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All sourcesNASA NTRSDOE OSTI
NASA NTRS1983

Kinematic precision of gear trains

Kinematic precision is affected by errors which are the result of either intentional adjustments or accidental defects in manufacturing and assembly of gear trains. A method for the determination of kinematic precision of gear trains is described. The method is based on the exact kinematic relations for the contact point motions of the gear tooth surfaces under the influence of errors. An approximate method is also explained. Example applications of the general approximate methods are demonstrated for gear trains consisting of involute (spur and helical) gears, circular arc (Wildhaber-Novikov) gears, and spiral bevel gears. Gear noise measurements from a helicopter transmission are presented and discussed with relation to the kinematic precision theory. Previously announced in STAR as N82-32733

Litvin, F. L.↗
NASA NTRS1987

Finite rotation and nonlinear beam kinematics

Standard means of representing finite rotation in rigid-body kinematics, including orientation angles, Euler parameters, and Rodrigues parameters, are reviewed and compared. General kinematical relations for a beam theory that treats arbitrarily large rotation are then presented. The standard methods of representing finite rotations are applied to these kinematical expressions, and comparison is made among the standard methods and additional methods found in the literature, such as quasi-coordinates and linear combinations of projection angles. The method of Rodrigues parameters is shown to stand out for both its simplicity and generality when applied to beam kinematics, a result that is really missing from the literature.

Hodges, Dewey H.↗
NASA NTRS1987

Kinematically redundant robot manipulators

Research on control, design and programming of kinematically redundant robot manipulators (KRRM) is discussed. These are devices in which there are more joint space degrees of freedom than are required to achieve every position and orientation of the end-effector necessary for a given task in a given workspace. The technological developments described here deal with: kinematic programming techniques for automatically generating joint-space trajectories to execute prescribed tasks; control of redundant manipulators to optimize dynamic criteria (e.g., applications of forces and moments at the end-effector that optimally distribute the loading of actuators); and design of KRRMs to optimize functionality in congested work environments or to achieve other goals unattainable with non-redundant manipulators. Kinematic programming techniques are discussed, which show that some pseudo-inverse techniques that have been proposed for redundant manipulator control fail to achieve the goals of avoiding kinematic singularities and also generating closed joint-space paths corresponding to close paths of the end effector in the workspace. The extended Jacobian is proposed as an alternative to pseudo-inverse techniques.

Baillieul, J.↗
NASA NTRS1990

Imaging spectrophotometry of ionized gas in NGC 1068. I - Kinematics of the narrow-line region

The kinematics of collisionally excited forbidden N II 6548, 6583 across the inner 1 arcmin diameter of the nearby Seyfert galaxy NGC 1068 is mapped using an imaging Fabry-Perot interferometer and low-noise CCD. The stack of monochromatic images, which spatially resolved the high-velocity gas, was analyzed for kinematic and photometric content. Profiles agree well with previous long-slit work, and their complete spatial coverage makes it possible to constrain the gas volume distribution. It is found that the narrow-line region is distributed in a thick center-darkened, line-emitting cylinder that envelopes the collimated radio jet. Three distinct kinematic subsystems, of which the cylinder is composed, are discussed in detail. Detailed behavior of the emission-line profiles, at the few points in the NE quadrant with simple kinematics, argues that the ionized gas develops a significant component of motion perpendicular to the jet axis.

Cecil, Gerald↗
NASA NTRS1993

Stellar kinematic groups. I - The Ursa Major group

The Ursa Major Group (UMaG) is studied as a test case for the authenticity of Stellar Kinematic Groups, using Coravel radial velocities, recent compilations of astrometric data, and new spectroscopic observations. Spectroscopic age indicators, particularly indices of the strength of chromospheric emission, are applied to solar-type candidate members of UMaG, and it is shown that stars that meet the spectroscopic criteria also have kinematics that agree better with the space motions of the nucleus of UMaG than does the starting sample as a whole. The primary limitation on the precision of kinematics is now parallaxes instead of radial velocities. These more restrictive kinematic criteria are then applied to other UMaG candidates and a list summarizing membership is presented. UMaG is also examined as a cluster, confirming its traditional age of 0.3 Gyr, and a mean Fe/H of -0.08 +/- 0.09 for those stars most likely to be bona fide members.

