SEARCH · Search NASA

Results for “direct kinematic methods”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 73 records · Page 4

All sources NASA NTRS DOE OSTI

NASA NTRS1984

Special cases of friction and applications

Two techniques for reducing friction forces are presented. The techniques are applied to the generalized problem of reducing the friction between kinematic pairs which connect a moveable link to a frame. The basic principles are: (1) Let the moveable link be supported by two bearings where the relative velocities of the link with respect to each bearing are of opposite directions. Thus the resultant force (torque) of friction acting on the link due to the bearings is approximately zero. Then, additional perturbation of motion parallel to the main motion of the moveable link will require only a very small force; (2) Let the perturbation in motion be perpendicular to the main motion. Equations are developed which explain these two methods. The results are discussed in relation to friction in geared couplings, gyroscope gimbal bearings and a rotary conveyor system. Design examples are presented.

Litvin, F. L.↗

NASA NTRS2003

First Results from a Hardware-in-the-Loop Demonstration of Closed-Loop Autonomous Formation Flying

A closed-loop system for the demonstration of autonomous satellite formation flying technologies using hardware-in-the-loop has been developed. Making use of a GPS signal simulator with a dual radio frequency outlet, the system includes two GPS space receivers as well as a powerful onboard navigation processor dedicated to the GPS-based guidance, navigation, and control of a satellite formation in real-time. The closed-loop system allows realistic simulations of autonomous formation flying scenarios, enabling research in the fields of tracking and orbit control strategies for a wide range of applications. The autonomous closed-loop formation acquisition and keeping strategy is based on Lyapunov's direct control method as applied to the standard set of Keplerian elements. This approach not only assures global and asymptotic stability of the control but also maintains valuable physical insight into the applied control vectors. Furthermore, the approach can account for system uncertainties and effectively avoids a computationally expensive solution of the two point boundary problem, which renders the concept particularly attractive for implementation in onboard processors. A guidance law has been developed which strictly separates the relative from the absolute motion, thus avoiding the numerical integration of a target trajectory in the onboard processor. Moreover, upon using precise kinematic relative GPS solutions, a dynamical modeling or filtering is avoided which provides for an efficient implementation of the process on an onboard processor. A sample formation flying scenario has been created aiming at the autonomous transition of a Low Earth Orbit satellite formation from an initial along-track separation of 800 m to a target distance of 100 m. Assuming a low-thrust actuator which may be accommodated on a small satellite, a typical control accuracy of less than 5 m has been achieved which proves the applicability of autonomous formation flying techniques to formations of satellites as close as 50 m.

Gill, E.↗

NASA NTRS1994

Analysis and prediction of ocean swell using instrumented buoys

During the period 20-23 September 1990, the remnants of Supertyphoon Flo moved into the central North Pacific Ocean with sustained wind speeds of 28 m/s. The strong wind and large fetch area associated with this storm generated long-period swell that propagated to the west coast of North America. National Data Buoy Center moored-buoy stations, located in a network that ranged from the Gulf of Alaska to the California Bight, provided wave spectral estimates of the swell from this storm. The greatest dominant wave periods measured were approximately 20-25 s, and significant wave heights measured ranged from 3 to 8 m. Wave spectra from an array of three nondirectional buoys are used to find the source of the long-period swell. Directional wave spectra from a heave-pitch-roll buoy are also used to make an independent estimate of the source of the swell. The ridge-line method, using time-frequency contour plots of wave spectral energy density, is used to determine the time of swell generation, which is used with the appropriate surface pressure analysis to infer the swell generation area. The diagnosed sources of the swell are also compared with nowcasts from the Global Spectral Ocean Wave Model of the Fleet Numerical Oceanography Center. A simple method of predicting the propagation of ocean swell, by applying a simple kinematic model of wave propagation to the estimated point and time source, is demonstrated.

