Showing papers on "Angular velocity published in 1984"

The Visual Ambiguity of a Moving Plane

Abstract: It is shown that the optic flow field arising from motion relative to a visually textured plane may be characterized by eight parameters that depend on the observer's linear and angular velocity and the coordinate vector of the plane. These three vectors are not, however, uniquely determined by the values of the eight parameters. First, the optic flow field does not supply independent values for the observer's speed and distance from the plane; it only gives the ratio of these two quantities. But more unexpectedly, the equations relating the observer's linear velocity and the plane's coordinate vector to the eight parameters are still satisfied if the two vectors are interchanged or reversed in direction, or both. So in addition to the veridical interpretation of the optic flow field there exist three spurious interpretations to be considered and if possible excluded. This purpose is served by the condition that an interpretation can be seriously entertained only if it attributes every image element to a light source in the observer's field of view. This condition immediately eliminates one of the spurious interpretations, and exhibits the other two as mutually inconsistent: one of them is tenable only if all the visible sources lie on the forward half of the plane (relative to the observer's linear velocity); the other only if they all lie on the backward half-plane. If the sources are distributed over both halves of the plane, only the veridical interpretation survives. Its computation involves solving a 3 $\times $ 3 eigenvalue problem derived from the flow field. If the upper two eigenvalues coincide, the observer must be moving directly towards the plane; if the lower two eigenvalues coincide, his motion must be directly away from it; in both cases the spurious interpretation merges with the veridical one. If all three eigenvalues are equal, it may be inferred that either the observer's linear velocity vanishes or the plane is infinitely distant.

Simulation of Taylor-Couette flow. Part 2. Numerical results for wavy-vortex flow with one travelling wave

Abstract: We use a numerical method that was described in Part 1 (Marcus 1984 a ) to solve the time-dependent Navier-Stokes equation and boundary conditions that govern Taylor-Couette flow. We compute several stable axisymmetric Taylor-vortex equilibria and several stable non-axisymmetric wavy-vortex flows that correspond to one travelling wave. For each flow we compute the energy, angular momentum, torque, wave speed, energy dissipation rate, enstrophy, and energy and enstrophy spectra. We also plot several 2-dimensional projections of the velocity field. Using the results of the numerical calculations, we conjecture that the travelling waves are a secondary instability caused by the strong radial motion in the outflow boundaries of the Taylor vortices and are not shear instabilities associated with inflection points of the azimuthal flow. We demonstrate numerically that, at the critical Reynolds number where Taylor-vortex flow becomes unstable to wavy-vortex flow, the speed of the travelling wave is equal to the azimuthal angular velocity of the fluid at the centre of the Taylor vortices. For Reynolds numbers larger than the critical value, the travelling waves have their maximum amplitude at the comoving surface, where the comoving surface is defined to be the surface of fluid that has the same azimuthal velocity as the velocity of the travelling wave. We propose a model that explains the numerically discovered fact that both Taylor-vortex flow and the one-travelling-wave flow have exponential energy spectra such that In [E(k)] ∝ k 1 , where k is the Fourier harmonic number in the axial direction.

Three-dimensional viscous flows with large secondary velocity

Abstract: A new system of approximation equations is derived for three-dimensional steady viscous compressible flows in which a primary-flow direction is present, but in which both transverse velocity components can be large. Previous approaches which address simplification of the steady Navier-Stokes equations are discussed, and a new approach is proposed. The transverse velocity vector which corrects a given potential flow has been decomposed into potential and rotational components. It is found that the potential-velocity vector may be assumed small, whereas the rotational-velocity vector may be assumed small, whereas the rotational velocity vector and hence the composite secondary flow can be of order unity. This assumption leads to a system of governing equations whose characteristic polynomial has a non-elliptic form for arbitrary Mach numbers. The resulting non-elliptic approximation equations can be solved as an initial/boundary-value problem. Computed results confirm the small scalar-potential approximation.

