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At least 73 records · Page 4

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NASA NTRS2005

Kinematics of a New High Precision Three Degree-of-Freedom Parallel Manipulator

Closed-form direct and inverse kinematics of a new three degree-of-freedom (DOF) parallel manipulator with inextensible limbs and base-mounted actuators are presented. The manipulator has higher resolution and precision than the existing three DOF mechanisms with extensible limbs. Since all of the manipulator actuators are base-mounted; higher payload capacity, smaller actuator sizes, and lower power dissipation can be obtained. The manipulator is suitable for alignment applications where only tip, tilt, and piston motions are significant. The direct kinematics of the manipulator is reduced to solving an eighth-degree polynomial in the square of tangent of half-angle between one of the limbs and the base plane. Hence, there are at most sixteen assembly configurations for the manipulator. In addition, it is shown that the sixteen solutions are eight pairs of reflected configurations with respect to the base plane. Numerical examples for the direct and inverse kinematics of the manipulator are also presented.

Tahmasebi, Farhad↗

NASA NTRS2011

Graph Theory Roots of Spatial Operators for Kinematics and Dynamics

Spatial operators have been used to analyze the dynamics of robotic multibody systems and to develop novel computational dynamics algorithms. Mass matrix factorization, inversion, diagonalization, and linearization are among several new insights obtained using such operators. While initially developed for serial rigid body manipulators, the spatial operators and the related mathematical analysis have been shown to extend very broadly including to tree and closed topology systems, to systems with flexible joints, links, etc. This work uses concepts from graph theory to explore the mathematical foundations of spatial operators. The goal is to study and characterize the properties of the spatial operators at an abstract level so that they can be applied to a broader range of dynamics problems. The rich mathematical properties of the kinematics and dynamics of robotic multibody systems has been an area of strong research interest for several decades. These properties are important to understand the inherent physical behavior of systems, for stability and control analysis, for the development of computational algorithms, and for model development of faithful models. Recurring patterns in spatial operators leads one to ask the more abstract question about the properties and characteristics of spatial operators that make them so broadly applicable. The idea is to step back from the specific application systems, and understand more deeply the generic requirements and properties of spatial operators, so that the insights and techniques are readily available across different kinematics and dynamics problems. In this work, techniques from graph theory were used to explore the abstract basis for the spatial operators. The close relationship between the mathematical properties of adjacency matrices for graphs and those of spatial operators and their kernels were established. The connections hold across very basic requirements on the system topology, the nature of the component bodies, the indexing schemes, etc. The relationship of the underlying structure is intimately connected with efficient, recursive computational algorithms. The results provide the foundational groundwork for a much broader look at the key problems in kinematics and dynamics. The properties of general graphs and trees of nodes and edge were examined, as well as the properties of adjacency matrices that are used to describe graph connectivity. The nilpotency property of such matrices for directed trees was reviewed, and the adjacency matrices were generalized to the notion of block weighted adjacency matrices that support block matrix elements. This leads us to the development of the notion of Spatial Kernel Operator SKO kernels. These kernels provide the basis for the development of SKO resolvent operators.

Jain, Abhinandan↗

NASA NTRS2012

The Kinematic and Microphysical Control of Storm Integrated Lightning Flash Extent

The objective of this preliminary study is to investigate the kinematic and microphysical control of lightning properties, particularly those that may govern the production of nitrogen oxides (NOx) in thunderstorms, such as flash rate, type and extent. The mixed-phase region is where the noninductive charging (NIC) process is thought to generate most storm electrification during rebounding collisions between ice particles in the presence of supercooled water. As a result, prior radar-based studies have demonstrated that lightning flash rate is well correlated to kinematic and microphysical properties in the mixed-phase region of thunderstorms such as updraft volume, graupel mass, or ice mass flux. There is also some evidence that lightning type is associated with the convective state. Intracloud (IC) lightning tends to dominate during the updraft accumulation of precipitation ice mass while cloud-to-ground (CG) lightning is more numerous during the downdraft-driven descent of radar echo associated with graupel and hail. More study is required to generalize these relationships, especially regarding lightning type, in a wide variety of storm modes and meteorological conditions. Less is known about the co-evolving relationship between storm kinematics, microphysics, morphology and three-dimensional flash extent, despite its importance for lightning NOx production. To address this conceptual gap, the NASA MSFC Lightning Nitrogen Oxides Model (LNOM) is applied to North Alabama Lightning Mapping Array (NALMA) and Vaisala National Lightning Detection NetworkTM (NLDN) observations following ordinary convective cells through their lifecycle. LNOM provides estimates of flash type, channel length distributions, lightning segment altitude distributions (SADs) and lightning NOx production profiles. For this study, LNOM is applied in a Lagrangian sense to well isolated convective cells on 3 April 2007 (single cell and multi-cell hailstorm, non-severe multicell) and 6 July 2007 (non-severe multi-cell) over Northern Alabama. The LNOM lightning characteristics are compared to the evolution of updraft and precipitation properties inferred from dual-Doppler and polarimetric radar analyses applied to observations from a nearby Doppler radar network, including the UA Huntsville Advanced Radar for Meteorological and Operational Research (ARMOR, C-band, polarimetric). The LNOM estimated SAD and lightning NOx production profiles are placed in the context of radar derived profiles of vertical motion, precipitation types and amounts. Finally, these analyses are used to determine if storm integrated flash channel extent is as well correlated to volumetric updraft and precipitation ice characteristics in the mixed phase region as flash rate for these individual convective cells.