Mettlach, Theodore↗

NASA NTRS2021

Comparing Theoretically Scaled Biomechanical Models

BACKGROUND An investigation into incorporating space suit aspects required a 50th-percentile male model which was not part of the existing dataset of models. Previously, theoretical models for 5th-percentile female and 95th-percentile male were created utilizing a scaled test subject as close as possible to the target height and weight. Scaling factors were created by taking the height ratio and applying it uniformly to the model body segments, then fine tuning to ensure the theoretical model’s height is as expected. This study was initiated to examine the existing method of isometrically scaling in OpenSim [1,2] and to create alternative methods which do not rely on an existing subject being close in height and weight to the theoretical model of interest. Generating a theoretical biomechanical model provides additional abilities without the reliance on available OpenSim models or real subjects. Gained abilities include creating different percentile models and attaining representative anthropometry for any target height/weight, such as targeting specific crew populations or gaps within the current dataset. METHODS AND RESULTS This study includes 3 methods for generating the theoretical model; utilizing the modified unscaled OpenSim Full Body Rajagopal Model (FBRM) [3,4], a dataset of scaled OpenSim models, and existing scaling factors from Dumas et al. [5]. All methods use the Anthropometric Survey of US Army Personnel (ANSUR II) [6] as an input of necessary anthropometric measurements. The following measurements are retrieved from the ANSUR II collection: mass, stature, cervicale height, acromial height, axilla height, waist height, trochanterion height, lateral femoral epicondyle height, lateral malleolus height, acromion-radiale length, radiale-stylion length, palm length, ball of foot length, bicristal breadth, bimalleolar breadth. Some of the measurements are direct segment lengths and others are utilized to derive segment lengths. Height, weight, and age ranges are the required inputs to parse the collection for a mean value of the measurements. A simple iterative process may be necessary for the output of mean mass and stature consistent with the theoretical model of interest. In some cases, one may specify exact values instead of a range but that is dependent upon whether those exact values pertain to a single subject from the ANSUR II collection. Equations from Dumas et al. were used to calculate scaling factors for the two methods that utilize OpenSim scaled and unscaled models. In the third method, Dumas’ scaling factors were used directly instead of generating our own. After scaling factors are achieved, they are applied along with the mass and segment lengths retrieved from ANSUR II in order to calculate the segment mass, Center of Mass (CoM), mass Moment of Inertia (MoI), and the joint location in the parent frame. The theoretical models from the different methods were compared to the previous existing method of isometrically scaling in OpenSim, as well as the standards found in NASA STD-3000 [7] and the NASA Human Integration Design Handbook [8]. The whole-body center of mass is the main comparison performed between the models and the standards. The body segment mass properties were also compared when possible. In some cases, the standards do not provide complete data, or the center of mass location is not provided with respect to the appropriate joint coordinate system. For a 50th-percentile male subject, results from isometric scaling in OpenSim and the method utilizing the unscaled FBRM were compared to the standards in NASA STD-3000. According to the standard, the whole-body vertical CoM location was taken from the head vertex to the CoM. The standards provide 80.2 cm for the CoM vertical component whereas isometric scaling in OpenSim and utilizing the unscaled FBRM provide 82.2 and 82.3 cm, respectively. Through definition, the whole-body CoM in the medial/lateral direction agreed across the models. Investigation is on-going to clearly identify the reference point pertaining to dorsal/ventral whole-body CoM position in standards and relate that to the theoretical models. REFERENCES [1] Delp, S.L., et al., “OpenSim: Open-source Software to Create and Analyze Dynamic Simulations of Movement”, IEEE Transactions on Biomedical Engineering, (2007). [2] Seth, A., Hicks J.L., Uchida, T.K., Habib, A., Dembia, C.L., Dunne, J.J., Ong, C.F., DeMers, M.S., Rajagopal, A., Millard, M., Hamner, S.R., Arnold, E.M., Yong, J.R., Lakshmikanth, S.K., Sherman,n M.A., Delp, S.L. OpenSim: Simulating musculoskeletal dynamics and neuromuscular control to study human and animal movement. Plos Computational Biology, 14(7). (2018) [3] R. K. Huffman, W. K. Thompson, C. A. Gallo, L. J. Quiocho, “Improvement of Scaling and Inverse Kinematic Results with Additional Upper Body Joints Added to Opensim Rajagopal Model”, NASA Human Research Program Investigator’s Workshop, (2019). [4] Huffman R.K., Thompson W., Gallo C., “Modified OpenSim Rajagopal Full Body Model”, New Technology Report, MSC-26872-1. (August 2020). [5] Dumas R., Cheze L. and Verriest J., 2007. “Adjustments to McConville et al. and Young et al. body segment inertial parameters”. Journal of Biomechanics 40, pp. 543-553 [6] Gordon C.C., 2012 “Anthropometric Survey of U.S. Army Personnel: Methods and Summary Statistics”, US Army Natick Soldier RD&E Center. [7] NASA STD-3000/REV-B, 1995. “The Man-System Integration Standards” [8] NASA/SP-2010-3407/REV-1, 2014. “The Human Integration Design Handbook (HIDH)”

