Showing papers on "Angular velocity published in 1992"

Visual tracking of known three-dimensional objects

Abstract: A method is described of visually tracking a known three-dimensional object as it moves with six degrees of freedom. The method uses the predicted position of known features on the object to find the features in images from one or more cameras, measures the position of the features in the images, and uses these measurements to update the estimates of position, orientation, linear velocity, and angular velocity of the object model. The features usually used are brightness edges that correspond to markings or the edges of solid objects, although point features can be used. The solution for object position and orientation is a weighted least-squares adjustment that includes filtering over time, which reduces the effects of errors, allows extrapolation over times of missing data, and allows the use of stereo information from multiple-camera images that are not coincident in time. The filtering action is derived so as to be optimum if the acceleration is random. (Alternatively, random torque can be assumed for rotation.) The filter is equivalent to a Kalman filter, but for efficiency it is formulated differently in order to take advantage of the dimensionality of the observations and the state vector which occur in this problem. The method can track accurately with arbitrarily large angular velocities, as long as the angular acceleration (or torque) is small. Results are presented showing the successful tracking of partially obscured objects with clutter.

The solar tachocline.

Abstract: Acoustic sounding of the Sun reveals that the variation of angular velocity with latitude is independent of depth in the convection zone. By contrast, deep within the radiative zone, the rotation appears to be rigid. The transition between the two rotation laws occurs in a thin, unresolved layer that we here call the tachocline. This paper is an examination of the structure and previous evolution of this layer. We assume that the stress exerted by the convection zone is prescribed, much as oceanographers take the wind stress on the sea surface as given.

Estimation of angular velocity and acceleration from shaft encoder measurements

Abstract: The output of a shaft encoder is basically a quantized measurement of the shaft angle. One method of angular velocity and acceleration measurement is by finite difference of angle measurements (net pulse counts) at regular time samples. It is shown that these estimates become significantly degraded as sampling rates increase. Kalman filtering of the angle measurements, based on some model of signal generation, is proposed. Asymptotic analysis of constant sampling rate as the intersample time tends to zero shows that the error variances tend to zero, but at decreasing rates for the angle, velocity, and acceleration errors. The analysis also suggests the use of multiple-integrator systems to model the angle signal. >

Smooth interpolation of orientations with angular velocity constraints using quaternions

Abstract: In this paper we present methods to smoothly interpolate orientations, given N rotational key frames of an object along a trajectory. The methods allow the user to impose constraints on the rotational path, such as the angular velocity at the endpoints of the trajectory. We convert the rotations to quaternions, and then spline in that non-Euclidean space. Analogous to the mathematical foundations of flat-space spline curves, we minimize the net “tangential acceleration” of the quaternion path. We replace the flat-space quantities with curved-space quantities, and numerically solve the resulting equation with finite difference and optimization methods.

Three-dimensional drawings in isometric conditions: relation between geometry and kinematics.

Abstract: Normal human subjects grasped a 3-D isometric handle with an otherwise unrestrained, pronated hand and exerted forces continuously to draw circles, ellipses and lemniscates (figure-eights) in specified planes in the presence or absence of a 3-D visual force-feedback cursor and a visual template. Under any of these conditions and in all subjects, a significant positive correlation was observed between the instantaneous curvature and angular velocity, and between the instantaneous radius of curvature and tangential velocity; that is, when the force trajectory was most curved, the tangential velocity was lowest. This finding is similar to that obtained by Viviani and Terzuolo (1982) for 2-D drawing arm movements and supports the notion that central constraints give rise to the relation between geometric and kinematic parameters of the trajectory.

The kinematics of stretching and alignment of material elements in general flow fields

Abstract: A rigorous, kinematic description of the stretching and alignment of infinitesimal material elements in general flow fields is presented. An evolution equation is derived, in the Lagrangian frame, for the alignment angles between a material element and the principal axes of strain. The equation identifies the precise roles played by the local angular velocity and the rotation of the strain axes in the alignment process and provides the framework in which to investigate the extent to which the straining field is ‘persistent ’. This general kinematical picture is specialized to study line and vortex stretching in fluid flows and analytically predicts the numerically observed alignment of the vorticity vector with the intermediate strain axis. The alignment equations are solved exactly for a number of special flow fields and investigated numerically for the ABC and STF flows. The kinematic formalism and numerical phenomenology suggests the use of new criteria to analyse the material element stretching properties of large-scale numerical simulations.