Carey, Lawrence↗

NASA NTRS2013

A Kinematic Calibration Process for Flight Robotic Arms

The Mars Science Laboratory (MSL) robotic arm is ten times more massive than any Mars robotic arm before it, yet with similar accuracy and repeatability positioning requirements. In order to assess and validate these requirements, a higher-fidelity model and calibration processes were needed. Kinematic calibration of robotic arms is a common and necessary process to ensure good positioning performance. Most methodologies assume a rigid arm, high-accuracy data collection, and some kind of optimization of kinematic parameters. A new detailed kinematic and deflection model of the MSL robotic arm was formulated in the design phase and used to update the initial positioning and orientation accuracy and repeatability requirements. This model included a higher-fidelity link stiffness matrix representation, as well as a link level thermal expansion model. In addition, it included an actuator backlash model. Analytical results highlighted the sensitivity of the arm accuracy to its joint initialization methodology. Because of this, a new technique for initializing the arm joint encoders through hardstop calibration was developed. This involved selecting arm configurations to use in Earth-based hardstop calibration that had corresponding configurations on Mars with the same joint torque to ensure repeatability in the different gravity environment. The process used to collect calibration data for the arm included the use of multiple weight stand-in turrets with enough metrology targets to reconstruct the full six-degree-of-freedom location of the rover and tool frames. The follow-on data processing of the metrology data utilized a standard differential formulation and linear parameter optimization technique.

Collins, Curtis L.↗

NASA NTRS2020

The Warm Gas in the MW: A Kinematical Model

We develop a kinematical model for the Milky Way Si IV-bearing gas to determine its density distribution and kinematics. This model is constrained by a column density line-shape sample extracted from the Hubble Space Telescope/Cosmic Origins Spectrograph archival data, which contains 186 active galactic nucleus sight lines. We find that the Si IV ion density distribution is dominated by an extended disk along the z-direction (above or below the midplane), i.e., n(z) = n0 exp(-(z z/0 ) 0.82 , where z0 is the scale height of - 6.3+1.5 -1.6 kpc (northern hemisphere) and 3.6+0.9 -1.0 kpc (southern hemisphere). The density distribution of the disk in the radial direction shows a sharp edge at 15–20 kpc given by, n(rXY) = n0 exp(-(rXY/r0) 3.36 , where r0≈12.5±0.6 kpc. The difference of density distributions over rXY and z directions indicates that the warm gas traced by Si IV is mainly associated with disk processes (e.g., feedback or cycling gas) rather than accretion. We estimate the mass of the warm gas (within 50 kpc) is log(M(50kpc) M(sun)) ≈ 8.1 (assuming Z≈0.5 Z(sun)), and a 3σ upper limit of log(M(250kpc) M(sun)) ≈ 9.1 (excluding the Magellanic system). Kinematically, the warm gas disk is nearly co-rotating with the stellar disk at vrot = 215 ± 3 km s-1, which lags the midplane rotation by about 8 km s-1 kpc-1 (within 5 kpc). Meanwhile, we note that the warm gas in the northern hemisphere has significant accretion with vacc of 69±7 km s-1 at 10 kpc (an accretion rate of -0.60+0.13- 0.11 M(sun) yr-1), while in the southern hemisphere, there is no measurable accretion, with an upper limit of 0.4M(sun) yr−1.

Zhijie Qu↗

NASA NTRS2014

Ionized Gas Kinematics at High Resolution. IV. Star Formation and a Rotating Core in the Medusa (NGC 4194)

NGC 4194 is a post-merger starburst known as The Medusa for its striking tidal features.We present here a detailed study of the structure and kinematics of ionized gas in the central 0.65 kpc of the Medusa. The data include radio continuum maps with resolution up to 0".18 (35 pc) and a 12.8 micron [Ne II] data cube with spectral resolution approx. 4 km/s: the first high-resolution, extinction-free observations of this remarkable object. The ionized gas has the kinematic signature of a core in solid-body rotation. The starburst has formed a complex of bright compact H II regions, probably excited by deeply embedded super star clusters, but none of these sources is a convincing candidate for a Galactic nucleus. The nuclei of the merger partners that created the Medusa have not yet been identified.