F N Matari↗

NASA NTRS1993

Design and control of a hand exoskeleton for use in extravehicular activities

To counter problems inherent in extravehicular activities (EVA) and complex space operations, an exoskeleton, a unique adaptive structure, has been designed. The exoskeleton fits on the hand and powers the proximal and middle phalanges of the index finger, the middle finger, and the combined ring and little finger. A kinematic analysis of the exoskeleton joints was performed using the loop-closure method. This analysis determined the angular displacement and velocity relationships of the exoskeleton joints. This information was used to determine the output power of the exoskeleton. Three small DC motors (one for each finger) are used to power the exoskeleton. The motors are mounted on the forearm. Power is transferred to the exoskeleton using lead screws. The control system for the exoskeleton measures the contact force between the operator and the exoskeleton. This information is used as the input to drive the actuation system. The control system allows the motor to rotate in both directions so that the operator may close or open the exoskeleton.

Shields, B.↗

NASA NTRS1989

On the dynamic singularities in the control of free-floating space manipulators

It is shown that free-floating space manipulator systems have configurations which are dynamically singular. At a dynamically singular position, the manipulator is unable to move its end effector in some direction. This problem appears in any free-floating space manipulator system that permits the vehicle to move in response to manipulator motion without correction from the vehicle's attitude control system. Dynamic singularities are functions of the dynamic properties of the system; their existence and locations cannot be predicted solely from the kinematic structure of the manipulator, unlike the singularities for fixed base manipulators. It is also shown that the location of these dynamic singularities in the workplace is dependent upon the path taken by the manipulator in reaching them. Dynamic singularities must be considered in the control, planning and design of free-floating space manipulator systems. A method for calculating these dynamic singularities is presented, and it is shown that the system parameters can be selected to reduce the effect of dynamic singularities on a system's performance.

Papadopoulos, E.↗

NASA NTRS2017

Implicit Formulation of Muscle Dynamics in OpenSim

Astronauts lose bone and muscle mass during spaceflight. Exercise countermeasure is the primary method for counteracting bone and muscle mass loss in space. New spacecraft exercise device concepts are currently being developed for the NASAs new crew exploration vehicle. The NASA Digital Astronaut Project (DAP) uses computational modeling to help determine if the new exercise devices will be effective as countermeasures. The NASA Digital Astronaut Project is developing the ability to utilize predictive simulation to provide insight into the change in kinematics and kinetics with a change in device and gravitational environment (1-g versus 0-g). For example, in space exercise the subject's body weight is applied in addition to the loads prescribed for musculoskeletal maintenance. How and where these loads are applied obviously directly impacts bone and tissue loads. Additionally, due to space vehicle structural requirements, exercise devices are often placed on vibration isolation systems. This changes the apparent impedance or stiffness of the device as seen by the user. Data collection under these conditions is often impractical and limited. Predictive modeling provides a means to have a virtual subject to test hypotheses. Predictive simulation provides a virtual subject for which we are able to perform studies such as sensitivity to device loading and vibration isolation without the need for laboratory kinematic or kinetic test data.Direct Collocation optimization provides an efficient means to perform task based optimization and predictive modeling. It is relatively straight forward to structure a physical exercise task in a Direct Collocation mathematical formulation: perform a motion such that you start at an initial pose, achieve a given amount of deflection i.e a squat, return to the initial pose, and minimize muscle activation cost. Direct Collocation is advantageous in that it does not require numerical integration to evaluate the objective function. Instead, the system dynamics are transformed to discrete time and the optimizer is constrained such that the solution is not considered to be a valid unless the dynamic equations are satisfied at all time points. The simulation and optimization are effectively done simultaneously. Due to the implicit integration, time steps can be more coarse than in a differential equation solver. In a gait scenario this means that that the model constraints and cost function are evaluated at 100 nodes in the gait cycle versus 10,000 integration steps in a variable-step forward dynamic simulation. Furthermore, no time is wasted on accurate simulations of movements that are far from the optimum. Constrained optimization algorithms require a Jacobian matrix that contains the partial derivatives of each of the dynamic constraints with respect to of each of the state and control variables at all time points. This is a large but sparse matrix. An implicit dynamics formulation requires computation of the dynamic residuals f as a function of the states x and their derivatives, and controls u:f(x, dxdt, u) 0If the dynamics of musculoskeletal system are formulated implicitly, the Jacobian elements are often available analytically, eliminating the need for numerical differentiation; this is obviously computationally advantageous. Additionally, implicit formulation of musculoskeletal dynamics do not suffer from singularities from low mass bodies, zero muscle activation, or other stiff system or