Design of a holonomic omnidirectional vehicle

Abstract: A novel design of a holonomic omnidirectional vehicle is introduced. The holonomic mechanism allows the vehicle to maneuver in an arbitrary direction from an arbitrary configuration on a plane. This significantly simplifies control problems and improves positioning accuracy. A fundamental method of obtaining omnidirectional motion with holonomic constraints with the floor, using a mechanism with spherical tires, is presented. Kinematic analysis of this mechanism gives the vehicle Jacobian relating actuator velocities to the vehicle velocity components. Analysis of lateral tire slip during vehicle rotation allows slip reduction methods. A prototype vehicle using this special mechanism and a computerized control system is designed and tested. In addition to rotation, the vehicle can perform very accurate translational motions, in two orthogonal directions, arbitrarily termed forward and sideways. Motions in these two degrees of freedom are decoupled from each other and are insensitive to variations in ground friction coefficient. >

The heavy top: a geometric treatment

Abstract: We consider the steady group motions of a rigid body with a fixed point moving in a gravitational field. For an asymmetric top, rotation about the axis of gravity is the only permissible group motion; for a Lagrange top, simultaneous rotation about the axis of gravity and spin about the axis of symmetry of the top is permissible. Our analysis of the heavy top follows the reduced energy momentum method of Simo el a1 , which is applicable to a wide range of conservative systems with symmetry. Steady group motions are characterized as solutions of a variational problem on the configuration space; local minima of the amended potential correspond to nonlinearly orbitally stable steady motions. The combination of a low-dimensional configuration space and a relatively large number of parameters that produce substantial qualitative changes in the dynamics makes possible a thorough, detailed analysis, which not only reproduces the classical results for this well known system, but leads to some results which we believe are new. motions of a heavy top with a fixed point. We rederive the classical equilibrium and stability conditions for sleeping tops and precessing Lagrange taps, analyse in detail the stability of a family of steady rotations of tilted tops which bifurcate from the branch of sleeping tops parametrized by angular velocity, and classify thc possible stability transitions of an arbitrary top as its angular velocity is increased. We obtain a simple, general expression far the charactenstic polynomial of the linearized equations of motion and analyse the linear stability of both sleeping tops and the family of tilted top motions previously mentioned. Finally, we demonstrate the coexistence of stable branches of steadily precessing tops that bifurcate from the branch of sleeping Lagrange lops throughout the range of angular velocities for which the sleeping top is stable.

Two-dimensional coding of linear acceleration and the angular velocity sensitivity of the otolith system

Abstract: There exist otolith-sensitive vestibular nuclei neurons with spatio-temporal properties that can be described by two response vectors that are in temporal and spatial quadrature. These neurons respond to the component of a stimulus vector on a plane rather than a single axis. It is demonstrated here that these "two-dimensional" linear accelerometer neurons can function as one-dimensional angular velocity detectors. The two-dimensional property in both space and time allows these neurons to encode the component of the stimulus angular velocity vector that is normal to the plane defined by the two response vectors. The angular velocity vector in space can then be reconstructed by three populations of such neurons having linearly independent response planes. Thus, we propose that these two-dimensional spatio-temporal linear accelerometer neurons, in addition to participating in functions of the otolith system that are based on detection of linear acceleration, are also involved in the generation of compensatory ocular responses during off-vertical axis rotations.

Verfahren zur Bestimmung der Fahrzeugquergeschwindigkeit und/oder des Schwimmwinkels

Abstract: In a method of determining the transverse velocity Vy and/or the drift angle beta of a steered vehicle, input values of the steering angle delta v (and possibly a rear steering angle), the vehicle longitudinal velocity vx, yaw angular velocity omega , transverse acceleration ax and wheel velocities are required for a mathematical model. A second version (Fig 5) uses measured or estimated brake pressures instead of a measured value of transverse acceleration. The determined velocity/angle may be used to assess or control the stability of the vehicle. The method requires fewer expensive sensors than the prior art.