Ionized↗

NASA NTRS1995

Precise Kinematic Positioning with Simultaneous GPS Pseudorange and Carrier Phase Measurements

This paper investigates three precise kinematic positioning techniques with simultaneous GPS pseudorange and carrier phase measurements. These techniques are simple, efficient, and well suited for real-time positioning applications. A simulation/covariance analysis is carried out comparing the relative performance of these techniques. The analysis indicates that GPS carrier phase measurements significantly strengthen kinematic positioning. When wide-area differential GPS for reducing SA clock errors and GPS ephemeris errors is available, a low Earth orbiting satellite can be positioned to 0.5-0.8 m in accuracy (3-D RSS). The accuracy is superior to positioning with pseudorange measurements alone by a factor of 2 to 3. Relative positioning performance and complexity between the three techniques are compared.

['Kinematic↗

NASA NTRS1973

A kinematic eddy viscosity model including the influence of density variations and preturbulence

A model for the kinematic eddy viscosity was developed which accounts for the turbulence produced as a result of jet interactions between adjacent streams as well as the turbulence initially present in the streams. In order to describe the turbulence contribution from jet interaction, the eddy viscosity suggested by Prandtl was adopted, and a modification was introduced to account for the effect of density variation through the mixing layer. The form of the modification was ascertained from a study of the compressible turbulent boundary layer on a flat plate. A kinematic eddy viscosity relation which corresponds to the initial turbulence contribution was derived by employing arguments used by Prandtl in his mixing length hypothesis. The resulting expression for self-preserving flow is similar to that which describes the mixing of a submerged jet. Application of the model has led to analytical predictions which are in good agreement with available turbulent mixing experimental data.

Cohen, L. S.↗

NASA NTRS1975

A Standard Kinematic Model for Flight Simulation at NASA Ames

A standard kinematic model for aircraft simulation exists at NASA-Ames on a variety of computer systems, one of which is used to control the flight simulator for advanced aircraft (FSAA). The derivation of the kinematic model is given and various mathematical relationships are presented as a guide. These include descriptions of standardized simulation subsystems such as the atmospheric turbulence model and the generalized six-degrees-of-freedom trim routine, as well as an introduction to the emulative batch-processing system which enables this facility to optimize its real-time environment.

Mcfarland, R. E.↗

NASA NTRS1974

Interplanetary stream magnetism: Kinematic effects

The particle density, and the magnetic field intensity and direction are calculated in corotating streams of the solar wind, assuming that the solar wind velocity is constant and radial and that its azimuthal variations are not two rapid. The effects of the radial velocity profile in corotating streams on the magnetic fields were examined using kinematic approximation and a variety of field configurations on the inner boundary. Kinematic and dynamic effects are discussed.

Burlaga, L. F.↗

NASA NTRS1976

A single axis study of flight simulator kinematics by difference techniques

The kinematic parameters of position, velocity, and acceleration of a flight simulator may be calculated by knowing the distance between two or more points on an axis and the time the simulator takes to traverse the space between each set of points. These parameters are calculated through the use of difference techniques. Given the true kinematic response of the simulator to computer generated commands, the entire motion system loop may be calibrated, and system operability verified.

Webster, L. D.↗

NASA NTRS1979

The grabens of Canyonlands National Park, Utah - Geometry, mechanics, and kinematics

Results are reported for three years of field and analytical study of a system of young and very well exposed grabens in southeastern Utah. A kinematic and mechanical model is developed for these specific grabens with the hope that this will aid in interpreting graben systems elsewhere on the earth and other planets. Because studies on other planets must be based entirely on photo analysis, an attempt is made to determine to what extent three-dimensional geometry could be inferred from photographs alone. An equation based on the model of graben geometry and kinematics relates thickness of faulted plates to graben parameters measurable on photographs. The initial width of a nascent graben is a simple function of the dip of the faults bounding the graben and of the thickness of the faulted brittle plate. The uniform spacing of the grabens is a natural result of the geometry of the system.

Mcgill, G. E.↗

NASA NTRS1979

Kinematics and dynamics of vortex rings in a tube

Kinematic theory and flow visualization experiments were combined to examine the dynamic processes which control the evolution of vortex rings from very low to very high Reynolds numbers, and to assess the effects of the wall as a vortex ring travels up a tube. The kinematic relationships among the size, shape, speed, and strength of vortex rings in a tube were computed from the theory. Relatively simple flow visualization measurements were used to calculate the total circulation of a vortex rings at a given time. Using this method, the strength was computated and plotted as a function of time for experimentally produced vortex rings. Reynolds number relationships are established and quantitative differences among the three Reynolds number groups are discussed.

