Abstract: The present disclosure discloses a swimming pool cleaning robot with a movement state detection function, including a main body on which a control module is arranged; a rotating member is rotatably arranged outside the main body; a water fender is also arranged outside the main body; part of the rotating member is located in the water fender; the swimming pool cleaning robot further includes a rotating speed detection assembly used for detecting a rotating speed of the rotating member; and the rotating speed detection assembly is electrically connected to the control module. The moving speed of the swimming pool cleaning robot can be accurately acquired by detecting the rotating member's rotating speed; a movement trajectory of the swimming pool cleaning robot can be controlled by controlling the swimming pool cleaning robot's moving direction; and the entire detection system has a simple and reliable structure and is convenient to maintain.

Abstract: A method for determining runout error includes generating a first magnetic field to interact with a second magnetic field generated by four or more poles of a magnet ring mounted to a first platform. The interaction may cause the first platform to rotate relative to a second platform. The method may further include receiving, from a magnetic field sensor, data including respective boundaries between neighboring poles of the four or more poles relative to a corresponding nominal boundary defined by substantially uniform boundary spacing. The method may include determining a magnetic field pattern from the data and, based on the pattern, determining an angular position of the four or more poles. The method may further include determining an angular difference between the determined angular position and a nominal angular position. The method may also include determining a runout error based on an amplitude of the angular difference.

Abstract: A rotational angle sensor system including: a rotatably mounted movement sensor; a sensor that is designed to detect a rotation of the movement sensor, wherein the rotation occurs at a measurement angle interval; an evaluation electronics system designed to receive an analogue signal from the sensor and to digitalise same using an internal resolution, and to emit a digital output signal reporting the rotation detected by the sensor, wherein the resolution of the digital output signal for a measurement angle interval of less than or equal to 360° is the same size as the internal resolution.

Abstract: A speed detection device includes a comparator module, a sensor lead with a node connected to the comparator module, and a limit set module. The limit set module is connected to the sensor lead node and to the comparator by an upper limit lead and a lower limit lead to provide upper and lower limits to the comparator that vary according to amplitude variation in voltage applied to the sensor lead.

Abstract: [Problem] To provide a vehicle notification device that allows others to easily recognize the vehicle. [Solution] A vehicle notification device comprises a base portion, an attaching portion that is provided on the base portion and that can be attached to or detached from a rotating body of a vehicle that is configured to be run by a manual drive force, a wireless transmitter configured to transmit a wireless signal that notifies the presence of itself to an external device that is external to the vehicle, and a power generator that generates electric power supplied to the wireless transmitter.

Abstract: A nonvolatile, absolute multi-turn rotation sensor employs a magnetic particle that is indexed around a serpentine channel with successive passes of a magnet caused by rotation of the rotation sensor shaft. Sensors at regular locations around the track allow determination of the position of the magnetic particle and thus the total number of revolutions of the shaft.

Abstract: An inductive sensor has an electrically nonconductive substrate, at least one electrically conducting coil that is integrally joined to the substrate, with the mechanical rigidity of the substrate significantly greater than that of the conducting coil, a metal plate covering the conducting coil, with the substrate comprised by the metal plate, and with the surface of the metal plate on the side oriented toward the conducting coil provided with an electrically insulating layer.

Abstract: A bicycle pedaling force detector is basically provided with that basically includes a first sensor circuit, a wireless communicator and a first electrical connection member. The first sensor circuit is coupled to a first housing that is configured to be mounted to a crank assembly. The wireless communicator is coupled to a second housing that is configured to be detachably mounted to a crank assembly. The second housing is a separate member from the first housing. The first electrical connection member is configured to electrically connect the wireless communicator and the first sensor circuit.

Abstract: A method of manufacturing a cable with resin molded body, wherein the cable with resin molded body includes a cable and a resin molded body formed by resin molding, wherein the resin molded body includes a main body to cover the tip portion of the cable and a flange integrally molded with the main body, and wherein the flange includes a bolt hole through which a bolt is inserted so as to fix the flange to the attachment object. The method includes molding the resin molded body by injecting a resin into a mold, the mold including a main body-molding portion for molding the main body, a flange-molding portion for molding the flange and a first resin inlet formed behind the flange-molding portion in relation to the main body-molding portion, and injecting the resin through the first resin inlet into the mold during the molding of the resin molded body.

