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Showing papers on "Angular displacement published in 2005"


Journal ArticleDOI
TL;DR: In this paper, a general-purpose data acquisition system and pure software implementation are presented for the measurement of instantaneous angular speed. But, the authors do not consider the use of hardware resources without incurring additional costs in the form of upgrades to the measurement system.

166 citations


Patent
22 Nov 2005
TL;DR: In this paper, a motion assistance device has a biological signal detection means, a joint angle detection means for detecting angular displacement of a joint, and a parameter identification means for substituting the estimated drive torque estimated by the drive torque estimation means and the angular displacement detected by the joint angles detection means into an equation of motion to specify the wearer-specific dynamics parameter, the equation relating to the entire system and including wearer specific dynamics parameter.
Abstract: A motion assistance device has a biological signal detection means for detecting a biological signal from the wearer of the device; a motion assistance device installation member having a drive source for applying torque acting to the wearer by use of each joint of the wearer as a rotating shaft; a control means for controlling the drive source to generate torque corresponding to the biological signal detected by the biological signal detection mean; a drive torque estimation means for estimating the drive torque generated by the drive source; a joint angle detection means for detecting angular displacement of a joint; and a parameter identification means for substituting the drive torque estimated by the drive torque estimation means and the angular displacement detected by the joint angle detection means into an equation of motion to specify the wearer-specific dynamics parameter, the equation relating to the entire system and including wearer-specific dynamics parameter. The control means controls the drive source according to a predetermined control method, based on the equation of motion into which the dynamics parameter identified by the parameter identification means is substituted.

99 citations


Journal ArticleDOI
TL;DR: The gaze control system takes a lesson from the Vestibulo-Ocular Reflex (VOR) and shows that a fast rotational step perturbation applied to the head is almost completely rejected andSinusoidal head perturbations are rapidly compensated for, thus keeping the gaze stabilized on its target within a 10 times smaller angular range than the perturbing head rotations.

38 citations


Patent
27 Jan 2005
TL;DR: In this paper, a control map is derived during production that includes a predetermined advance angle profile representing the energization of the phase winding with respect to the angular position of the rotor over a range of rotor speeds.
Abstract: An electrical machine, such as a switched reluctance motor, has a rotor and at least one electrically energizable phase winding. A control map is derived during production that includes a predetermined advance angle profile representing the energization of the phase winding with respect to the angular position of the rotor over a range of rotor speeds. This is stored in memory in a controller together with an angle correction factor to be applied to a predetermined portion of the advance angle profile. The angle correction factor compensates for the difference between a desired input power and the measured input power. The correction factor may be transmitted to the controller by means of radio frequency signals.

37 citations


Journal ArticleDOI
TL;DR: Du et al. as mentioned in this paper designed a new type of metal forming press that consists of a large constant-speed motor (CSM) and a small variable-speed servomotor (VSM).
Abstract: This paper is the second part of our study on designing a new type of metal forming press. In the first part of the study (Du, R., and Guo, W. Z., 2003, ASME J. Mech. Des., 125(3), pp. 582-592), a new controllable mechanical press is introduced that consists of a large constant-speed motor (CSM) and a small variable-speed servomotor (VSM). The CSM provides up to 80% of the power while the VSM tunes the motion of the ram. This new design has a number of advantages: it is flexible (i.e., its ram motion is programable), fast (its speed is limited only by the mechanical motion), and energy efficient (the CSM can use a large flywheel to ease the large instantaneous metal forming force). This paper focuses on the motion control and experiment validation. First, the inverse kinematics is presented, which gives the relationship between the ram travel and (i) the input angular displacements, velocities, and accelerations of the two motors. Next, a trajectory-planning method is given. Then, the sensitivity analysis is carried out, which helps to determine the key dimensions of the press and the error compensation scheme. Finally, two experiments are shown to demonstrate that the new press can accomplish different tasks.