Brasseur, J. G.↗

NASA NTRS1981

Kinematic properties of the helicopter in coordinated turns

A study on the kinematic relationship of the variables of helicopter motion in steady, coordinated turns involving inherent sideslip is described. A set of exact kinematic equations which govern a steady coordinated helical turn about an Earth referenced vertical axis is developed. A precise definition for the load factor parameter that best characterizes a coordinated turn is proposed. Formulas are developed which relate the aircraft angular rates and pitch and roll attitudes to the turn parameters, angle of attack, and inherent sideslip. A steep, coordinated helical turn at extreme angles of attack with inherent sideslip is of primary interest. The bank angle of the aircraft can differ markedly from the tilt angle of the normal load factor. The normal load factor can also differ substantially from the accelerometer reading along the vertical body axis of the aircraft. Sideslip has a strong influence on the pitch attitude and roll rate of the helicopter. Pitch rate is independent of angle of attack in a coordinated turn and in the absence of sideslip, angular rates about the stability axes are independent of the aerodynamic characteristics of the aircraft.

Chen, R. T. N.↗

NASA NTRS1981

Influence of sideslip on the kinematics of the helicopter in steady coordinated turns

A steep coordinated helical turn at extreme angles of attack with inherent sideslip is of primary interest in this study. Unlike fixed-wing aircraft, the helicopter in a steady coordinated turn will inherently sideslip. A set of exact kinematic equations describing this motion in steady helical turns has been developed, and a rational definition for the load factor that best characterizes a coordinated turn for a helicopter has been proposed. An analysis has also been completed on the effects of sideslip on the kinematic relationships in a coordinated turn which is based on new closed-form solutions which relate the aircraft angular rates and pitch and roll attitudes to the turn parameters, angle of attack, and sideslip. The results show that the bank angle of the aircraft can differ markedly from the tilt angle of the normal load factor and that the normal load factor can also differ substantially from the accelerometer reading along the vertical body axis of the aircraft. Generally, sideslip has a strong influence on the pitch attitude and roll rate of the helicopter. The study also indicates that pitch rate is independent of angle of attack in a coordinated turn and that in the absence of sideslip, angular rates about the stability axes are independent of the aerodynamic characteristics of the aircraft.

Chen, R. T. N.↗

NASA NTRS1982

The effects of random errors in rawinsonde data on derived kinematic quantities

The sensitivity of kinematic parameters to random errors contained in rawinsonde data is assessed. Parameters under consideration include relative vorticity, vorticity advection, horizontal divergence, kinematic vertical motion, and temperature advection. It is shown that horizontal divergence is the most affected, with reliability a function of height. Vorticity advection is the next most altered by random error, and in this case, the effects of wind errors are greater on the gradient of vorticity than on the vorticity itself. Vertical motions are most affected by random perturbations at 300 mb and above, and temperature advection is found to be the least sensitive to random perturbations.

Belt, C. L.↗

NASA NTRS1982

A comparison of adiabatic and kinematic vertical motions using mesoscale data

Results are compared from the adiabatic and kinematic methods of determining vertical motion during a period of severe convective storms when special meso alpha-scale rawinsonde data were available. The two procedures were tested using data from the first regional-scale day of AVE-SESAME '79 which coincided with the Red River Valley tornado outbreak of April 10-11, 1979. At 700 mb, each technique showed good agreement with the weather patterns, but the kinematic procedure gave superior results at 500 mb. The overall goodness of the adiabatic method during this particular case was not solely due to the high-resolution SESAME data since synoptic-scale mechanisms played a major role in creating a storm-conducive environment. With the advent of computer aided analysis systems such as AFOS, forecasters will have quicker access to a greater variety of information. Present results suggest that the adiabatic method can yield useful information for severe storm forecasters, especially in the lower troposphere. An interesting follow-on study would use sounding data from geostationary VAS satellites to compute adiabatic vertical motions at finer time and space resolutions than is now possible using RAOB data alone. Geostrophic winds derived from satellite thermal data probably can be used.

Fuelberg, H. E.↗

NASA NTRS1983

Kinematics of velocity and vorticity correlations in turbulent flow

The kinematic problem of calculating second-order velocity moments from given values of the vorticity covariance is examined. Integral representation formulas for second-order velocity moments in terms of the two-point vorticity correlation tensor are derived. The special relationships existing between velocity moments in isotropic turbulence are expressed in terms of the integral formulas yielding several kinematic constraints on the two-point vorticity correlation tensor in isotropic turbulence. Numerical evaluation of these constraints suggests that a Gaussian curve may be the only form of the longitudinal velocity correlation coefficient which is consistent with the requirement of isotropy. It is shown that if this is the case, then a family of exact solutions to the decay of isotropic turbulence may be obtained which contains Batchelor's final period solution as a special case. In addition, the computed results suggest a method of approximating the integral representation formulas in general turbulent shear flows.

Bernard, P. S.↗