Soderblom, David R.↗
NASA NTRS1994

Kinematic signature of a rotating bar near a resonance

Recent work based on H I, star count and emission data suggests that the Milky Way has rotating bar-like features. In this paper, I show that such features cause distinctive stellar kinematic signatures near Outer Lindblad Resonance (OLR) and Inner Lindblad Resonance (ILR). The effect of these resonances may be observable far from the peak density of the pattern and relatively nearby the solar position. The details of the kinematic signatures depend on the evolutionary history of the 'bar' and therefore velocity data, both systematic and velocity dispersion, may be used to probe the evolutionary history as well as the present state of Galaxy. Kinematic models for a variety of sample scenarios are presented. Models with evolving pattern speeds show significantly stronger dispersion signatures than those with static pattern speeds, suggesting that useful observational constraints are possible. The models are applied to the proposed rotating spheroid and bar models; we find (1) none of these models chosen to represent the proposed large-scale rotating spheroid are consistent with the stellar kinematics and (2) a Galactic bar with semimajor axis of 3 kpc will cause a large increase in velocity dispersion in the vicinity of OLR (approximately 5 kpc) with little change in the net radial motion and such a signature is suggested by K-giant velocity data. Potential future observations and analyses are discussed.

Weinberg, Martin D.↗
NASA NTRS1995

Measuring stellar kinematics in galaxies with the near-infrared (2-0) (12) CO absorption bandhead

The shape and strength of the near-infrared (2-0) (12)CO absorption bandhead provide astronomers with a unique tool for measuring stellar kinematics in galaxies with strong dust obscuration. However, the asymmetric shape of the bandhead introduces complexities when extracting the kinematics from an observed spectrum. This paper discusses the benefits, drawbacks, and observational constraints associated with using this bandhead to measure kinematics in galaxies, focusing on applications in high spectral-resolution data. Additionally, we discuss techniques found useful for extracting the kinematics from the absorption feature, and outline our success with two different methods.

Gaffney, Niall I.↗
NASA NTRS2003

Three-dimensional ocular kinematics during eccentric rotations: evidence for functional rather than mechanical constraints

Previous studies have reported that the translational vestibuloocular reflex (TVOR) follows a three-dimensional (3D) kinematic behavior that is more similar to visually guided eye movements, like pursuit, rather than the rotational VOR (RVOR). Accordingly, TVOR rotation axes tilted with eye position toward an eye-fixed reference frame rather than staying relatively fixed in the head like in the RVOR. This difference arises because, contrary to the RVOR where peripheral image stability is functionally important, the TVOR like pursuit and saccades cares to stabilize images on the fovea. During most natural head and body movements, both VORs are simultaneously activated. In the present study, we have investigated in rhesus monkeys the 3D kinematics of the combined VOR during yaw rotation about eccentric axes. The experiments were motivated by and quantitatively compared with the predictions of two distinct hypotheses. According to the first (fixed-rule) hypothesis, an eye-position-dependent torsion is computed downstream of a site for RVOR/TVOR convergence, and the combined VOR axis would tilt through an angle that is proportional to gaze angle and independent of the relative RVOR/TVOR contributions to the total eye movement. This hypothesis would be consistent with the recently postulated mechanical constraints imposed by extraocular muscle pulleys. According to the second (image-stabilization) hypothesis, an eye-position-dependent torsion is computed separately for the RVOR and the TVOR components, implying a processing that takes place upstream of a site for RVOR/TVOR convergence. The latter hypothesis is based on the functional requirement that the 3D kinematics of the combined VOR should be governed by the need to keep images stable on the fovea with slip on the peripheral retina being dependent on the different functional goals of the two VORs. In contrast to the fixed-rule hypothesis, the data demonstrated a variable eye-position-dependent torsion for the combined VOR that was different for synergistic versus antagonistic RVOR/TVOR interactions. Furthermore, not only were the eye-velocity tilt slopes of the combined VOR as much as 10 times larger than what would be expected based on extraocular muscle pulley location, but also eye velocity during antagonistic RVOR/TVOR combinations often tilted opposite to gaze. These results are qualitatively and quantitatively consistent with the image-stabilization hypothesis, suggesting that the eye-position-dependent torsion is computed separately for the RVOR and the TVOR and that the 3D kinematics of the combined VOR are dependent on functional rather than mechanical constraints.