physical exercise↗

NASA NTRS2012

Understanding Shock Dynamics in the Inner Heliosphere with Modeling and Type II Radio Data: the 2010-04-03 Event

The 2010 April 03 solar event was studied using observations from STEREO SECCHI, SOHO LASCO, and Wind kilometric Type II data (kmTII) combined with WSA-Cone-ENLIL model simulations performed at the Community Coordinated Modeling Center (CCMC). In particular, we identified the origin of the coronal mass ejection (CME) using STEREO EUVI and SOHO EIT images. A flux-rope model was fit to the SECCHI A and B, and LASCO images to determine the CMEs direction, size, and actual speed. J-maps from STEREO COR2HI-1HI-2 and simulations fromCCMC were used to study the formation and evolution of the shock in the inner heliosphere. In addition, we also studied the time-distance profile of the shock propagation from kmTII radio burst observations. The J-maps together with in-situ datafrom the Wind spacecraft provided an opportunity to validate the simulation results andthe kmTII prediction. Here we report on a comparison of two methods of predictinginterplanetary shock arrival time: the ENLIL model and the kmTII method; andinvestigate whether or not using the ENLIL model density improves the kmTIIprediction. We found that the ENLIL model predicted the kinematics of shock evolutionwell. The shock arrival times (SAT) and linear-fit shock velocities in the ENLILmodel agreed well with those measurements in the J-maps along both the CME leading edge and the Sun-Earth line. The ENLIL model also reproduced most of the largescale structures of the shock propagation and gave the SAT prediction at Earth with an error of 17 hours. The kmTII method predicted the SAT at Earth with an error of 15 hours when using n0 4.16 cm3, the ENLIL model plasma density near Earth; but itimproved to 2 hours when using n0 6.64 cm3, the model density near the CMEleading edge at 1 AU.

Space weather forecast↗

NASA NTRS2004

Cone Model for Halo CMEs: Application to Space Weather Forecasting

In this study, we present an innovative analytical method to determine the angular width and propagation orientation of halo Coronal Mass Ejections (CMEs). The relation of CME actual speed with apparent speed and its components measured at different position angle has been investigated. The present work is based on the cone model proposed by Zhao et al. We have improved this model by: (1) eliminating the ambiguity via a new analytical approach, (2) using direct measurements of projection onto the plane of the sky (POS), and (3) determining the actual radial speeds from projection speeds at different position angles to clarify the uncertainty of projection speeds in previous empirical models. Our analytical approach allows us to use coronagraph data to determine accurately the geometrical features of POS projections, such as major axis, minor axis, and the displacement of the center of its projection, and to determine the angular width and orientation of a given halo CME. Our approach allows for the first time the determination of the actual CME speed, width, and source location by using coronagraph data quantitatively and consistently. The method greatly enhances the accuracy of the derived geometrical and kinematical properties of halo CMEs, and can be used to optimize Space Weather forecasts. The applied model predications are in good agreement with observations.

