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Showing papers on "Angular displacement published in 1974"


Journal ArticleDOI
03 May 1974-Nature
TL;DR: Bacteria rotate at the angular velocity at which the torque generated by the flagellar motor2 is balanced by the torque due to the viscous drag, and in general, M = bηΩ, where M is the torque, η is the viscosity, Ω is theangular velocity, and b is a coefficient which depends on the size and the shape of the cell, the position of the axis of rotation, and the distance between the cell and the wall
Abstract: TETHERED bacteria1 rotate at the angular velocity at which the torque generated by the flagellar motor2 is balanced by the torque due to the viscous drag In general, M = bηΩ, where M is the torque, η is the viscosity, Ω is the angular velocity, and b is a coefficient which depends on the size and the shape of the cell, the position of the axis of rotation, and the distance between the cell and the wall For a sphere of radius a (not too close to the wall) M = 8πη a3Ω (ref 3) Viscous forces are so large in comparison with inertial forces4 that Ω will change with M virtually instantaneously; any discontinuities in the one will be evident in the other Consider a cell of radius a and uniform density ρ rotating at an angular velocity Ω0; if its motor is suddenly disengaged, Ω will decay exponentially to 0 with a time constant ρ a2/15η, and the cell will stop in Ωρ a2/15η radians For Escherichia coli this is less than a millionth of a revolution The cell also is subject to rotational diffusion, but this will be evident only if the coupling between the flagellum and the body of the cell is fluid The root-mean-square deviation in the angular position is (2Dt)½, where D is the rotational diffusion constant and t is the time For a cell which can rotate freely, D = kT/bη, where k is Boltzmann's constant and T is the absolute temperature

225 citations


Patent
04 Nov 1974
TL;DR: In this paper, the authors present an approach for determining linear or angular measurements or measurements of positions on a planar or curved surface, which apparatus uses at least one delay element, such as a magnetostrictive element, which is capable of supporting an accoustic wave signal.
Abstract: Apparatus for determining linear or angular measurements or measurements of positions on a planar or curved surface, which apparatus uses at least one delay element, such as a magnetostrictive element, for example, which is capable of supporting an accoustic wave signal. The one or more delay elements may be in the form of bands, rods, wires, planar or spherical structures, and the like, and can be arranged in various embodiments to provide linear or angular position information for single, dual, and multiaxis geometry. They can be used, for example, to provide single or multispeed resolver operation and three-axis attitude read-out. In preferred embodiments the apparatus uses phase measurement techniques so that high accuracy can be achieved.

44 citations


Patent
19 Sep 1974
TL;DR: In this paper, a tightening method and a system for practicing same are disclosed for tightening a fastener to a desired axial load, where torque is applied to the fastener until it is tightened to its yield point.
Abstract: A tightening method and system for practicing same are disclosed herein for tightening a fastener to a desired axial load. According to the method, torque is applied to the fastener until it is tightened to its yield point and either the torque applied at the yield point or the angular rotation of the fastener at the yield point are determined and are used to determine the axial load acting on the joint assembly and these determined characteristics are used to determine either the torque or angular rotation required to tighten the fastener to the desired load. Thereafter, torque is again applied to the fastener and when the actual torque being applied or actual angular rotation of the fastener substantially equals that required to tighten the fastener to the desired load, the application of torque is discontinued. The tightening system disclosed for practicing the method includes a wrench for applying torque to a fastener and including means for developing a signal representative of the torque applied to or angular rotation of the fastener and means for developing an actuating signal when the fastener has been tightened to its yield point. The actuating signal shuts off the wrench and feeds the signal representative of torque or angular rotation at the yield point to a memory device including predetermined load-torque relationships or a predetermined load-angular rotation relationship for the fastener. From these relationships the torque or angular rotation required to tighten the fastener to the desired load can be determined and a signal representative thereof is developed and stored for comparison with a signal representative of the actual torque or angular displacement of the fastener as the wrench again applies torque to the fastener. When the compared signals are substantially equal, a control signal is developed for shutting off the wrench.

41 citations


Patent
26 Jun 1974
TL;DR: In this article, a force measuring instrument employs light interference fringes for measuring extremely small magnitudes of force such as those encountered in the weighing of small objects or in determining the forces of attraction or repulsion between two relatively small bodies.
Abstract: A force measuring instrument employs light interference fringes for measuring extremely small magnitudes of force such as those encountered in the weighing of small objects or in determining the forces of attraction or repulsion between two relatively small bodies. A fixed mirror of the displacement mechanism is provided with needle point pivot shafts in which balance oscillations can be dampened by applying a viscous damping material in the conical recesses receiving the pivot points. Torsion fiber beams permit a small angular displacement of the fixed mirror. A low frequency dither signal may be applied to the platform for overcoming stiction at the pivot points.