Abstract: A magnetic encoder including an object to be detected, a casing opposite to the object, a magnet and a magnetic sensor accommodated in the casing is provided. The casing of the magnetic encoder has an opposite wall opposite to the object. The opposite wall has a thickened portion and a thin portion integrally formed with the thickened portion. The thin portion has a smaller thickness than the thickened portion. The magnetic sensor is situated at the thin portion.

Abstract: The present specification provides a method, apparatus and system for sensing a signal with automatic adjustments for changing signal levels. A novel fractional peak discriminator circuit is provided which can be incorporated into a system for measuring periodic signals from moving elements. The circuit can be used regardless of whether the periodic signals are detected using optics, magnetic detector or other methods.

Abstract: A rotation angle detecting unit includes an IC package having a magnetism detecting element, a sealing body, and leads; and a covering member having a fixing part and a supporting part, which are integrally formed from resin. The element outputs a signal according to change of a magnetic field generated upon rotation of a magnetism generating device attached to a detection object. The sealing body covers the element. The leads are connected to the element, and project from the sealing body. The fixing part is fixed to a supporting body so that the covering member is attached to the supporting body. The supporting part supports the package such that the element can output the signal. The package is press-fitted into the supporting part after its formation, so that the package is supported by the supporting part with a predetermined pressure applied to part of an outer wall of the sealing body.

Abstract: A magnetic field sensor and a method used therein provide an output signal in angle units representative of an angle of rotation of a target of and also an output signal in speed units representative of a speed of rotation of the target object. A power control circuit can cycle a magnetic field sensor on and off in accordance with a sensed rotation speed of the object.

Abstract: The invention relates to downhole motors for rotating drill bits. The downhole motors may comprise stators, turbines or the like. The drilling motor may comprise a drilling apparatus comprising a drill bit connected to a rotor rotatably housed within a stator (or a turbine rotor in a housing), the rotor comprising at least one magnetic field source or magnetic field detector, and the stator comprising at least one magnetic field source if the rotor comprises a magnetic field detector or comprising at least one magnetic field detector if the rotor comprises a magnetic field source, thereby allowing the rotation speed of the rotor relative to the stator to be measured.

Abstract: A rotation angle detection device includes: a detection portion that detects detection angle that univocally corresponds to rotation angle of a rotating body which is within a predetermined range, wherein the detection angle linearly increases from a minimum value to a maximum value as the rotation angle increases within a unit range, and the detection angle changes from the maximum value to the minimum value or from the minimum value to the maximum value at a boundary between unit ranges that are adjacent to each other; and a correction portion that corrects the detection angle so that the detection angle detected in the predetermined range has linear characteristics, if the boundary between the unit ranges is contained in the predetermined range.

Abstract: A control system for use in safety critical human/machine control interfaces is described, more particularly a joystick type control system and particularly a joystick type control system utilizing magnetic positional sensing. The control system provides a control input device having a movable magnet, a pole-piece frame arrangement positioned about the magnet, at least three magnetic flux sensors being positioned in said pole-piece frame arrangement and a monitoring arrangement for monitoring the output signal of each of said at least three sensors.

Abstract: A method of processing signals in a rotary encoder of the kind which comprises at least one annular track of encoding regions arranged as an alternating pattern of first encoding regions and second encoding regions. The encoder including first and second detectors, each of which is arranged to produce a first alternating output signal as the track of encoding regions rotates about its axis past the detector. The detector identifying a usable pair of transitions and a rejectable pair of transitions and utilizing the pairs of transitions to produce a compensated position measurement for the rotary encoder.

Abstract: A rotation angle detector for detecting a rotation angle of a detectable rotation body, comprises: a primary rotation body to be attached to the detectable rotation body and to rotate as integral with the detectable rotation body; a secondary rotation body to rotate as a predetermined rotation ratio for the primary rotation body; a primary rotation detection mechanism to output a signal to be varied periodically as corresponding to a rotation of the primary rotation body; a secondary rotation detection mechanism to output a signal to be varied periodically as corresponding to a rotation of the secondary rotation body; a signal processing unit to calculate the rotation angles of the primary and the secondary rotation bodies using the signals that the primary and the secondary rotation detection mechanisms output; and an operation processing unit to calculate the rotation angle of the detectable rotation body.