Xie, Hong↗

NASA NTRS2015

Spherical Coordinate Systems for Streamlining Suited Mobility Analysis

Introduction: When describing human motion, biomechanists generally report joint angles in terms of Euler angle rotation sequences. However, there are known limitations in using this method to describe complex motions such as the shoulder joint during a baseball pitch. Euler angle notation uses a series of three rotations about an axis where each rotation is dependent upon the preceding rotation. As such, the Euler angles need to be regarded as a set to get accurate angle information. Unfortunately, it is often difficult to visualize and understand these complex motion representations. It has been shown that using a spherical coordinate system allows Anthropometry and Biomechanics Facility (ABF) personnel to increase their ability to transmit important human mobility data to engineers, in a format that is readily understandable and directly translatable to their design efforts. Objectives: The goal of this project was to use innovative analysis and visualization techniques to aid in the examination and comprehension of complex motions. Methods: This project consisted of a series of small sub‐projects, meant to validate and verify a new method before it was implemented in the ABF's data analysis practices. A mechanical test rig was built and tracked in 3D using an optical motion capture system. Its position and orientation were reported in both Euler and spherical reference systems. In the second phase of the project, the ABF estimated the error inherent in a spherical coordinate system, and evaluated how this error would vary within the reference frame. This stage also involved expanding a kinematic model of the shoulder to include the rest of the joints of the body. The third stage of the project involved creating visualization methods to assist in interpreting motion in a spherical frame. These visualization methods will be incorporated in a tool to evaluate a database of suited mobility data, which is currently in development. Results: Initial results demonstrated that a spherical coordinate system is helpful in describing and visualizing the motion of a space suit. The system is particularly useful in describing the motion of the shoulder, where multiple degrees of freedom can lead to very complex motion paths.

Benson, Elizabeth↗

NASA NTRS2020

Calibrating a 3-Axis Accelerometer Instrument with a Less Accurate Calibration Device Part 1: Mathematical Methodology

A three-axis accelerometer instrument (3xAI) can provide the angular attitude of a 3D object using the gravity vector (g) as the sole reference. Calibrating such an instrument requires placing it at known (to some accuracy plus uncertainty) angular articulations with respect to g. This paper will show a potential process for calibrating a 3xAI by using a 2-axis rotary system (calibration device) to provide these articulations. Any calibration device (CD) with such capacity will contain internal misalignments. These misalignments, even if made relatively small or approximated to zero in the kinematics model (KM), can be detrimental to the calibration of the instrument when high measurement accuracy is required. This is especially true if the selected set of articulations chosen for calibration do not include their symmetrical counterpoints (a point where the misalignment has equal magnitude but is opposite in direction to a point chosen). The consequence of not including the combination, point and counterpoint, for any misalignment involved in the calibration, results in a biased instrument. This paper will demonstrate a calibration of the instrument using symbolic math resulting in a closed-form solution of the instrument coefficients. The main objective is to show the impact of all the CD misalignments to the instrument coefficients. This process is the basis for a more sophisticated method (shown in a future paper) for obtaining the instrument coefficients while simultaneously obtaining an estimate of the calibration device internal misalignments.

Angle↗

NASA NTRS1981

Combination of Kinematics with Flow Visualization to Compute Total Circulation

A method is described in which kinematics is exploited to compute the total circulation of a vortex from relatively simple flow visualization experiments. There are several advantages in the technique, including the newly acquired ability to calculate the changes in strength of a single vortex as it evolves. The main concepts and methodology are discussed in a general way for application to vortices which carry along with them definable regions of essentially irrotational fluid; however, the approach might be generalized to other flows which contain regions of concentrated vorticity. As an illustrative example, an application to the study of the transient changes in total circulation of individual vortex rings as they travel up a tube is described, taking into account the effect of the tube boundary. The accuracy of the method, assessed in part by a direct comparison with a laser Doppler measurement is felt to be well within experimental precision for vortex rings over a wide range of Reynolds numbers.