Swirling Flow between Rotating Plates

Abstract: The flow of the classical linearly viscous fluid between two infinite parallel planes rotating with constant (but different) angular velocities about a common axis has received a great deal of attention during the past 60 years (cf. Parter [12]). However, until recently the assumptions which have been employed to study this problem have always led to solutions which are axisymmetric. Recently Berker [3] in his study of the flow between parallel planes rotating with the same constant angular velocities about a common axis exhibited a one parameter family of solutions that are not axisymmetric. In this study we prove that when the planes rotate with different angular velocities about a common axis or distinct axes there is a one parameter family of solutions (for “large” viscosities).

On the rotation of the Sun

Abstract: An asymptotic method is developed to estimate the rotational splitting of sectoral five-minute solar oscillations. Integral formulae are obtained which can be inverted to yield the variation with depth of the Sun's angular velocity near the equatorial plane. The result is a functional of smoothed data, and does not rely on a detailed theoretical model of the Sun. The method has been tested with artificial data (computed from a theoretical solar model) of a kind similar to some real solar data obtained recently by Duvall & Harvey (Nature, Lond. 310, 19 (1984)). The results are encouraging, for they reproduce at least the broadest feature of the somewhat arbitrary angular velocity with which the theoretical model was endowed. When applied to the real data, the method yields a result similar to that derived by Duvall et al. (Nature, Lond. 310, 22 (1984)) by another procedure.

A new approach to finite element modelling of flexible rotors

Abstract: A 3‐dimensional formalism adapted to critical speed and stability analysis of rotating machinery is presented. Gyroscopic effects are properly taken into account in the expression of the kinetic energy through a proper kinematic description which takes account of the local changes of angular velocity induced by the deformation. Two approaches are suggested according to the respective stiffness and geometric properties of the rotating and fixed parts: the rotating frame approach and the inertial frame approach. In both cases, an axisymmetric finite element modelling of the rotor is proposed which takes into account the 3‐dimensional nature of the system while keeping the number of degrees of freedom to a reasonable level. In order to perform the stability analysis, a preliminary reduction of the system is achieved using the component mode method. Critical speeds are calculated next either by the classical sweeping procedure or by a direct method when the restrictive conditions of its applicability are met. The concepts proposed are then applied to an example in order to demonstrate their adequacy.

From rotations and inclinations to zero configurational velocity surfaces I. A natural rotating coordinate system

Abstract: There are three purposes for this and a companion paper. The first is to derive the conditions which will lead to the sharpest possible 'zero velocity' surfaces for the solutions of both the 3-body and the n-body problems. The second purpose is to determine the 'natural rotating coordinate system' for an n-body system; that is, one where the coordinate system contains all of the rotational motion. The third purpose is to derive an equality which will yield, as a special case, the important and very useful Sundman in-

A search for rotational velocity changes among eclipsing binary stars.

Abstract: The rotations of 26 close binary stars are compared, as they were observed at three epochs separated by five to twelve years. Significant changes in the rotation of the hot gainer are noted in three Algol systems. The implications of these changes for sporadic mass flows known to occur among Algols are discussed briefly.

Thermoelastic plane waves in a rotating solid

Abstract: Plane waves in a homogeneous and isotropic unbounded thermoelastic solid rotating with a uniform angular velocity are discussed in the context of the generalised thermoelasticity theory of Green and Lindsay. The effects of rotation of the body on the phase velocity, energy loss and decay coefficient are discussed in some detail for waves of small and large frequencies, and for small coupling between the thermal and mechanical fields. Results of earlier works are deduced as particular cases of the more general results obtained here.