Abstract: An angular position sensor and method that relies on a stationary circular array of Hall sensors and a rotatable circular array of magnets arranged about a common axis. A periodic and simultaneous reading of all of the Hall sensor outputs is used to determine angular velocity.

Abstract: A rotation sensor includes a detecting portion, a rotational state determining portion and a pulse generating portion. The detecting portion detects a rotation of a rotational member and outputs a detection signal. The rotational state determining portion determines a rotational state of the rotational member on the basis of the detection signal in a predetermined period. The pulse generating portion generates and outputs a first pulse and a second pulse, of which waveforms differ from each other, in response to a rotational direction of the rotational member after the predetermined period. The pulse generating portion further generates and outputs a third pulse regardless of the rotational state of the rotational member in the predetermined period.

Abstract: An example cycle meter adjusting device includes a circuit configured to provide voltage pulses and an adjustable potentiometer configured to vary the frequency of the voltage pulses provided by the circuit. A coupling interface is configured to selectively communicate the voltage pulses provided by the circuit to a cycle meter having a display. The voltage pulses adjust a number of cycles shown on the display. Another example cycle meter adjuster includes a circuit configured to provide voltage pulses. A controller is configured to selectively adjust a frequency of the voltage pulses. A connection interface is configured to communicate the voltage pulses to a cycle meter.

Abstract: A bicycle frame having a cavity constructed to receive a sensor device. The cavity has a shape and a contour that generally matches a shape and a contour of the sensor device. Such a configuration maintains the aerodynamic contour of the frame when the sensor device is positioned in the cavity. An optional plug occupies the cavity when the sensor device is not positioned therein. Preferably, the sensor device is constructed to wirelessly communicate bicycle operation information to a receiver that is remotely located relative to the sensor device. More preferably, the cavity is formed in a fork of the bicycle and the sensor device is configured to monitor operation of a front wheel and wirelessly communicate the operation information to the remote receiver.

Abstract: Device for measuring speed of a cycle having a frame, at least one wheel, a fastening axle about which the wheel is adapted to rotate, and a nut adapted to be threaded upon a threaded portion of the axle. The device includes a mechanism for detecting the rotation of the wheel, the device including a fixed sensor mounted on a portion of the cycle frame, adapted to detect the passing of an associated movable sensor element fixed for movement to the wheel, as well as a signal processor for processing the signal generated by the fixed sensor. At least one of, or both, the fixed sensor and the signal processor are housed in a casing fixed to the nut of the fastening axle for the wheel. The casing is fixed to an arm extending radially from the nut.

Abstract: An apparatus is disclosed for measuring a variable angular position of a movable part. The apparatus comprises at least two resonators formed by coupled slow-wave structures, and at least two movable targets having electrodynamic profiles, the targets also having a variable angular position. The angular position of the target is representative of the angular position of the movable part. An electromagnetic field is excited in the resonators at a frequency at which electromagnetic parameters of the resonators depend upon the position of the targets. A change in the angular position of the targets therefore causes a change in electrodynamic parameters of the resonators. The change in the electrodynamic parameters of the resonators is converted into a reading, such as an output voltage, which is indicative of the measured angular position.

Abstract: Device for measuring speed of a cycle having a frame, at least one wheel, a fastening axle about which the wheel is adapted to rotate, and a nut adapted to be threaded upon a threaded portion of the axle. The device includes a mechanism for detecting the rotation of the wheel, the device including a fixed sensor mounted on a portion of the cycle frame, adapted to detect the passing of an associated movable sensor element fixed for movement to the wheel, as well as a signal processor for processing the signal generated by the fixed sensor. At least one of, or both, the fixed sensor and the signal processor are housed in a casing fixed to the nut of the fastening axle for the wheel. The casing is fixed to an arm extending radially from the nut.

Abstract: A bicycle signal output device comprises a magnet structured to be mounted to one of a first part and a moving part of a bicycle, a coil structured to be mounted to the other one of the first part and the moving part of the bicycle, and a signal generating unit that operates using electrical power generated by the coil in response to relative motion between the magnet and the coil.

Abstract: A tachometer circuit includes a flutter reduction circuit and a tachometer. The tachometer circuit cancels pointer flutter in the tachometer without adversely affecting pointer response.