Brasseur, J. G↗

NASA NTRS2021

VLTI-MATISSE Chromatic Aperture-Synthesis Imaging of η Carinae’s Stellar Wind Across the Brα Line: Periastron Passage Observations in February 2020

Context: Eta Carinae is a highly eccentric, massive binary system (semimajor axis∼15.5 au) with powerful stellar winds and a phase-dependent wind-wind collision (WWC) zone. The primary star, ηCar A, is a luminous blue variable (LBV); the secondary, η Car B, is a Wolf-Rayet or O star with a faster but less dense wind. Aperture-synthesis imaging allows us to study the mass loss from the enigmatic LBV η Car. Understanding LBVs is a crucial step toward improving our knowledge about massive stars and their evolution. Aims: Our aim is to study the intensity distribution and kinematics of η Car’s WWC zone. Methods: Using the VLTI-MATISSE mid-infrared interferometry instrument, we perform Brα imaging of η Car’s distorted wind. Results: We present the first VLTI-MATISSE aperture-synthesis images of η Car A’s stellar wind in several spectral channels distributed across the Brα 4.052 μm line (spectral resolving power R∼960). Our observations were performed close to periastron passage in February 2020 (orbital phase∼14.0022). The reconstructed iso-velocity images show the dependence of the primary stellar wind on wavelength or line-of-sight (LOS) velocity with a spatial resolution of 6 mas (∼14 au). The radius of the faintest outer wind regions is∼26 mas (∼60 au). At several negative LOS velocities, the primary stellar wind is less extended to the northwest than in other directions. This asymmetry is most likely caused by the WWC. Therefore, we see both the velocity field of the undisturbed primary wind and the WWC cavity. In continuum spectral channels, the primary star wind is more compact than in line channels. A fit of the observed continuum visibilities with the visibilities of a stellar wind CMFGEN model (CMFGEN is an atmosphere code developed to model the spectra of a variety of objects) provides a full width at half maximum fit diameter of the primary stellar wind of 2.84±0.06 mas (6.54±0.14 au). We compare the derived intensity distributions with the CMFGEN stellar wind model and hydrodynamic WWC models.

G Weigelt↗

NASA NTRS1985

Bounding solutions of geometrically nonlinear viscoelastic problems

Integral transform techniques, such as the Laplace transform, provide simple and direct methods for solving viscoelastic problems formulated within a context of linear material response and using linear measures for deformation. Application of the transform operator reduces the governing linear integro-differential equations to a set of algebraic relations between the transforms of the unknown functions, the viscoelastic operators, and the initial and boundary conditions. Inversion either directly or through the use of the appropriate convolution theorem, provides the time domain response once the unknown functions have been expressed in terms of sums, products or ratios of known transforms. When exact inversion is not possible approximate techniques may provide accurate results. The overall problem becomes substantially more complex when nonlinear effects must be included. Situations where a linear material constitutive law can still be productively employed but where the magnitude of the resulting time dependent deformations warrants the use of a nonlinear kinematic analysis are considered. The governing equations will be nonlinear integro-differential equations for this class of problems. Thus traditional as well as approximate techniques, such as cited above, cannot be employed since the transform of a nonlinear function is not explicitly expressible.

Stubstad, J. M.↗

NASA NTRS1986

Bounding solutions of geometrically nonlinear viscoelastic problems

Stubstad, J. M.↗

NASA NTRS1998

Inverse Compton Scattering in Mildly Relativistic Plasma

We investigated the effect of inverse Compton scattering in mildly relativistic static and moving plasmas with low optical depth using Monte Carlo simulations, and calculated the Sunyaev-Zel'dovich effect in the cosmic background radiation. Our semi-analytic method is based on a separation of photon diffusion in frequency and real space. We use Monte Carlo simulation to derive the intensity and frequency of the scattered photons for a monochromatic incoming radiation. The outgoing spectrum is determined by integrating over the spectrum of the incoming radiation using the intensity to determine the correct weight. This method makes it possible to study the emerging radiation as a function of frequency and direction. As a first application we have studied the effects of finite optical depth and gas infall on the Sunyaev-Zel'dovich effect (not possible with the extended Kompaneets equation) and discuss the parameter range in which the Boltzmann equation and its expansions can be used. For high temperature clusters (k(sub B)T(sub e) greater than or approximately equal to 15 keV) relativistic corrections based on a fifth order expansion of the extended Kompaneets equation seriously underestimate the Sunyaev-Zel'dovich effect at high frequencies. The contribution from plasma infall is less important for reasonable velocities. We give a convenient analytical expression for the dependence of the cross-over frequency on temperature, optical depth, and gas infall speed. Optical depth effects are often more important than relativistic corrections, and should be taken into account for high-precision work, but are smaller than the typical kinematic effect from cluster radial velocities.