35 citations


Patent
26 Sep 2005
TL;DR: In this paper, a method for determining the angular position of a rotating object and rotary encoder is described, using a sensor that senses the coding pattern, including determining the coarse angular position with respect to the sensor whilst taking account of the coding patterns at first instant.
Abstract: A method for determining the angular position of a rotating object and rotary encoder is disclosed. In one embodiment, the method includes a method for determining the angular position of an object rotating about a rotation axis in a rotation direction and having a coding pattern, using a sensor that senses the coding pattern, including ascertaining the coarse angular position of the rotating object with respect to the sensor whilst taking account of the coding pattern at a first instant. The exact angular position of the rotating object is ascertained with respect to the sensor whilst taking account of the coarsely ascertained angular position and also whilst taking account of at least one section of the coding pattern which extends counter to the rotation direction proceeding from that location of the coding pattern which is assigned to the coarse angular position. An output signal is provided containing items of information about the exact angular position of the rotating object with respect to the sensor.

24 citations


Patent
27 Feb 2005
TL;DR: In this article, the horizontal movement line is used to control the horizontal axis motion and Z-axis motion of the platform and is designated the horizontal motion line, and a mounting beam for positioning and supporting the Z and horizontal axis motors and visual display element(s).
Abstract: Embodiments of the invention move objects throughout two-dimensional and three-dimensional space by using a movement line that is coupled with a plurality of opposing sides of the platform. The movement line is used to control the horizontal axis motion and Z-axis motion of the platform and is designated the horizontal movement line. Displacing a portion of the horizontal movement line allows vertical displacement of the platform to be traversed. There is no need for a complex computer control system since the Z-axis displacement is substantially independent of horizontal movement over a coverage area serviced by the platform. Nested embodiments utilizing one or more rope allow for three-dimensional movement of an object or angular displacement of an object with respect to the vertical axis. A mounting beam for positioning and supporting the Z-axis and horizontal axis motors and visual display element(s) and other optional multimedia devices may also be positioned independently of the platform. In addition, since the line may be commanded from one point, distantly located motors and electrical cables are not required. Many types of useful devices may then be attached to the platform including devices that require external power or devices that possess their own power and are operated via wireless signals.

23 citations


Journal ArticleDOI
TL;DR: An optical approach for angular displacement measurement (ADM) based on the attenuated total reflection technique is presented and the calculated result of sensitivity demonstrates that the intensity measurement is more efficient than the angular interrogation.
Abstract: An optical approach for angular displacement measurement (ADM) based on the attenuated total reflection technique is presented As a laser beam is incident upon a planar optical waveguide, an m line is obtained by scanning the incident angle Theoretical analysis shows that the m line sharply shifts with a tiny variation of the thickness of the waveguided layer And the specific schemes for ADM, which are based on the angular interrogation and the intensity measurement, are analyzed The calculated result of sensitivity demonstrates that the intensity measurement is more efficient than the angular interrogation Furthermore, small incident angles indicate higher sensitivity to the angular displacement than relatively large incident angles for the intensity measurement

21 citations


Patent
08 Mar 2005
TL;DR: In this article, a boat can include a rudder device using an electric actuator to allow the rudder to rotate about a rotational shaft, and a steering wheel 7 for operation by an operator.
Abstract: A steering system can be provided for a boat. Such a boat can include a rudder device using an electric actuator to allow a rudder to rotate about a rotational shaft, and a steering wheel 7 for operation by an operator. The steering system can include a steering wheel displacement sensor for detecting the displacement of the steering wheel and a controller for calculating the rotational displacement of the rudder device corresponding to the detected steering wheel displacement and sending an actuation signal to the electric actuator based on the calculated rotational displacement, in which the controller receives a signal indicating an engine speed for producing a propulsive force in the boat, and changes, in accordance with the engine speed, the ratio of the rotational displacement of the rudder relative to the steering wheel displacement.

19 citations


Patent
20 Jun 2005
TL;DR: In this paper, a rotary mechanism is used to sweep a volume and project 2D profile images on the screen, and a correction function is constructed to compensate for the error.
Abstract: This invention describes methods and systems for correcting frame position error on one category of volumetric 3D displays that generates volumetric 3D images by using a rotary mechanism to move a screen to sweep a volume and projecting 2D profile images on the screen. The screen motion is in general rotating or reciprocating and a mechanism of rotational nature is generally applied to drive the motion. The method has three major steps. The first step provides a measure of the frame position error with respect to the theoretical position. The error is a periodical function of the angular position of the moving screen, due to the nature of the mechanisms. The second step constructs a correction function that shifts the position of frame image of each frame with respect to the frame center to compensate the error. The error measurement and the construction of the correction function can be performed statically or dynamically. The third step shifts the image frames to be displayed according to the correction function and projects them in the volumetric 3D display. This invention also includes preferred driving mechanisms that match the periodical nature of the error function.