Abstract: An image forming device includes a device frame and a photoconductive drum. The device frame includes a driving device, a driving gear that transmits a driving force from the driving device, and an urging member that supports the driving gear in a manner capable of moving along a moving direction of a photoconductive drum and urges the driving gear in an opposite direction from a direction in which the photoconductive drum is inserted. The photoconductive drum is inserted in the device frame and includes a driven gear to be engaged with the driving gear.

Abstract: In a method for detecting rotational speed of an internal combustion engine (1), a sector wheel (4) which is driven by the internal combustion engine (1) is scanned, the run of a specific segment of the sector wheel is detected, the duration of said segment-run is measured and a rotational speed value is determined therefrom, the duration of the run a specific segment is re-measured, a relative variation between two consecutive segment-runs is determined and the rotational speed value is determined therefrom.

Abstract: A method for determining the position of an element driven along a travel segment by a shaft of a motor includes counting current ripples detected in an armature current signal of the motor as the motor shaft rotates to drive the element. A first time interval between when the motor is turned on with power being supplied to the motor and when the first current ripple is detected is determined. A second time interval between when the last current ripple is detected after the motor has been turned off with the power supplied to the motor being interrupted and when the motor shaft stops rotating is determined. First and second current ripple components corresponding to the first and time intervals, respectively, are estimated. The position of the element along the travel segment is determined based on the counted current ripples and the estimated first and second current ripple components.

Abstract: A self-compensating control circuit for use with a magneto-resistive sensor. The control circuit includes a first stage amplification and offset function that removes a DC component from the input signal and maximizes an AC component of the input signal within the dynamic range of the control circuit. Subsequent stages remove the remaining DC component, if any, and provide suitable additional amplification. A comparator provides a digital output based on the processed input signal and a threshold signal.

Abstract: A method and apparatus is disclosed for monitoring an angular displacement, such as angle position and the direction of displacement. The method and apparatus includes at least one resonator placed in proximity to a electrodynamic profile and exciting within said resonator an alternating electromagnetic field. The electromagnetic field should be at a frequency at which the electromagnetic field contacts the electrodynamic profile and then variations of the electromagnetic field parameters are measured for the resonator caused by rotating the electrodynamic profile. Excitation of the resonator is by an electromagnetic field in the form of at least one slowed electromagnetic wave having a suitable energy distribution of the electric and magnetic fields for measuring the electromagnetic field parameters.

Abstract: An after-change supply prevention unit prevents a cross coil from being supplied with a driving pulse signal with a duty ratio corresponding to a deflection angle calculated based on a period of a running pulse in a duration in which a period range judging unit judges that the period of the running pulse generated with the running of a vehicle is not in a predetermined range after the input state of the running pulse is shifted from the input state at the stoppage of the vehicle to the input state in running of the vehicle. While the supply of the driving pulse signal is prevented, a driving pulse signal with a duty ratio corresponding to a deflection angle calculated based on the period of the running pulse at the stoppage of the vehicle is supplied to the cross coil.

Abstract: An instrument display method and system for use in a passenger vehicle has a number of advantageous features including particularly novel, compact, inexpensive and inherently stable electric motors. A first motor includes a rotor assembly having a shaft and a cylindrical magnet which is positioned about a stator assembly to rotate thereabout. The shaft extends through a stator of the stator assembly, a vacuum fluorescent display (VFD), and an indicia bearing layer. A mask such as a needle pointer is secured to the shaft of the rotor assembly at the indicia bearing layer to convey the value of instrument data to the passenger. A light emitting panel receives light from the VFD and transmits the light to other positions along the display system where other substantially identical electric motors move their needle pointers to likewise convey additional data to the passenger. The first motor is surface mounted directly on the back of the VFD which has electrical conductors formed therein.

Abstract: A method for measuring rotational speed in which a plurality of signal sources disposed along the periphery of a rotating system is monitored by a sensor, and the signals generated by the sensor are added by a counter to form a speed signal sum N. An associated time reference value A.sub.N is determined for each speed signal sum N, and the speed signal sum N and the time reference value A.sub.N for each signal source are saved in pairs in a storage medium. To determine the rotational speed, the time reference value A.sub.N-M which had been saved exactly one revolution before along with the speed signal sum N-M is then retrieved from the storage medium by a processor, which determines the difference of the time reference values A.sub.N and A.sub.N-M (the revolution time for one revolution of the rotating system), and then determines the reciprocal value of the revolution time, which represents the speed.