33 citations


Patent
14 Jun 1974
TL;DR: In this paper, a pair of galvanometers are used to adjust the angular displacement of the mirror which scans the beam in the direction between the successive lines, thus correcting the geometric distortion of the pin cushion type of the image.
Abstract: Apparatus is disclosed for use with image forming apparatus having a pair of galvanometers one of which, in response to a ramp signal rotates a mirror which scans lines in one direction across the image and the other of which in response to a staircase signal rotates another mirror in a direction perpendicular to the direction of the lines to scan successive ones of the lines. The apparatus includes circuits responsive to the galvanometer drive signal amplitudes for producing a compensating signal which is representative of the angular displacement of the mirrors and thus of the position to which the beam is scanned at any instant. This compensating signal and the signal which drives the galvanometer which scans the beam between successive lines are combined to adjust the angular displacement of the mirror which scans the beam in the direction between the successive lines, thus correcting the geometric distortion of the pin cushion type of the image.

29 citations


Patent
29 Oct 1974
TL;DR: In this paper, a cylindrical object is covered with a strip of sheet material having a width less than the length of the object and is applied by rotating the object while feeding the sheet material at a right angle to the rotational axis of the shape to provide convolute windings around opposite end portions of the objects.
Abstract: The cylindrical object is covered with a strip of sheet material having a width less than the length of the object and is applied by rotating the object while feeding the sheet material at a right angle to the rotational axis of the object to provide convolute windings around opposite end portions of the object and guiding the sheet material in angular relationship to the rotational axis of the object to provide spiral windings around the medial portion of the object. A pair of rolls support and rotate the object while the sheet material is fed from a carriage which moves along a path of travel parallel to the drive rolls and the angular position of the carriage is varied to thereby change the relationship between the rotational axis of the supply roll and the rotational axis of the object so as to permit both convolute and spiral windings to be applied to the object.

27 citations


Patent
13 Nov 1974
TL;DR: In this article, a movable part is mounted on a stationary part; said parts have a pattern of equally wide parallel lines separated by interspaces, and when the parts overlap in use of the instrument, the line patterns form a moire pattern to indicate the angular position of the object.
Abstract: An instrument for indicating or checking the angular position of an object. A movable part is mounted on a stationary part; said parts have a pattern of equally wide parallel lines separated by interspaces. When the parts overlap in use of the instrument the line patterns form a moire pattern to indicate the angular position of the object.

24 citations


Patent
03 Apr 1974
TL;DR: In this paper, a variable range gauge follower is used to measure the diameter of work pieces, consisting of a pair of pivotable arms each having a contact at one end adapted to engage the surface of the work piece.
Abstract: A variable range gauge follower apparatus for measuring the diameter of work pieces comprising a pair of pivotable arms each having a contact at one end adapted to engage the surface of the work piece. Each of the arms has fixed to it for conjoint movement a segment member having an angular position Inductosyn at its circumferential edge. Associated with each Inductosyn is a magnet sensing head stationarily fixed so as to be able to sense the induced current as a function of the angular displacement of the segment. Means are provided for phase measurement of the two signals which when compared with a predetermined starting signal determines the angular change of the arms and thus the diameter of the work piece. The two arms are each mounted in a shaft journaled in a frame-like body and are coupled for conjoint rotation by a pair of meshing gears to establish an initial spacing or opening between the two arms. The gears are provided with means for their uncoupling during actual operation.

23 citations


Patent
15 Apr 1974
TL;DR: In this article, a signal source position is determined using an angle-measuring, interferter system employing a longitudinal antenna array having a baseline length greater than the signal wavelength.
Abstract: A signal source position is determined using an angle-measuring, interferter system employing a longitudinal antenna array having a baseline length greater than the signal wavelength. The long, multi-lambda (nλ) baseline produces ambiguous phase measurement ( ). Thus, the true angular position or bearing could correspond either to φ, or φ±360°, or φ±2.sup.. 360°, -φ±(n-1)360°, or φ-n .360°. Ambiguities are resolved by the longitudinal array angular motion relative to the signal source and by phase tracking the signal during the relative movement. To determine the true signal position, (2n) different software solutions for signal position are set up to process the 2n different angular data produced by each phase measurement (φ). The "Lobe Tracking" procedure (there are n-number of data lobes in a (nλ) array) which is achieved by phase tracking provides the means of matching the n-different angular data produced by the phase measurement (φ) to the n-different solutions set-up. From the n-different solutions set-up for signal position, only one will converge to the true signal position and the rest will diverge. The convergence or divergence depends on matching the vehicles position translation to the angular position change relative to the signal source. The solution elimination process is set up by certain solution conveyance criteria. Also the elimination process is enhanced by solution rejection based on unacceptability of angular data or lobe. Since lobe tracking matches the angular data produced by the measurement to the solution, unacceptability of data constitutes rejection of the solution.