18 citations


Patent
08 Dec 2005
TL;DR: In this paper, the authors disclosed methods and apparatus for compensated measurement of angular displacement within an instrument (600), such as a total station Improved and compensated measurement is obtained by using a combination of eg an angular resolver (145) and an inertial sensor (645).
Abstract: There is disclosed methods and apparatus for compensated measurement of angular displacement within an instrument (600), such as a total station Improved and compensated measurement of angular displacement is obtained by using a combination of eg an angular resolver (145) and an inertial sensor (645) A compensated angular position measurement is produced by combining at least portions of the output signals obtained from the angular resolver and the inertial sensor, respectively

Patent
07 Jun 2005
TL;DR: The angular position of the crankshaft and camshafts can be determined by affixing a dipole magnet to each of them such that the magnet field of the magnet rotates with the rotating member and then placing a angular position sensor adjacent each rotating member to detect the rotation of each magnetic field as discussed by the authors.
Abstract: An engine controller system employs angular position sensors which are operable to very accurately determine the position of rotating engine members. Information about the angular position of the engine members is used to alter operation of the engine for improved efficiency and/or reduced emissions from the engine. The angular position of the crankshaft and camshafts can be determined by affixing a dipole magnet to each of them such that the magnet field of the magnet rotates with the rotating member and then placing a angular position sensor adjacent each rotating member to detect the rotation of each magnetic field. In another embodiment, the angular position of each end of at least one of the rotating members is determined to allow the processor to determine the torsional deflection of the member and the engine controller system is responsive to that determined deflection to further alter operation of the engine.

Patent
16 Sep 2005
TL;DR: In this article, a part of optical members that compose the optical system is held to allow angular displacement relative to the housing, and the position of the part of the optical members is maintained in a predetermined state.
Abstract: An image stabilization apparatus comprises a housing accommodating an optical system in the interior thereof. A part of optical members that compose the optical system is held to allow angular displacement relative to the housing, and the position of the part of the optical members is maintained in a predetermined state. The part of the optical members is driven to restore the position angularly displaced. A driving amount is controlled based on information of the angular displacement. A mode for controlling the housing that is suitable for vibration applied to the housing is determined, and the mode is informed to a user.

Patent
09 Feb 2005
TL;DR: In this paper, an electrophotographic printer includes an exposure unit having a MEMS scanner operating at a frequency of about 5 KHz and an angular displacement of about 20 degrees zero-to-peak mechanical scan angle.
Abstract: An electrophotographic printer includes an exposure unit having a MEMS scanner operable to scan a beam of light across a photoconductor. The MEMS scanner includes a mirror having an aspect ratio similar to the shape of the facets of a conventional rotating polygon scanner. In a preferred embodiment, the scan mirror has a length of about 750 microns in a dimension parallel to its axis of rotation and a length of about 8 millimeters in a dimension perpendicular to its axis of rotation. The MEMS scanner is operable to scan at a frequency of about 5 KHz and an angular displacement of about 20 degrees zero-to-peak mechanical scan angle.

Patent
20 Dec 2005
TL;DR: In this article, an endless belt is spanned around at least one driving member and at least two supporting members, and the driving member is driven by a pulse motor, and a difference between detected angular displacement and a target angular displacement is calculated, a frequency of a driving pulse used to drive the pulse motor is calculated based on the difference and a reference driving pulse frequency.
Abstract: An endless belt is spanned around at least one driving member and at least one supporting member. The driving member is driven by a pulse motor. An angular displacement of the driving member is detected, a difference between detected angular displacement and a target angular displacement is calculated, a frequency of a driving pulse used to drive the pulse motor is calculated based on the difference and a reference driving pulse frequency, and the pulse motor is controlled based on a driving pulse with calculated frequency. The target angular displacement is set so as to cancel a specific velocity fluctuation component of a surface velocity of the belt produced when the drive member is rotated at a constant angular velocity and that is smaller than amount of surface movement of the belt in one driving pulse.

Journal ArticleDOI
TL;DR: In this article, the Atlas simulator motion platform provides unlimited angular displacement about any axis using omni-directional wheels (or simply omniwheels), which is a novel actuation concept employing omni directional wheels.
Abstract: Using a novel actuation concept employing omni-directional wheels (or simply omni-wheels), the Atlas simulator motion platform provides unlimited angular displacement about any axis. The Atlas conc...