Measurement of steady-state and transient load-angle, angular velocity, and acceleration using an optical encoder

Abstract: The measurement of steady-state and transient load-angle, angular velocity, and acceleration using an optical encoder is described. The accuracy of measurement is assessed, and results are given for the run-up of a three-phase reluctance motor. Accurate values of speed and load-angle are determined, but the measurement of acceleration is more difficult, and significant errors are present for values in excess of approximately 50 mechanical rad/s/sup 2/. Predicted results for a computer model are in reasonable agreement. >

Learning control for robot tasks under geometric endpoint constraints

Abstract: A learning control scheme for a class of robot manipulators whose endpoint is moving under geometrical constraints on a surface is proposed. In this scheme, the input torque command is composed of two different signals updated separately at every trial by different ways. One is updated by the angular velocity error vector which is projected to the tangent plane of the constraint surface in joint space. The other is updated by the magnitude of contact force error at the manipulator endpoint. Not only the uniform boundedness of position and velocity trajectory errors but also the uniform convergence of position and velocity trajectories to their desired ones with repeating practices are proved theoretically. In addition, it is shown that the contact force itself converges to the desired one in the sense of L/sup 2/-norm with repeating practices. Computer simulation results by using a 3 DOF manipulator are presented to demonstrate the effectiveness of the proposed method and to examine the speed of convergence of force trajectories besides position and velocity trajectories. >

The dynamics of spatial orientation during complex and changing linear and angular acceleration.

Abstract: The dynamics of spatial orientation perception were examined in a series of experiments in which a total of 43 subjects were passively exposed to various combinations of linear and angular acceleration during centrifuge runs. Perceptual effects during deceleration were much stronger than effects during acceleration. The dynamics of spatial orientation perception differed substantially from changes in the vestibulo-ocular reflex (VOR). VOR was fairly well predicted by a current model, but our experiments revealed perceived change in attitude (roll, pitch, yaw tilt position in space) and perceived angular velocity in space that was not reflected by parallel changes in the plane or magnitude of the VOR. This series of experiments establishes several facts concerning spatial orientation perception beyond the predictive domain of any current model. New concepts are needed and several are suggested to deal with changing reactions to complex combinations of linear and angular accelerations.

Effects of evolving rotating equilibrium configurations on the cooling and spin-down of pulsars

Abstract: We model a pulsar by a uniform density rotating spheroid covered by a solid crust. During the spin-down (up) epoch, pulsars can adjust their shapes to their equilibrium configurations, which depend on the stellar rotation velocity Ω, due to plastic flow and continuous crust breaking resulting from various mechanisms even though the crust is supposedly rigid. We show that this results in a coupling among the stellar temperature (T), the rotation velocity (Ω) and the eccentricity (e), and cooling and spin-down therefore mutually affect each other

Constant image quality CT scanner with variable radiation flux density

Abstract: An x-ray source (20) rotates about a fixed cylinder (16) within which a subject of non-uniform cross-section is received. Radiation from the x-ray source passes through the subject and impinges on an arc of radiation detectors (28). Because the subject is of non-uniform cross-section, the average x-ray energy fluence impinging on the detectors across the arc varies with the relative angular position of the x-ray source and the subject. In one embodiment, a motor (18) which rotates the x-ray tube relative to the subject is controlled by a digital motor control (50). The digital motor control varies the rotational speed to a preselected angular velocity indicated by a look-up table (52) at each of a multiplicity of angular positions around the subject. The angular velocity is slowed when radiation is passing through thicker portions of the subject and accelerated when passing through thinner portions of the subject such that the average x-ray energy fluence received by the radiation detectors is substantially constant regardless of the angular position of the x-ray source. In another embodiment, an x-ray tube control circuit (82) alters the tube current such that the average x-ray energy fluence received by the detectors becomes angular position independent. In this manner, the signal-to-noise ratio at each angular position is the same and structural noise is eliminated in the resultant reconstructed image.

Nutations of the Earth

Abstract: The figure of the Earth is very nearly that of an oblate spheroid. Its moments of inertia about principal axes in the equatorial plane differ from each other only by about two parts in 105, and may be taken to have a common value A, for the purposes of nutation theory. The moment of inertia C about the third principal axis, in the direction of the poles, is larger by about one part in 300. The dynamical ellipticity, defined as e == (C A)/ A, has the dominant role in determining the Earth's nutations. The flattening of the Earth's surface, i.e. its geometrical ellipticity, is defined as the fractional difference between the equatorial axis and the polar axis, and is also about 1/300. This equatorial bulge and the associated difference between C and A are almost wholly accounted for by centrifugal forces associated with a rotation of the Earth about its polar axis at a mean rate of one cycle per sidereal day (1 cpsd), equivalent to an angular velocity 00 which is 7.29212 x 10-5 rad sec-1 at present. We will find it convenient to express all angular velocities in units of 00• In the following, an angular velocity JD.o, or the equivalent frequency f cpsd, will often be

Theory for the experimental observation of chaos in a rotating waterwheel.