Method of machining a workpiece in a turret lathe and an NC lathe for performing this method

Abstract: A method of machining a workpiece, which is rotatable about a first axis, by a tool pivotable about a second axis parallel to the first axis and drivable about a third axis perpendicular to the second axis. To allow the circumference of the workpiece to be machined off-center without the necessity of moving the first or the second axis transversely to the plane defined by these two axes, the workpiece and the tool are rotated or pivoted about the first or second axis, respectively, at the same time, in the same direction and at the same angular velocity and, simultaneously, the second axis is displaced transversely to the first axis at such a velocity that the equation X 2 =Y 2 +A 2 always applies, wherein X is the distance of the second axis from the first axis, Y is the distance of the first axis from the plane defined by the second and third axes and A is the distance of the second axis from the vertical projection of the first axis onto this plane.

Controller of multi-joint structure machine

Abstract: PURPOSE:To suppress the vibrations by attaching an acceleration detector at the tip of an arm of a multi-joint structure machine and calculating an angular velocity round an attachment point of a pivot from the output of the acceleration detector and the relative angle of the arm to feed back the calculated angular velocity to a control system. CONSTITUTION:Arms 3, 5 and 7 are operated by cylinders 4, 6 and 8, and the relative angles of these arms are detected by detectors 10-12. These detected angles are transmitted to an acceleration compensation controller 19 from a detection circuit 13. The angular velocity is detected by detectors 14-16 and sent to the controller 19 via a detection circuit 17 and a filter circuit 18. The controller 19 calculates angular velocities round the attachment points O1-O3 of pivots and delivers them to a comparison arithmetic device 21. Then an angular velocity command is given to each arm based on the output of the device 21 and the angular velocity given from an input device 20. Thus the vibrations of arms are suppressed, and the flow rates supplied to cylinders 4-8 are delivered to a servo amplifier 22. Thus electric hydraulic servo valves 23-25 are driven. Then the cylinders are started.

Adiabatic theory in rapidly rotating magnetospheres

Abstract: The Jovian magnetosphere is a rapid rotator in the sense that the corotation velocity exceeds the gyrovelocity for most of the low-energy plasma particles. Ordinarily, an electric drift velocity greater than the gyrovelocity will destroy the near periodicity of the bounce motion, so the parallel invariant J will no longer be valid. However, this paper shows that J invariance actually remains valid in rapidly rotating magnetospheres so long as departures from rigid rotation are not too great. Northrop and Birmingham have already proved J invariance for the case of rapid but exactly rigid rotation, and this paper extends their results to nonrigid, rapid rotation with corotation lag and/or convection. These results allow the magnetic field to be arbitrarily asymmetric. The guiding-center equations in the rotating frame are also used to obtain conditions for plasma corotation in arbitrarily asymmetric but rigidly rotating magnetic fields. The plasma bulk velocity equals the corotation velocity for any trapped particle population that is steady state in the corotating frame provided E + (Ω × r) × B/c = 0 and all first-order drifts are negligible. These conditions are satisfied, and corotation is expected, for a steady-state cold plasma on equipotential field lines of any geometry threading a rigidly rotating central conductor.

Angular velocity sensor

Abstract: The present invention relates to a sensor for sensing orthogonal components of angular velocity of rotation of the sensor about any axis in a plane perpendicular to a reference jet axis within the sensor, wherein a fluid jet is deflected relative to two pairs of electrically resistive, temperature sensitive elements in response to rotation of the sensor, wherein each pair of elements forms the sensing branch of a bridge circuit, the jet deflection causing differential cooling and bridge unbalance which is an indication of the deflection of the fluid jet from the reference jet axis which is in turn an indication of the rate and direction of angular rotation, wherein each pair of elements is disposed in a plane perpendicular to the reference jet axis, each pair sensing an orthogonal component of angular velocity of rotation.

Apparatus for detecting angle and angular velocity of rotation member and method of assembling it

Abstract: An apparatus for detecting a rotating angle and an angular velocity of a rotation member, such as a steering column mounted in a vehicle, and a method of assembling it. The apparatus has a disc secured onto an outer peripheral portion of a steering shaft, and a sensor mounted on a steering column tube. The steering column tube has a projecting form into which a luminescent element and a light receiving element are provided. The projecting form is designed not to contact with the disc.