Non-NASA Center↗
NASA NTRS2003

Space Telescope Imaging Spectrograph Long-Slit Spectroscopy of the Narrow-Line Region of NGC 4151: Kinematics and Emission-Line Ratios - 1

Long-slit spectra of the Seyfert galaxy NGC 4151 from the UV to the near-infrared have been obtained with the Space Telescope Imaging Spectrograph (STIS) to study the kinematics and physical conditions in the narrow-line region (NLR). The kinematics shows evidence for three components, a low-velocity system in normal disk rotation, a high-velocity system in radial outflow at a few hundred kilometers per second relative to the systemic velocity, and an additional high-velocity system also in outflow with velocities up to 1400 km s(-l), in agreement with results from STIS slitless spectroscopy. We have explored two simple kinematic models and suggest that radial outflow in the form of a wind is the most likely explanation. We also present evidence indicating that the wind may be decelerating with distance from the nucleus. We find that the emission-line ratios along our slits are all entirely consistent with photoionization from the nuclear continuum source. A decrease in the ratios [O III] lambda 5007/H beta and [O III] lambda 5007/[O II] lambda 3727 suggests that the density decreases with distance from the nucleus. This trend is borne out by the [S II] ratios as well. We find no strong evidence for interaction between the radio jet and the NLR gas in either the kinematics or the emission-line ratios, in agreement with the recent results of Kaiser et al., who found no spatial coincidence of NLR clouds and knots in the radio jet. These results are in contrast to other recent studies of nearby active galactic nuclei that find evidence for significant interaction between the radio source and the NLR gas.

Nelson, C. H.↗
NASA NTRS2004

Primate Anatomy, Kinematics, and Principles for Humanoid Design

The primate order of animals is investigated for clues in the design of Humanoid Robots. The pursuit is directed with a theory that kinematics, musculature, perception, and cognition can be optimized for specific tasks by varying the proportions of limbs, and in particular, the points of branching in kinematic trees such as the primate skeleton. Called the Bifurcated Chain Hypothesis, the theory is that the branching proportions found in humans may be superior to other animals and primates for the tasks of dexterous manipulation and other human specialties. The primate taxa are defined, contemporary primate evolution hypotheses are critiqued, and variations within the order are noted. The kinematic branching points of the torso, limbs and fingers are studied for differences in proportions across the order, and associated with family and genus capabilities and behaviors. The human configuration of a long waist, long neck, and short arms is graded using a kinematic workspace analysis and a set of design axioms for mobile manipulation robots. It scores well. The re emergence of the human waist, seen in early Prosimians and Monkeys for arboreal balance, but lost in the terrestrial Pongidae, is postulated as benefiting human dexterity. The human combination of an articulated waist and neck will be shown to enable the use of smaller arms, achieving greater regions of workspace dexterity than the larger limbs of Gorillas and other Hominoidea.

Ambrose, Robert O.↗
NASA NTRS1986

Inverse kinematic solution for near-simple robots and its application to robot calibration

This paper provides an inverse kinematic solution for a class of robot manipulators called near-simple manipulators. The kinematics of these manipulators differ from those of simple-robots by small parameter variations. Although most robots are by design simple, in practice, due to manufacturing tolerances, every robot is near-simple. The method in this paper gives an approximate inverse kinematics solution for real time applications based on the nominal solution for these robots. The validity of the results are tested both by a simulation study and by applying the algorithm to a PUMA robot.

Hayati, Samad A.↗
NASA NTRS1987

An optimal resolved rate law for kinematically redundant manipulators

The resolved rate law for a manipulator provides the instantaneous joint rates required to satisfy a given instantaneous hand motion. When the joint space has more degrees of freedom than the task space, the manipulator is kinematically redundant and the kinematic rate equations are underdetermined. These equations can be locally optimized, but the resulting pseudo-inverse solution has been found to cause large joint rates in some cases. A weighting matrix in the locally optimized (pseudo-inverse) solution is dynamically adjusted to control the joint motion as desired. Joint reach limit avoidance is demonstrated in a kinematically redundant planar arm model. The treatment is applicable to redundant manipulators with any number of revolute joints and to non-planar manipulators.

Bourgeois, B. J.↗
NASA NTRS1988

Analysis of a closed-kinematic chain robot manipulator

Presented are the research results from the research grant entitled: Active Control of Robot Manipulators, sponsored by the Goddard Space Flight Center (NASA) under grant number NAG-780. This report considers a class of robot manipulators based on the closed-kinematic chain mechanism (CKCM). This type of robot manipulators mainly consists of two platforms, one is stationary and the other moving, and they are coupled together through a number of in-parallel actuators. Using spatial geometry and homogeneous transformation, a closed-form solution is derived for the inverse kinematic problem of the six-degree-of-freedom manipulator, built to study robotic assembly in space. Iterative Newton Raphson method is employed to solve the forward kinematic problem. Finally, the equations of motion of the above manipulators are obtained by employing the Lagrangian method. Study of the manipulator dynamics is performed using computer simulation whose results show that the robot actuating forces are strongly dependent on the mass and centroid locations of the robot links.