22 citations


Patent
08 Jan 1974
TL;DR: A gyroscopically stabilized single wheel vehicle comprising an outer wheel mounted on a rim, a frame and two directions or degrees of freedom of motion system for mounting the frame on the rim within the wheel is described in this article.
Abstract: A gyroscopically stabilized single wheel vehicle comprising an outer wheel mounted on a rim, a frame and two directions or degrees of freedom of motion system for mounting the frame on the rim within the wheel. The frame supports a driver''s seat, fuel tank, a source of motive power, and the controls necessary for operation of the vehicle. In addition, a propeller is mounted on the frame and driven from the source of motive power and provides a thrust along a horizontal axis. One direction of freedom of motion between the frame and the wheel is controlled by a steering wheel. The other direction of freedom of motion is stabilized by elevators secured to the frame and controllable in their pitch. Rotational displacement of the frame with respect to the wheel around a generally vertical axis creates a primary or initial precessional velocity which tends to tilt the wheel out of a vertical plane. The thrust of the propeller increases this tilt, thereby creating a secondary precessional velocity to rotate the wheel around that vertical axis, thereby effecting a change in the direction of travel of the vehicle. As a turn is being completed and the steering wheel is returned to its center position and then turned in the opposite direction, a velocity vector in the opposite direction is created to bring the wheel back into a vertical plane. The steering wheel is then returned to its center position.

17 citations


Patent
20 Dec 1974
TL;DR: In this article, a stable reference gyroscopic apparatus is provided in the form of an angular displacement sensor which employs an end-supported vibratory rod or wire, instead of the commonly used rotatable element.
Abstract: Stable reference gyroscopic apparatus is provided in the form of an angular displacement sensor which employs an end-supported vibratory rod or wire, instead of the commonly used rotatable element. The apparatus of the invention incorporates an improved means for maintaining the vibrational amplitude of the center of the vibratory element constant, and electronic circuit means for causing the orbit of center of the vibratory element to remain in a straight line, both means being effective to eliminate the major sources of potential drift in the sensor.

Patent
Victor Auerbach1
30 Sep 1974
TL;DR: In this paper, a rotating scanning telescopic sensor, and a fixed mirror positioned so that the sensor scans both the direct and the reflected line-of-sight of the celestial object in the course of each rotation was used.
Abstract: An attitude determining system for vehicles, such as spacecraft or for ground-based environments measures the angle between a reference and the line-of-sight to a star or other celestial object of known position or to aircraft and missiles. The system includes a rotating scanning telescopic sensor, and a fixed mirror positioned so that the sensor scans both the direct and the reflected line-of-sight of the celestial object in the course of each rotation. Associated transducers and electronic circuits determine the relative angular positions of the telescopic sensor at the instants it detects the direct and the reflected radiation from the celestial object. A computation based on the two angles gives the angular position of the celestial object relative to the vehicle reference. The system cancels or substantially reduces errors due to optical or electronic inaccuracies which identically affect the direct and the reflected angular position measurements.

Patent
Perry L. Wells1
30 Sep 1974
TL;DR: In this article, a toroidal electrolyte-type angular transducer is provided for measuring angular displacement or tilt from a vertical plane, where three conducting paths in the electrolyte are established between two measuring electrodes and an auxiliary electrode respectively and a common electrode.
Abstract: A toroidal electrolyte-type angular transducer is provided for measuring angular displacement or tilt from a vertical plane. Three conducting paths in the electrolyte are established between two measuring electrodes and an auxilliary electrode respectively and a common electrode. Angular displacement is simply related to the values of the conductances in the various paths. In a preferred embodiment of the invention several guard-ring electrodes are included to divert spurious leakage currents from the common electrode so that the leakage current will not affect the measurement. The guard-ring electrodes are maintained at the same potential appearing at the collector electrode to ensure that no leakage currents pass between the two. Another preferred embodiment the invention provides that the two measuring electrodes are driven by voltages equal in magnitude and opposite in sign. A high gain operational amplifier is interconnected between the auxiliary electrode and the common electrode. By means of this arrangement a single voltage reading may be obtained which is directly proportional to angular displacement.