Molnar, S. M.↗

NASA NTRS2014

Spherical Coordinate Systems for Streamlining Suited Mobility Analysis

When describing human motion, biomechanists generally report joint angles in terms of Euler angle rotation sequences. However, there are known limitations in using this method to describe complex motions such as the shoulder joint during a baseball pitch. Euler angle notation uses a series of three rotations about an axis where each rotation is dependent upon the preceding rotation. As such, the Euler angles need to be regarded as a set to get accurate angle information. Unfortunately, it is often difficult to visualize and understand these complex motion representations. One of our key functions is to help design engineers understand how a human will perform with new designs and all too often traditional use of Euler rotations becomes as much of a hindrance as a help. It is believed that using a spherical coordinate system will allow ABF personnel to more quickly and easily transmit important mobility data to engineers, in a format that is readily understandable and directly translatable to their design efforts. Objectives: The goal of this project is to establish new analysis and visualization techniques to aid in the examination and comprehension of complex motions. Methods: This project consisted of a series of small sub‐projects, meant to validate and verify the method before it was implemented in the ABF's data analysis practices. The first stage was a proof of concept, where a mechanical test rig was built and instrumented with an inclinometer, so that its angle from horizontal was known. The test rig was tracked in 3D using an optical motion capture system, and its position and orientation were reported in both Euler and spherical reference systems. The rig was meant to simulate flexion/extension, transverse rotation and abduction/adduction of the human shoulder, but without the variability inherent in human motion. In the second phase of the project, the ABF estimated the error inherent in a spherical coordinate system, and evaluated how this error would vary within the reference frame. This stage also involved expanding a kinematic model of the shoulder, to include the torso, knees, ankle, elbows, wrists and neck. Part of this update included adding a representation of 'roll' about an axis, for upper arm and lower leg rotations. The third stage of the project involved creating visualization methods to assist in interpreting motion in a spherical frame. This visualization method will be incorporated in a tool to evaluate a database of suited mobility data, which is currently in development.

Benson, Elizabeth↗

NASA NTRS1993

The effects of flaring in H1 on the observed velocity field of spirals

This work is part of a larger project in which we want to determine the shapes of dark halos around spiral galaxies. Rotation curves 'probe' the halos in the radial direction. The derived halo mass distributions are badly constrained. The local halo densities fully determine the width of the gas distribution once the gaseous velocity dispersion is known. There where the dark halo dominates, the Full Width at Half Maximum (FWHM) of the gas layer is proportional to (rho(sub halo))(exp -0.5). Therefore, measuring the width of the gas layer probes the halo density directly. In a dark halo dominated potential, the FWHM of the gas layer increases linearly with radius. This increase of the thickness of the gas layer is known as 'flaring'. Flaring has been found inside the stellar disk. Beyond the edge of the stellar disk, the analysis is hampered by the onset of the warp. Since the galaxy we are studying, NGC 4244, has no significant warp we hope to extend Rupen's analysis into the halo dominated regime. The usual method to derive a rotation curve from an observed 2-dimensional velocity field is to assume that the hydrogen is distributed in infinitely thin rings. For a flaring disk, any line of sight samples many different parts of the galaxy, all having different densities and projected velocities. In order to fully exploit the information contained in the gas distribution, we have to understand the effects of flaring on the observables (the spectrum for each point of the galaxy). We have investigated the effects of a flaring disk on the observed velocity field. It is obvious that the largest (kinematical) effects are to be expected for low density dark halos at large inclinations. For low mass galaxies we expect that the flaring of the H1 layer will have a major effect on the observed kinematics. For galaxy with intermediate V(sub max,halo) seen at intermediate inclinations, one overestimates Vsin(i) typically by a few percent. For more massive galaxies, any effects arising from the flaring H1 layer are minuscule unless the inclination is not too far from 90 deg.

Olling, Rob↗