Abstract: We study the chaos for a set of coupled, nonlinear partial-differential equations that originate from the equation of motion and the Fourier transform of the mass-conservation equation for the Malkus waterwheel. Dissipation for this system is produced by an adjustable brake. The braking force, proportional to the angular velocity of the wheel, is responsible for the appearance of chaos. The variation of the moment of inertia with time is taken into account. In the large-time limit, the moment of inertia of the composite system, consisting of the wheel and water, tends to a constant, and the three controlling equations of the set of coupled limit equations reduce to a special case of the Lorenz equations, in which the Rayleigh number \ensuremath{\rho} (here characterizing the distribution of water inflow along the perimeter of the wheel) can also assume negative values. Chaotic attractors of the higher harmonics of the water density have been investigated. Boundaries between various regimes of the wheel's limit behavior (uniform rotation, periodic reversals of spin, chaotic reversals) in the Lorenz parameter space have been found. The Lorenz parameter space has thus been explored in considerably more detail than by previous authors.

A hydroelastic model of macromechanics in the endolymphatic vestibular canal

Abstract: A hydroelastic model describing the mechanics of the human semicircular canal is presented that extends previous work to address the influence of the shape of the labyrinth and the interaction between the endolymph and the cupula. The analysis is based extensively on the three-dimensional geometry and structure of the system and exploits the slender toroidal geometry to obtain an asymptotic solution describing the velocity distribution of the endolymph, the pressure distribution and the deflection of the cupula. All parameters appearing in the model are explicitly defined in terms of physical properties and the geometry. Results for the structure of an infant human endolymphatic canal agree well with experimental measurements of the end-organ velocity gain and phase over the entire physiological range of angular head frequencies. From 0.09 to 1.5 Hz the mechanical response relative to head velocity is essentially constant and the end-organ acts as an angular velocity transducer. Below 0.09 Hz the velocity gain is diminished and above 1.5 Hz the velocity gain is enhanced. For a 1 rad sinusoidal rotation of the head, the analysis predicts an average cupula displacement for the infant canal of approximately 8 × 10−5 cm at 0.09 Hz and 2 × 10−3 cm at 2.0 Hz.

Stability of Taylor-Dean flow in a small gap between rotating cylinders

Abstract: A linear stability analysis has been implemented for Taylor–Dean flow. a viscous flow between rotating concentric cylinders with a pressure gradient acting in the azimuthal direction. The analysis is made under the assumption that the gap spacing between the cylinders is small compared to the mean radius (small-gap approximation). A parametric study covering wide ranges of μ. the ratio of angular velocity of the outer cylinder to that of inner cylinder. and β. a parameter characterizing the ratio of representative pumping and rotation velocities is conducted. For − 1 [les ] μ 0.3. The most stable state is always accompanied by a shortest critical axial wavelength. Instability modes with different azimuthal wavenumber have similar stability characteristics because the basic state is either close to or at the most stable situation. This similarity is absent from either Taylor or Dean flow.

Magnetic fields and differential rotation in stars

Abstract: In a star with a magnetic field that is not symmetric about the rotation axis, non-uniform rotation in the electrically conducting stellar material shears the field and generates magnetic torques. This leads to a competition between the efforts of the magnetic stresses to remove non-uniformities in angular velocity, and those of the velocity field to bury and destroy magnetic flux. Illustrative calculations are presented for a compressible model in an idealized two-dimensional geometry. They show how, with values of diffusion coefficients appropriate to a radiative envelope, the Lorentz stresses can rapidly establish a state of approximately uniform rotation for relatively modest fields strenghts

Method and apparatus for preventing vehicle handling instabilities

Abstract: A method and apparatus for preventing vehicle handling instabilities, in which a vehicle yaw angular velocity required value (μ soll ) is formed from measured quantities (vehicle velocity, steering wheel angle). The vehicle yaw angular velocity actual value (μ ist ) is formed from at least one sensor signal, the difference between the yaw angular velocity required value (μ soll ) and the yaw angular velocity actual value (μ ist ) is determined by subtracting the yaw angular velocity actual value (μ ist ) from the yaw angular velocity required value (μ soll ), and the handling situation or the vehicle yaw behavior to be detected is determined from this difference. The time derivative of the difference is formed to determine whether the vehicle exhibits understeer or oversteer. The slip threshold value (σ soll ) is varied in the direction of the value 0 when it is deduced from the detected handling situation that a changed lateral guidance force is required on the wheels of the vehicle driven axle.