Patent
16 Mar 2005
TL;DR: In this paper, a rotational symmetric precision part was measured with a rotating centering means and a dog, drivable via a drive, and a revolving centering mean, and software means were provided to determine slip between the dog and the rotational precision part through a comparative calculation.
Abstract: A device for measuring a rotationally symmetric precision part, having a dog, drivable via a drive, and a revolving centering means, the dog and the revolving centering means being positioned in such a way that a rotationally symmetric precision part to be measured may be non-positively clamped coaxially between dog and centering means. A first angle measuring system is assigned to the dog, which provides signals that permit the drive-side angular position of the dog to be stated, and a further angle measuring system is assigned to the revolving centering means, which provides signals that permit the output-side angular position of the centering means to be stated. Software means are provided which determine slip between the dog and the rotationally symmetric precision part through a comparative calculation on the basis of the drive-side angular position and the output-side angular position.

Patent
27 Apr 2005
TL;DR: In this paper, the angular displacement grating sensor sends two pulses in each turn of the pulley, with each pulse period corresponding to a certain length; the pulse signal is real-time received and processed in the operating and processing part; and the current depth is shown in the display.
Abstract: The depth measuring instrument includes measuring rope for reaching the measured body, pulley, angular displacement grating sensor, operating and processing part and display. The measuring rope includes local surface of the pulley, the pulley is linked with the photoelectric code disc of the angular displacement grating sensor; the angular displacement grating sensor sends two pulse signal in each turn of the pulley, with each pulse period corresponding to certain length; the pulse signal is real-time received and processed in the operating and processing part; and the current depth is shown in the display. The present invention is used in measuring well depth, base depth, etc. and has the advantages of good real-time property, high precision, high efficiency, etc.

Journal ArticleDOI
TL;DR: In this paper, the random motion of a rigid body under a white noise perturbation is studied and a formula for the angular velocity in an average sense is given. But the stability near a principle axis is not discussed.
Abstract: We use stochastic analysis to study the random motion of a rigid body under a white noise perturbation. We obtain a formula for the angular velocity in an average sense and discuss the stability near a principle axis.

Patent
14 Mar 2005
TL;DR: An apparatus for multi-axis rotation and translation consisting of a spherical body, a plurality of roller assemblies each engaging the outer surface of the spherical body and a multiplicity of actuators for driving said roller assemblies, a frame for supporting the plurality of rollers, and translation means for translating the frame along each of three orthogonal axes.
Abstract: An apparatus for multi-axis rotation and translation comprises a spherical body, a plurality of roller assemblies each engaging the outer surface of the spherical body, a plurality of actuators for driving said roller assemblies, a frame for supporting the plurality of roller assemblies and the plurality of actuators and translation means for translating the frame along each of three orthogonal axes. The actuators are selectively operated to drive the roller assemblies thereby imparting unlimited angular displacement to the spherical body and rotating the spherical body about any axis passing through its geometric center. The translation means may be operated to translate said spherical body along at least one of said three orthogonal axes. The apparatus is particularly applicable to use as a manipulator with six degrees of freedom (unlimited rotational displacement and translational displacement limited only by the boundaries of the workspace).

Patent
02 Feb 2005
TL;DR: In this paper, a sensing device for an intelligent electric bicycle with a torque sensing mode is presented, and a rigid connection between the center shaft and the chain wheel is changed into an elastic connection.
Abstract: The utility model discloses a sensing device for intelligent electric bicycle The device comprises a plurality of magnetic steels respectively and relatively fixed to a center shaft and a chain wheel, a hall element relatively fixed to a five-way, an outward convex ring and an inward convex ring respectively fixed to the center shaft and the chain wheel, and an angular displacement can be generated between an external tooth and an internal tooth through a pressing spring The sensing device for intelligent electric bicycle is adopted with a torque sensing mode, and a rigid connection between the center shaft and the chain wheel is changed into an elastic connection When an electric bicycle is started and accelerated or met with resistance (namely with resistance torque), the rotation angle of the chain wheel is lagged behind the center shaft, and the stronger the resistance, the larger the rotation angle, the longer the lagged time The equipped magnetic steel and the hall element are used for detecting sensitive time, and sensitive time is converted to an electrical signal, and the electrical signal is sent to a controller for regulating output current or electric voltage, and thus the speed regulation and power-assisted effect is obtained