Angular velocity sensor

Abstract: PURPOSE:To detect an angular velocity without generating an offset, by fitting two tuning forks to the same side surface of a rigid body, and constituting so that each vibration surface becomes a right angle to each other CONSTITUTION:The turning fork 5a and the tuning fork 5b are fitted to a supporting member 4a and 4b so that their vibration surfaces become a right angle to each other When an electric power source having constant frequency being near resonance frequency of the tuning fork 5a is connected to piezoelectric elements 2a, 2b, the tuning fork 5a starts its vibration When a prism 1 is rotated around its long axis, the tuning fork 5b is resonated by amplitude being proportional to an angular velocity by force operation on the prism 1 and Coriolis' force, and voltage being proportional to the angular velocity is generated from piezoelectric elements 2c, 3d The vibration surfaces of the tuning fork 5a and 5b are fitted so as to become a right angle to each other, therefore, the vibration modes are entirely different, and no resonance is generated, therefore, the tuning fork 5b is not vibrated by vibration of the tuning fork 5a, and no offset is generated

Kinetic sources of lower-limb angular displacement in the recovery phase of sprinting.

Abstract: One female sprinter was filmed at the 100-m mark (speed 6.5 m X S-1) of a 400-m run. Four moments occurring at each end of the thigh and shank segments during lower-limb recovery were calculated. These were: proximal and distal net muscle moments, a moment due to proximal joint accelerative force and, a moment due to distal joint-force resulting from motion and inertia of the distal connected segment. Individual contributions of each moment to segmental angular displacement were calculated by double integration, and angular velocity at toe-off was multiplied by time to yield its contribution. Contributions of the proximal muscle moments throughout recovery were 21 rad and 7.5 rad for the thigh and shank segments, respectively. Such large angular displacements did not occur because the three remaining moments opposed the proximal muscle moment. These large moments are mutually offsetting and interactive, acceleration of proximal joints provides a substantial moment during contralateral stance, and segmental angular velocity at toe-off is a significant contributor. Consequently, a phenomenon producing a change in any moment (e.g. muscular fatigue, slippery surface) will require modification of other moments for angular displacement to be maintained within reasonable limits.

Position control apparatus

Abstract: A position control apparatus has a variable gain-type velocity amplifier (115) provided within a servo control circuit, and a low velocity sensing circuit (114) for sensing a predetermined low velocity of a motor (100) immediately before the motor is stopped. When the rotational velocity of the motor (100) drops to the predetermined low velocity immediately before stoppage during orientation control, the velocity amplifier is changed over in response to a signal from the gain of the low velocity sensing circuit (114), thereby raising servo loop gain.

Apparatus for detecting the angular position and angular velocity of a rotatable member and a method of assembling the apparatus

Abstract: An apparatus for detecting the angular position and angular velocity of a rotatable member such as a rotatable part of a steering system mounted in a vehicle and a method of assembling the apparatus. The apparatus includes a disc (14) secured on the outer periphery of a steering shaft (12), and a sensor (16) mounted on a steering column tube (18). The sensor (16) has projecting portions in which a light emitting element (160) and a light receiving element (162) are provided, respectively. The projecting portions are designed not to contact the disc (14) to avoid damaging the disc during assembly.

Doppler effect laser velocity measuring system

Abstract: The frequency shift of reflected laser beam from a target is transformed o an angular measurement which is proportional to the velocity of the target relative to the measurement platform. The system uses the refraction angle of the reflected beam from a movable optical grating to produce the angular measurement.

A computational aspect of kinetic depth effect.