Nguyen, Charles C.↗
NASA NTRS1989

Kinematic modeling of the Galaxy. I - The Yale Bright Star Catalogue

A code has been developed to investigate the kinematic properties of stellar populations of the Galaxy by modeling the distributions of proper motion and line-of-sight velocity. The coordinate frames of reference are discussed in detail and the general matrix transformations valid beyond the solar neighborhood are given. As a first application, the kinematic properties of the magnitude-selected sample of 3993 stars in the Bright Star Catalogue with V less than 6.0 and (B-V) greater than 0 are selected. The observed kinematic distributions are compared with a conventional model that has an exponential disk with scale heights, components of velocity dispersion ellipsoid, and asymmetric drift taken from the literature and defined as functions of spectral type. The comparisons suggest that a significant fraction of the Bright Star Catalogue belongs to a relatively young population that is not properly represented in the model.

Ratnatunga, Kavan U.↗
NASA NTRS1989

Stellar kinematics in the galactic centre

The observations of the stellar kinematics in the central 8 pc of the Galaxy are presented. It is shown that the spectroscopy of the 2.3 microns CO absorption feature, in late type stars, yields the stellar velocity dispersion and the average stellar radial velocity as a function of galactocentric distance. A sample spectra that illustrates the observed velocity shifrs and velocity dispersion is given. The analysis shows that the velocity dispersion of the stars is large, and that it dominates the stellar kinematics. The use of these kinematic data, to probe the mass distribution in the Galactic center, is considered.

Mcginn, M. T.↗
NASA NTRS1989

Modeling of control forces for kinematical constraints in the dynamics of multibody systems: A new approach

Conventionally kinematical constraints in multibody systems are treated similar to geometrical constraints and are modeled by constraint reaction forces which are perpendicular to constraint surfaces. However, in reality, one may want to achieve the desired kinematical conditions by control forces having different directions in relation to the constraint surfaces. The conventional equations of motion for multibody systems subject to kinematical constraints are generalized by introducing general direction control forces. Conditions for the selections of the control force directions are also discussed. A redundant robotic system subject to prescribed end-effector motion is analyzed to illustrate the methods proposed.

Ider, Sitki Kemal↗
NASA NTRS1989

Kinematics, controls, and path planning results for a redundant manipulator

The inverse kinematics solution, a modal position control algorithm, and path planning results for a 7 degree of freedom manipulator are presented. The redundant arm consists of two links with shoulder and elbow joints and a spherical wrist. The inverse kinematics problem for tip position is solved and the redundant joint is identified. It is also shown that a locus of tip positions exists in which there are kinematic limitations on self-motion. A computationally simple modal position control algorithm has been developed which guarantees a nearly constant closed-loop dynamic response throughout the workspace. If all closed-loop poles are assigned to the same location, the algorithm can be implemented with very little computation. To further reduce the required computation, the modal gains are updated only at discrete time intervals. Criteria are developed for the frequency of these updates. For commanding manipulator movements, a 5th-order spline which minimizes jerk provides a smooth tip-space path. Schemes for deriving a corresponding joint-space trajectory are discussed. Modifying the trajectory to avoid joint torque saturation when a tip payload is added is also considered. Simulation results are presented.

Gretz, Bruce↗
NASA NTRS1989

Computational neural learning formalisms for manipulator inverse kinematics

An efficient, adaptive neural learning paradigm for addressing the inverse kinematics of redundant manipulators is presented. The proposed methodology exploits the infinite local stability of terminal attractors - a new class of mathematical constructs which provide unique information processing capabilities to artificial neural systems. For robotic applications, synaptic elements of such networks can rapidly acquire the kinematic invariances embedded within the presented samples. Subsequently, joint-space configurations, required to follow arbitrary end-effector trajectories, can readily be computed. In a significant departure from prior neuromorphic learning algorithms, this methodology provides mechanisms for incorporating an in-training skew to handle kinematics and environmental constraints.

Gulati, Sandeep↗