Journal ArticleDOI
TL;DR: In this article, the geometric effects due to our galaxy's peculiar motion on circles-in-the-sky in CMB maps, and show that their shape remains circular, as detected by a local observer with arbitrary peculiar velocity.
Abstract: For an observer in the Hubble flow, the last scattering surface (LSS) is well approximated by a 2-sphere. If a non-trivial topology of space is detectable, then this sphere intersects some of its topological images, eventually giving rise, in cosmic microwave background (CMB) radiation maps (which are projections of the LSS onto the observer's sky sphere), to circles-in-the-sky, i.e., pairs of matching circles of equal radii, centred at different points on the sky. We examine the geometric effects due to our galaxy's peculiar motion on circles-in-the-sky in CMB maps, and show that their shape remains circular, as detected by a local observer with arbitrary peculiar velocity. In general, a circle is detected as a circle of different radius, displaced relative to its original position, and centred at a point which does not correspond to its detected centre in the comoving frame. Further, there is an angular displacement of points on the circles. These effects all arise from aberration of cosmic microwave background radiation, exhausting the purely geometric effects due to the peculiar motion of our galaxy, and are independent of the large scale curvature of space, the expansion of the universe and the acceleration of the observer, since aberration is a purely local phenomenon. For a Lorentz-boosted observer with the speed of our entire galaxy, the maximum changes in the angular radius of a circle, its maximum centre displacement as well as the maximum angular distortion are all shown to be of order β = (v/c) 1.23 × 10−3 radians. In particular, two back-to-back matching circles in a finite universe will have an upper bound of 2|β| in the variation of either their radii, the angular position of their centres, or the angular distribution of points. Although below current WMAP's resolution, these results are within Planck's and other more accurate missions' resolution.

Patent
07 Oct 2005
TL;DR: In this paper, a rotating plate device is used for supporting and orienting one of the objects in an angular manner in a pipeline, which can be translated in translation in relation to the second supporting means along the second main axis.
Abstract: The invention relates to a device and a method for assembling oriented objects, such as parts of a pipeline. Said device comprises means for rotational displacement about a rotational axis (5) of a first and a second base (1, 2). The first base (1) has a first main axis (6) which is perpendicular to the rotational axis (5) and comprises first means for supporting (7) objects that can be displaced in translation along the first main axis (6). The second base (2) has a second main axis (9) which is perpendicular to the rotational axis (5) and comprises second means for supporting (10) objects and a revolving plate device (14) for supporting and orienting one of the objects in an angular manner. Said revolving plate device (14) can be displaced in translation in relation to the second supporting means (10) along the second main axis (9). Visualisation means enable at least the rotational angle of the plate (15) and the position of the second base (2) to be visualised.

Patent
15 Nov 2005
TL;DR: In this paper, the angular position of a fastening cleat is adjusted such that the average variation in the value of the free angular movement is returned to the median of the angular movement range.
Abstract: A method and device for measuring and adjusting the angular movement of a fastening cleat on a clipless pedal, includes a motion detector which is fixed to the pedal to detect any angular movement in relation to the fastening cleat and transmit data to a data-processing device which calculates values of the angular movement as a function of time, and the average of the variations in the angular movement. The contactless motion detector includes a magnetic sensor which is fixed to the pedal, and is disposed facing a magnet that is fixed beneath the cleat and can detect any variation in the orientation of the magnetic field as a function of the angular movement of the cleat. The angular position of the fastening cleat is adjusted such that the average variation in the value of the free angular movement is returned to the median of the free angular movement range.

