which undermines the concept of differential corrections, is an ionospheric storm caused by high solar activity. The ionosphere is a spherical shell of ionized gases over earth and affects radiowave communication passing through it. A...
2008 IEEE/ION Position, Location and Navigation Symposium, 2008
Abstract This paper develops a single-frequency filter for smoothing GPS code measurements usin... more Abstract This paper develops a single-frequency filter for smoothing GPS code measurements using a nonlinear method. The method zeroes steady-state divergence errors caused by ionospheric storms. The filter has significant potential to improve the availability of safety-critical ...
Volume 2: 34th Annual Mechanisms and Robotics Conference, Parts A and B, 2010
ABSTRACT In the past, we have introduced the Beam Constraint Model (BCM), which captures pertinen... more ABSTRACT In the past, we have introduced the Beam Constraint Model (BCM), which captures pertinent non-linearities to predict the constraint characteristics of a generalized beam flexure in terms of its stiffness and error motions. In this paper, a non-linear strain energy ...
Redundant constraints are generally avoided in mechanism design because they can lead to binding ... more Redundant constraints are generally avoided in mechanism design because they can lead to binding or loss in expected mobility. However, in certain distributed-compliance flexure mechanism geometries, this problem is mitigated by the phenomenon of elastic averaging. Elastic averaging is a design paradigm that, in contrast with exact constraint design principles, makes deliberate and effective use of redundant constraints to improve performance and robustness. The principle of elastic averaging and its advantages are illustrated in this paper by means of a three-beam parallelogram flexure mechanism, which represents an overconstrained geometry. In a lumped-compliance configuration, this mechanism is prone to binding in the presence of nominal manufacturing and assembly errors. However, with an increasing degree of distributed-compliance, the mechanism is shown to become more tolerant to such geometric imperfections. The nonlinear elastokinematic effect in the constituent beams is show...
A novel parallel-kinematic flexure mechanism that provides highly decoupled motions along the thr... more A novel parallel-kinematic flexure mechanism that provides highly decoupled motions along the three translational directions (X, Y, and Z) and high stiffness along the three rotational directions (θx, θy, and θz) is presented. Geometric decoupling ensures large motion range along each translational direction and enables integration with large-stroke ground-mounted linear actuators or generators, depending on the application. The proposed design, which is based on a systematic arrangement of multiple rigid stages and parallelogram flexure modules, is analyzed via nonlinear finite elements analysis (FEA). A proof-of-concept prototype is fabricated to validate the predicted large range and decoupled motion capabilities. The analysis and the hardware prototype demonstrate an XYZ motion range of 10 mm × 10 mm × 10 mm. Over this motion range, the nonlinear FEA predicts cross-axis errors of less than 7.8%, parasitic rotations less than 10.8 mrad, less than 14.4% lost motion, actuator isola...
Volume 2: 34th Annual Mechanisms and Robotics Conference, Parts A and B, 2010
ABSTRACT The constraint-based design of flexure mechanisms requires a qualitative and quantitativ... more ABSTRACT The constraint-based design of flexure mechanisms requires a qualitative and quantitative understanding of the constraint characteristics of flexure elements that serve as constraints. This paper presents the constraint characterization of a slender, uniform and symmetric cross-...
To utilize beam flexures in constraint-based flexure mechanism design, it is important to develop... more To utilize beam flexures in constraint-based flexure mechanism design, it is important to develop qualitative and quantitative understanding of their constraint characteristics in terms of stiffness and error motions. This paper provides a highly generalized yet accurate closed-form parametric load-displacement model for two-dimensional beam flexures, taking into account the nonlinearities arising from load equilibrium applied in the deformed configuration. In particular, stiffness and error motions are parametrically quantified in terms of elastic, load-stiffening, kinematic, and elastokinematic effects. The proposed beam constraint model incorporates a wide range of loading conditions, boundary conditions, initial curvature, and beam shape. The accuracy and effectiveness of the proposed beam constraint model is verified by nonlinear finite elements analysis.