Abstract: A method is proposed to determine the rigid structure as well as the three dimensional motion of an object from a sequence of orthographically projected images. It is assumed that the velocities as well as the positions of the points attached to the object are observable in the images. The “instantaneous rigidity condition” wich states that the relative position vector between any two points is orthogonal to the corresponding relative velocity vector is derived from the condition of rigidity. Assuming further that the rotational velocity component is constant throughout the period of observation, each of the projected relative velocity vectors is shown to move along one of the elliptical trajectories, all of which are similar to one another. The orientations of the longer axes are common to every trajectory. Then one can determine the equations of the ellipses by observing only two points in three views or three points in two views. The solution is obtained from a set of linear equations. The length of the longer axis enables one to determine the relative velocity. The instantaneous rigidity condition is then used to obtain the relative position. The special cases where the rotational axis is either perpendicular to or parallel with the image plane are discussed. The above results are discussed in relation to the relevant psychophysical observations as well as theoretical studies.

Apparatus for detecting angular velocity

Abstract: PURPOSE:To enable the detection of an angular velocity, by providing an output signal generating means for generating an output signal required in reducing the difference of the value of a vibration number signal and the predetermined number of vibrations and a mean for regulating an actual circumferential temp. to a predetermined circumferential temp. by the association with the output signal. CONSTITUTION:When temp. difference is present between an actual circumferential temp. T and a predetermined circumferential To, an angular velocity sensor 10 is selectively heated to bring said difference to zero and the actual resonance frequencies (f) of both vibrators of the sensor 10 are almost held to predetermined resonance frequencies fo as understood from the drawing. Therefore, the offset amount mixed in the angular velocity signal Vomega from the angular velocity sensor 10 becomes almost constant while the separation of the offset amount from the value of the angular velocity signal Vomega becomes easy and the angular velocity of an object can be calculated as a value with good accuracy.

Jet flow in an angular velocity sensor

Abstract: An angular velocity sensor utilizing the Coriolis effect on a fluid jet employs increased spacing between the sensing elements to increase the scale factor and to reduce flow disturbances. A metal diaphragm pump is utilized to improve the ability to control the flow rate. Flow disturbances are further reduced by using a single, symmetrical central flowhole, eliminating curtain holes, and providing only two discharge paths oriented 180° apart.

Angular acceleration controlling method

Abstract: PURPOSE: To shorten the moving time by controlling an angular acceleration so that the torque applied to a motor of the first and the second arms becomes the maximum within the allowable range, at the time of slow-up, etc., based on an inputted positioning data. CONSTITUTION: A robot is constituted of a support 1 of a main frame, the first W the second arms 11, 12, and motors 13, 14 for driving them, etc., and it is controlled through a driving circuit part 2 by a numerical control device 3. This control device 3 is constituted of an arithmetic unit 31, a storage device 32 and a speed command device 33, determines at every operation an angular velocity of the motor of the time of slow-up, etc. from a positioning data in the storage device 32, and executes a driving control. Its angular velocity control inputs a data of a standard slow-up/down curve and two points, the optimum slow-up(down) time is derived by an optimizing method from the allowable maximum torque, etc. of the first and the second motors, also its curve is derived, and it is executed repeatedly. COPYRIGHT: (C)1985,JPO&Japio

Rotational Splitting of Global Solar Oscillations and Its Relevance to Tests of General Relativity

Abstract: The estimation of the sun's internal angular velocity using rotational splitting of low-order, low-degree global oscillations in the limb-darkening function is reviewed. Observed spatial properties of the eigenfunctions confirm the multiplet classifications previously identified by the existence of Zeeman-like frequency patterns characteristic of rotational splitting. From the observed rotational splitting, a sidereal rotational frequency of ≥3.0 μ Hz is derived for the deep interior; this value is more than six times greater than the equatorial rotational frequency of the photosphere. Upper limits have also been estimated for the internal magnetic field by analyzing the splitting for departures from uniform spacing. The inferred angular velocity distribution, together with the estimated upper limit on the internal magnetic field, yield a gravitational quadrupole moment,J2 of (5.5±1.3)×10−6. When this result is combined with different published results from planetary radar observations, values of 0.987±0.006 and 0.991±0.006 are obtained for (2+2γ−β)/3, a combination of Eddington-Robertson PPN parameters which in general relativity takes the value of 1.