Patent
21 Feb 1974
TL;DR: In this paper, the stroke, speed and acceleration of a cam profile can be represented graphically or by analogous or digital signals by utilizing a displacement sensor which cooperates with the cam profile and an angular displacement sensor, and the digital signals are then converted into analogous form by a conversion and synchronization circuit which can then be applied to an X-Y recorder.
Abstract: The stroke, speed and acceleration of a cam profile can be represented graphically or by analogous or digital signals by utilizing a displacement sensor which cooperates with the cam profile and an angular displacement sensor which cooperates with the cam. The displacement sensor provides a pulse train which is processed to furnish digital signals of the stroke, speed and acceleration of the cam which are variable in time and the angular movement sensor provides a digital signal of angular displacement of the cam on rotation of the cam. The digital signals are then converted into analogous form by a conversion and synchronization circuit which can then be applied to an X-Y recorder.

Patent
15 Jul 1974
TL;DR: In this article, an angular displacement transducer having a mounting base for mounting an inertial element sensitive to low frequency angular displacements and a fluid mass with a pickoff for sensing displacement of the mounting base relative to the fluid mass is presented.
Abstract: An angular displacement transducer having a mounting base for mounting an inertial element sensitive to low frequency angular displacements and an inertial element sensitive to high frequency angular displacements. The low frequency sensitive inertial mass is a solid rotor device having a pickoff for sensing angular displacement between the solid inertial mass and the mounting base. A feedback centering circuit responsive to the pickoff output maintains the solid inertial mass in a substantially neutral position relative to the mounting base for displacement frequencies below the band of interest and allows the solid mass to move in an open loop fashion within its band of interest. The inertial mass sensitive to high frequency angular displacements is a fluid mass having a pickoff for sensing displacement of the mounting base relative to the fluid mass. A feedback centering circuit responsive to the fluid mass displacement sensor output is disposed to impart the motion of the mounting base to the fluid mass for displacement frequencies below the band of interest and allows the fluid mass to operate open loop within its band of interest. The solid inertial mass pickoff output is directed to a low pass filter and the fluid inertial mass pickoff output is directed to a high pass filter. The response time of the feedback centering circuit for the solid inertial mass is long enough in the band of interest to produce pickoff output related to angular displacement in the low frequency range and the response time of the feedback centering circuit for the fluid inertial mass, while shorter, is long enough in the band of interest to produce pickoff output related to angular displacement in the high frequency range. The outputs from the high and low pass filters are summed and presented as angular displacement sensor output over the wide band of high and low frequencies. Adjustment of feedback centering circuit gain and viscosity of fluid inertial mass viscosity may provide a wide band angular velocity sensor.

Patent
12 Nov 1974
TL;DR: In this paper, an angular rate sensor employing an elongated flexible rod which when driven vibrates in a plane fixed in relation to its housing is employed to measure the angle between the plane of vibration and a fixed reference point on the housing which provides a measure of the angular rate.
Abstract: An angular rate sensor employing an elongated flexible rod which when driven vibrates in a plane fixed in relation to its housing. The housing is filled with a viscous gas for damping the oscillation of the rod in planes other than the driven plane. When the instrument is subjected to an input angular rate about an axis parallel to the symmetry axis, the plane of vibration is then angularly displaced from its fixed or driven plane. This angular displacement is proportional to the angular input rate. An electromagnetic drive circuit initiates and sustains oscillation of the rod and an electromagnetic pickoff circuit is employed to measure the angle between the plane of vibration and a fixed reference point on the housing which provides a measure of the angular rate.

Patent
18 Nov 1974
TL;DR: In this article, the focal length of a zoom lens is variable by rotating a ring-shaped selector about the optical axis through the medium of a radially extending handle, and focussing prior to the making of exposures at close range is effected by rotating the handle about its own axis.
Abstract: An objective system for motion picture cameras wherein the focal length of a zoom lens is variable by rotating a ring-shaped selector about the optical axis through the medium of a radially extending handle, and focussing prior to the making of exposures at close range is effected by rotating the handle about its own axis. Prior to rotation of the handle about its axis, the selector must be moved to an angular position corresponding to the shortest focal length of the lens and the handle is thereupon depressed radially inwardly against the opposition of a spring so that an eccentric pin at its inner end enters a socket in a slide which is reciprocable in the lens barrel and is coupled to a sleeve for the optical elements of the lens by means of a follower which also serves to couple the sleeve to the selector. The handle can be depressed in a single angular position and can be moved outwardly to become disengaged from the slide only after it reassumes the single angular position. The selector may be completely or nearly completely concealed in the interior of a tubular extension of the front wall of the camera body.