Analytical load–displacement relations for flexure mechanisms, formulated by integrating the indi... more Analytical load–displacement relations for flexure mechanisms, formulated by integrating the individual analytical models of their building-blocks (i.e., flexure elements), help in understanding the constraint characteristics of the whole mechanism. In deriving such analytical relations for flexure mechanisms, energy based approaches generally offer lower mathematical complexity, compared to Newtonian methods, by reducing the number of unknowns—specifically, the internal loads. To facilitate such energy based approaches, a closed-form nonlinear strain energy expression for a generalized bisymmetric spatial beam flexure is presented in this paper. The strain energy, expressed in terms of the end-displacement of the beam, considers geometric nonlinearities for intermediate deformations, enabling the analysis of flexure mechanisms over a finite range of motion. The generalizations include changes in the initial orientation and shape of the beam flexure due to potential misalignment or ...
The constraint-based design of flexure mechanisms requires a qualitative and quantitative underst... more The constraint-based design of flexure mechanisms requires a qualitative and quantitative understanding of the constraint characteristics of flexure elements that serve as constraints. This paper presents the constraint characterization of a uniform and symmetric cross-section, slender, spatial beam—a basic flexure element commonly used in three-dimensional flexure mechanisms. The constraint characteristics of interest, namely stiffness and error motions, are determined from the nonlinear load–displacement relations at the beam end. Appropriate assumptions are made while formulating the strain and strain energy expressions for the spatial beam to retain relevant geometric nonlinearities. Using the principle of virtual work, nonlinear beam governing equations are derived and subsequently solved for general end loads. The resulting nonlinear load–displacement relations capture the constraint characteristics of the spatial beam in a compact, closed-form, and parametric manner. This con...
This paper optimizes a GPS smoothing filter to minimize biases caused by ionosphere divergence du... more This paper optimizes a GPS smoothing filter to minimize biases caused by ionosphere divergence during anomalous storms. Ionospheric storms represent the most severe threat to high-integrity differential GPS systems, such as Ground-Based Augmentation Systems (GBAS). Substituting the optimized filter for the Hatch Filter typically used in GBAS reduces ionosphere divergence bias by over 10% for a fixed level of noise attenuation.
Aircraft use navigation guides to help pilots land especially in low visibility conditions. The c... more Aircraft use navigation guides to help pilots land especially in low visibility conditions. The commonly used Instrument Landing System is very effectively yet expensive and inflexible. The Global Positioning System (GPS) can be used to design potentially cheaper and more versatile navigation systems. The Local Area Augmented System (LAAS) is one of the proposed systems for navigation. However it is yet to be certified by the Federal Aviation Administration (FAA) owing to its susceptibility to certain rare events which can potentially cause a system failure in LAAS. LAAS implements the idea of using differential corrections from a nearby reference station to increase the accuracy of the position estimate of the user. One of the biggest threats to LAAS, which undermines the concept of differential corrections, is an ionospheric storm caused by high solar activity. The ionosphere is a spherical shell of ionized gases over earth and affects radiowave communication passing through it. A...
2008 IEEE/ION Position, Location and Navigation Symposium, 2008
Abstract This paper develops a single-frequency filter for smoothing GPS code measurements usin... more Abstract This paper develops a single-frequency filter for smoothing GPS code measurements using a nonlinear method. The method zeroes steady-state divergence errors caused by ionospheric storms. The filter has significant potential to improve the availability of safety-critical ...
Volume 2: 34th Annual Mechanisms and Robotics Conference, Parts A and B, 2010
ABSTRACT In the past, we have introduced the Beam Constraint Model (BCM), which captures pertinen... more ABSTRACT In the past, we have introduced the Beam Constraint Model (BCM), which captures pertinent non-linearities to predict the constraint characteristics of a generalized beam flexure in terms of its stiffness and error motions. In this paper, a non-linear strain energy ...
Redundant constraints are generally avoided in mechanism design because they can lead to binding ... more Redundant constraints are generally avoided in mechanism design because they can lead to binding or loss in expected mobility. However, in certain distributed-compliance flexure mechanism geometries, this problem is mitigated by the phenomenon of elastic averaging. Elastic averaging is a design paradigm that, in contrast with exact constraint design principles, makes deliberate and effective use of redundant constraints to improve performance and robustness. The principle of elastic averaging and its advantages are illustrated in this paper by means of a three-beam parallelogram flexure mechanism, which represents an overconstrained geometry. In a lumped-compliance configuration, this mechanism is prone to binding in the presence of nominal manufacturing and assembly errors. However, with an increasing degree of distributed-compliance, the mechanism is shown to become more tolerant to such geometric imperfections. The nonlinear elastokinematic effect in the constituent beams is show...