Multiple reference frame controller for active filters and power line conditioners

Abstract: An electrical control system includes multiple frames of reference in the error path of a controller. In each such frame, a particular chosen component of the error vector appears as a constant vector and is passed through a pure integrator thus acquiring infinite gain. In the steady state, the net error vector can then be forced to have zero content at each of the targeted frequencies (as set by the rotational velocity of the frames of reference). Both parallel and series configuration of the controller are provided, as well as the control methods used by the controllers.

Detection of rotating gravity signals

Abstract: It is shown in the preceding paper that neurons with two-dimensional spatio-temporal properties to linear acceleration behave like one-dimensional rate sensors: they encode the component of angular velocity (associated with a rotating linear acceleration vector) that is normal to their response plane During off-vertical axis rotation (OVAR) otolith-sensitive neurons are activated by the gravity vector as it rotates relative to the head Unlike "one-dimensional" linear accelerometer neurons which exhibit equal response magnitudes for both directions of rotation, "two-dimensional" neurons can be shown to respond with unequal magnitudes to clockwise and counterclockwise off-vertical axis rotations The magnitudes of the sinusoidal responses of these neurons is not only directionally selective but also proportional to rotational velocity Thus, responses from such "two-dimensional" neurons may represent the first step in the computations necessary to generate the steady-state eye velocity during OVAR An additional step involving a nonlinear operation is necessary to transform the sinusoidally modulated output of these neurons into a signal proportional to sustained eye velocity Similarly to models of motion detection in the visual system, this transformation is proposed to be achieved through neuronal operations involving mathematical multiplication followed by a leaky integration by the velocity storage mechanism The proposed model for the generation of maintained eye velocity during OVAR is based on anatomical and physiological properties of vestibular nuclei neurons and capable of predicting the experimentally observed steady-state characteristics of the eye velocity

Wheel speed correction device which compensates for changes in tire diameter and during vehicle turns

Abstract: A wheel speed correction device for use in a vehicle corrects for the change of the circumferential wheel speed caused by variations in the wheel tire diameter, differences in the paths of the left and right wheels when the vehicle turns, and/or abnormal slipping between the tire and the road surface. The wheel speed correction device has a device for measuring a wheel rotation angular speed of each wheel, a device for correcting a coefficient representing a tire diameter and producing a corrected coefficient for each wheel, a device for calculating, from the measured angular speed, a diameter-corrected wheel speed using the corrected coefficients, a device for obtaining a turning correction amount from a difference between diameter-corrected wheel speeds of the left and right wheels, and a device for correcting the diameter-corrected wheel speed using the turning correction amount.

Navigation device and direction detection method therefor

Abstract: The navigation device includes vehicle condition discriminating unit for discriminating whether the vehicle is stopped or not, angular velocity detecting unit for detecting change of direction of the vehicle and producing angular velocity data on the basis of the detected change of direction, absolute direction detecting unit for detecting geomagnetism and producing absolute direction data on the basis of the detected geomagnetism, offset processing unit for producing corrected angular velocity data from the angular velocity data and a first reference value, and offset reset unit for renewing the first reference value. The offset reset unit renews the first reference value with the angular velocity data which is obtained when the vehicle is discriminated to be stopped, a change rate of the angular velocity data is within a predetermined second reference value and a change rate of the absolute direction data is within a predetermined third reference value.

Observations of toroidal plasma rotation induced by ICRH in JET

Abstract: Changes of the toroidal rotation velocity of up to 3*104 m s-1 have been observed during ICRH in JET. The plasma increases its toroidal rotation in the direction of the plasma current. The change in velocity is obtained from the measurement of the Doppler shifted X-ray lines emitted from He-like nickel present in the centre of the plasma. By analyzing various heating scenarios and also measuring the fast anisotropic ion energy content of the plasma the authors conclude the rotation is connected with the creation of fast ions during ion cyclotron resonance heating. Toroidal acceleration of the plasma in connection with MHD instabilities leading to similar magnitude of rotational velocity is also seen.

Method for detecting misfires in gasoline internal combustion engine

Abstract: In a method of detecting misfires in a gasoline internal combustion engine, the angular velocities of rotation of the engine detected by an angular velocity sensor are calculated over a period of time, and when the difference between the average value of the angular velocities of rotation and the maximum or minimum value thereof is equal to or larger than a predetermined threshold value, the occurrence of misfires is determined. The threshold value is changed according to the operating conditions of the engine such as engine speed or load. Thus, in the method, most suitable, threshold values are set over wide ranges spanning from low speed to high speed, and from light load to heavy load. The abnormal rotation of the engine due to misfires can thereby be with high accuracy.