Patent
03 Jul 1974
TL;DR: A tilt indicator has two pendulums pivoted on a body whose tilt is to be indicated and limited by ratchet means to rotation in opposite directions and prevented from return rotation as mentioned in this paper.
Abstract: A tilt indicator having two pendulums pivoted on a body whose tilt is to be indicated and limited by ratchet means to rotation in opposite directions and prevented from return rotation so the angular position of each pendulum is an indication of the maximum tilt of the body in its permitted direction of rotation.

Patent
16 Sep 1974
TL;DR: In this paper, a method and apparatus for processing a pair of d.c. signals representing information having angular and amplitude components, in particular information relating to the unbalance of a body to be balanced, is provided.
Abstract: In a method and apparatus for processing a pair of d.c. signals representing information having angular and amplitude components, in particular, information relating to the unbalance of a body to be balanced, coordinate transformation means are provided in order to transform the coordinates of the two d.c. signals in response to a control signal, the control signal being continually adjusted in a direction dependent upon the polarity of the outputs of the coordinate transformation means, until one of the outputs of the coordinate transformation means becomes 0. In this case, the control signal corresponds to the angular information of the two d.c. voltages, and the output on the other output terminal of the coordinate transformation means corresponds to the amplitude information. Means are also provided for stopping the adjustment of the control signal, whereby a source of d.c. signals corresponding to angular information may be applied to the inputs of the coordinate transformation means, in order to enable adjustment of the d.c. signals so that they correspond to the same angle as the signal applied to the control input of the coordinate transformation means. The two d.c. signals may correspond to the angular position of a body to be balanced.

Patent
16 May 1974
TL;DR: A vibrating wire attitude reference sensing system as mentioned in this paper utilizes a uniquely vibrated wire kept in constant motion and whose plane of vibration is rotated a predetermined small amount in an oscillatory fashion. Sensing equipment monitors the change in angular position and transforms this information into pulses which perform two functions.
Abstract: A vibrating wire attitude reference sensing system utilizes a uniquely vibrated wire kept in constant motion and whose plane of vibration is rotated a predetermined small amount in an oscillatory fashion. Sensing equipment monitors the change in angular position and transforms this information into pulses which perform two functions. A first function is to transmit the pulses to components that force the plane of vibration to a new angle. The other function is to transmit the pulses to equipment that counts records and determines the angle of rotation.

Patent
Ronald L. Syria1
18 Oct 1974
TL;DR: In this paper, a pulse-generating circuit driven as a function of wheel angular velocity is used to produce electrical signals related to vehicle wheel rotation, which are shaped, filtered and passed to associated equipment, such as regulated braking circuits, to perform the regulating function.
Abstract: An automotive control system utilizes a pulse-generating circuit driven as a function of wheel angular velocity to produce electrical signals related to vehicle wheel rotation. The signals are shaped, filtered and passed to associated equipment, such as regulated braking circuits, to perform the regulating function. The frequency doubling circuit is provided to accommodate different sensing systems which produce fewer output signals for a given angular displacement of a vehicle wheel.

Journal ArticleDOI
TL;DR: In this article, it is shown that with respect to the center of mass, the angular momentum of a rigid body is equal to the inertia tensor times the instantaneous angular velocity.
Abstract: Summary It is well known that with respect to the centre of mass the angular momentum of a rigid body is equal to the inertia tensor times the instantaneous angular velocity. The question with respect to what other points this relation is valid is investigated by formulating it in a vector equation. By means of elementary vector relations and by utilizing the fact that any motion can be resolved into a translation and a rotation, the equation is transformed in such a manner that it can be given a geometrical interpretation. In making this interpretation, one must distinguish between motion with translation and motion without. In the case of motion withouttranslation the relation is found to be valid in particular with respect to any point on the instantaneous axis of rotation. For motion withtranslation the relation is valid for points on the axis only if the latter goes through the centre of mass. It is also valid for some points on the right circular cylinder containing the centre of mass and with the i...