Journal ArticleDOI
TL;DR: In this article, an optimal feedback regulation of a rigid body motion with the help of internal rotor system, taking into consideration the internal friction of the rotors, is presented, and the optimal feedback control law is obtained as a function of the angular velocity and the orientation redundant parameters.
Abstract: This paper presents a solution for optimal feedback regulation of a rigid body motion with the help of internal rotor system, taking into consideration the internal friction of the rotors The optimal feedback control law is obtained as a function of the angular velocity and the orientation redundant parameters Both of the angular velocity and the orientation parameters are regulated In this study, stabilizer rotor system is used for regulation of the rigid body motion by the reaction rotors which can be developed by electric motors rigidly mounted on the body Some known results on the optimal control of equilibrium positions of a rigid body are generalized and new results are obtained Simulation results are presented

Journal ArticleDOI
TL;DR: In this article, an experimentally testable criterion for the demonstration of an angular version of the EPR paradox is presented. But the criterion is not applicable to the case of the angular angular position measurement.
Abstract: The violation of local uncertainty relations is a valuable tool for detecting entanglement, especially in multi-dimensional systems. The orbital angular momentum of light provides such a multi-dimensional system. We study quantum correlations for the conjugate variables of orbital angular momentum and angular position. We determine an experimentally testable criterion for the demonstration of an angular version of the EPR paradox. For the interpretation of future experimental results from our proposed setup, we include a model for the indeterminacies inherent to the angular position measurement. For this measurement angular apertures are used to determine the probability density of the angle. We show that for a class of aperture functions a demonstration of an angular EPR paradox, according to our criterion, is to be expected.

Journal ArticleDOI
TL;DR: In this article, a photoelectric angular position sensor is proposed for determining the rotation orientation of a steerable underground boring tool, which can resist harsh environmental conditions such as vibration, excessive ambient temperature, dirt, moisture and dew.
Abstract: In order to avoid the disadvantages of the present angular position sensors for determining the rotation orientation of a steerable underground boring tool, a new photoelectric method utilizing photoelectric switches and the corresponding sensor are established. The sensor comprises a gravitational ball, one or more light sources and an array of photodetectors, and realizes angular position measurement by setting a block between the light source and the corresponding photodetector which is rotated to the lowest point. The concrete configurations are described in detail and a typical prototype is illustrated. The photoelectric angular position sensor is compact, simple, low-cost. It can resist harsh environmental conditions such as vibration, excessive ambient temperature, dirt, moisture and dew, so it is especially well-suited for a steerable underground boring tool.

PatentDOI
TL;DR: In this article, the steering of a towed linear acoustic antenna is controlled by a body having a longitudinal axis, the body being provided with a fastener for fastening it releasably to the towed object, and a plurality of stabilizer fins, each of which is coupled to the body and extends along an axis that is transverse to the longitudinal axis of said body.
Abstract: A device for controlling steering of a towed underwater object, in particular a towed linear acoustic antenna. The device comprises a body having a longitudinal axis, the body being provided with a fastener for fastening it releasably to the towed object, and a plurality of stabilizer fins, each of which is coupled to the body and extends along an axis that is transverse to the longitudinal axis of said body, the angular position of each fin relative to the body being pivotable about its transverse axis by control, so as to modify the angles of inclination of said fins.

Patent
10 Aug 2005
TL;DR: In this paper, a slope surface displacement measuring method and its equipment is described, which includes an angular displacement sensor with small turning torque and high sensitivity, supporting frame and multistrand fine wire rope.
Abstract: The present invention discloses a slope surface displacement measuring method and its equipment. Said invention includes angular displacement sensor with small turning torque and high sensitivity, supporting frame and multistrand fine wire rope. The angle displacement sensor is mounted on the supporting frame, one end of the multistrand fine wire rope and supporting frame are respectively relatively fixed on the slope body or non-movable rock body, another end of the multistrand fine wire rope is winded round angular displacement sensor, then the slided dimension of said slope body can be converted into line displacement by means of multistrand fine wire rope, and the line displacement can be converted into angular displacement by means of angular displacement sensor.

Patent
30 Jul 2005
TL;DR: In this paper, the rotational angular position of the camshaft of a reciprocating piston engine in relation to the crankshaft was determined magnetically by extrapolation from at least two adjusting shaft rotational angle measurements, the time difference between the adjusting shaft measurement time points, and the interval between the last measurement time point and reference time point.
Abstract: The method is for the determining of the rotational angular position of the camshaft (11) of a reciprocating piston engine in relation to the crankshaft (12). An assessed value is extrapolated for the rotational angle from at least two adjusting shaft rotational angle measurements, the time difference between the adjusting shaft measurement time points, and the interval between the last measurement time point and reference time point, and from this assessed value, the crankshaft rotational angle measured value, and the transmission characteristic, the value of the rotational angular position is determined magnetically.