A novel parallel-kinematic flexure mechanism that provides highly decoupled motions along the thr... more A novel parallel-kinematic flexure mechanism that provides highly decoupled motions along the three translational directions (X, Y, and Z) and high stiffness along the three rotational directions (θx, θy, and θz) is presented. Geometric decoupling ensures large motion range along each translational direction and enables integration with large-stroke ground-mounted linear actuators or generators, depending on the application. The proposed design, which is based on a systematic arrangement of multiple rigid stages and parallelogram flexure modules, is analyzed via nonlinear finite elements analysis (FEA). A proof-of-concept prototype is fabricated to validate the predicted large range and decoupled motion capabilities. The analysis and the hardware prototype demonstrate an XYZ motion range of 10 mm × 10 mm × 10 mm. Over this motion range, the nonlinear FEA predicts cross-axis errors of less than 7.8%, parasitic rotations less than 10.8 mrad, less than 14.4% lost motion, actuator isola...
Volume 2: 34th Annual Mechanisms and Robotics Conference, Parts A and B, 2010
ABSTRACT The constraint-based design of flexure mechanisms requires a qualitative and quantitativ... more ABSTRACT The constraint-based design of flexure mechanisms requires a qualitative and quantitative understanding of the constraint characteristics of flexure elements that serve as constraints. This paper presents the constraint characterization of a slender, uniform and symmetric cross-...
To utilize beam flexures in constraint-based flexure mechanism design, it is important to develop... more To utilize beam flexures in constraint-based flexure mechanism design, it is important to develop qualitative and quantitative understanding of their constraint characteristics in terms of stiffness and error motions. This paper provides a highly generalized yet accurate closed-form parametric load-displacement model for two-dimensional beam flexures, taking into account the nonlinearities arising from load equilibrium applied in the deformed configuration. In particular, stiffness and error motions are parametrically quantified in terms of elastic, load-stiffening, kinematic, and elastokinematic effects. The proposed beam constraint model incorporates a wide range of loading conditions, boundary conditions, initial curvature, and beam shape. The accuracy and effectiveness of the proposed beam constraint model is verified by nonlinear finite elements analysis.
Analytical load–displacement relations for flexure mechanisms, formulated by integrating the indi... more Analytical load–displacement relations for flexure mechanisms, formulated by integrating the individual analytical models of their building-blocks (i.e., flexure elements), help in understanding the constraint characteristics of the whole mechanism. In deriving such analytical relations for flexure mechanisms, energy based approaches generally offer lower mathematical complexity, compared to Newtonian methods, by reducing the number of unknowns—specifically, the internal loads. To facilitate such energy based approaches, a closed-form nonlinear strain energy expression for a generalized bisymmetric spatial beam flexure is presented in this paper. The strain energy, expressed in terms of the end-displacement of the beam, considers geometric nonlinearities for intermediate deformations, enabling the analysis of flexure mechanisms over a finite range of motion. The generalizations include changes in the initial orientation and shape of the beam flexure due to potential misalignment or ...
The constraint-based design of flexure mechanisms requires a qualitative and quantitative underst... more The constraint-based design of flexure mechanisms requires a qualitative and quantitative understanding of the constraint characteristics of flexure elements that serve as constraints. This paper presents the constraint characterization of a uniform and symmetric cross-section, slender, spatial beam—a basic flexure element commonly used in three-dimensional flexure mechanisms. The constraint characteristics of interest, namely stiffness and error motions, are determined from the nonlinear load–displacement relations at the beam end. Appropriate assumptions are made while formulating the strain and strain energy expressions for the spatial beam to retain relevant geometric nonlinearities. Using the principle of virtual work, nonlinear beam governing equations are derived and subsequently solved for general end loads. The resulting nonlinear load–displacement relations capture the constraint characteristics of the spatial beam in a compact, closed-form, and parametric manner. This con...
Uploads