Abstract: A method of manufacturing a rotation sensor can effectively prevent a sensor element from moving during a resin molding process for forming a resin portion that covers the sensor element to provide excellent waterproofness and airtightness. During a first resin injection step, an end of a bobbin of the sensor element is fixed or held in place by a slide core. Thereafter the slide core is extracted and resin is again injected in a second injection step into a vacated portion that is formed by extraction of the slide core. In the finished rotation sensor, the resin completely surrounds and encloses the bobbin, except at an exposed end of a magnetic pole piece. A metal mounting bracket is embedded in the resin at a spacing away from the bobbin. The bobbin has a positioning cavity to receive the slide core during the molding. The resin covering an upper part of the bobbin is at least four times as thick as the resin covering the coil of the sensor element.

Abstract: A method and system for driving an air core gauge whereby pointer resolution of an air core gauge is improved across a full range of motion. The method including the steps of generating a first gauge control signal responsive to a signal, the first gauge control signal having a first duty cycle corresponding to a first pointer position; generating a second gauge control signal responsive to the signal, the second gauge control signal having a second duty cycle corresponding to a second pointer position; and modulating between the first gauge control signal and the second gauge control signal alternating drive periods to drive the gauge pointer to display an average pointer position.

Abstract: An apparatus includes a rotatably mounted magnetic rotor, a first coil mounted in proximity of the magnetic rotor, the first coil mounted such that, if the coil is flowing with electric current, the magnetic rotor is within immediate proximity of at least part of a magnetic field created by the coil. The apparatus includes a second coil mounted in proximity of the magnetic rotor, the second coil mounted such that, if the coil is flowing with electric current, the magnetic rotor is within immediate proximity of at least part of a magnetic field created by the coil. A current source is coupled to the first coil, for generating an AC signal and applying the AC signal across the first coil whereby an AC output signal develops across the second coil, the AC output signal having a magnitude that varies in relation to the rotational position of the rotor. A measuring circuit detects the AC output signal and develops therefrom a measure of the position of the rotor.

Abstract: There is disclosed a meter driving device which can perform a smooth indication through a simple process in response to an input pulse even if the frequency of the input pulse is relatively low.An edge detector generates a one-shot pulse each time the edge of an input pulse is detected by the edge detector. CPU performs a digital filtering process to the one-shot pulse in response to a start signal having a constant update cycle that is provided from a timer. Thus, the high-frequency components are removed from the one-shot pulse so that a DC component is taken out to provide an angular shift .theta. of an indicating arm corresponding to the frequency of the input pulse. This DC component is used to move the indicating arm through a indicator drive device.

Abstract: A speed measuring device for use with shallow draft jet pump propelled boats includes a magnetized paddle wheel with diametrically opposed paddles having similar charges and adjacent paddles having opposite charges which is mounted in a housing adjacent a "hall-effect" device which translates the rate of rotation of the paddle wheel into a speed measurement reading due to the changes in the frequency of changes in the electrical field produced by rotation. The present invention is different from all other speed measuring devices in that the paddles do not protrude beyond the outer surface of the hull of the watercraft and therefore cannot become damaged by sand, rocks, or other floating debris. The invention includes a substantially flat base plate with a progressive recess on the underside thereof. This progressive recess carries water to a cavity or housing within which the paddle wheel is rotatably mounted.

Abstract: A meter driving system measures a period of input signals, and operates meters based on the measured period data. When no period data arrive in a preset period of time after the last period data, the lapsed time is treated as the period data so as to renew the meter indication. The meter driving system is very responsive to a signal whose frequency is gradually decreased, thereby giving the indication with little delay.

Abstract: A pulse-width modulation system provides means for controlling dual-coil, air-core gauges at a various rates over 360 degrees. The system moves a dial needle from one octant of the gauge to the next in response to coded data representing measurands by holding one coil at 100% duty cycle while applying a PWM of a varying duty signal to the other coil. When the magnitude of the measurand dictates that the needle should move into another octant of the dial, the PWM signal and the 100% duty cycle signal are interchanged between the coils in a manner permitting the needle to move to other octants of the dial. The system includes a variable PWM count clock that permits selecting at least PWM rates and periods for forming PWM duty cycles ranging from 0% to 100%.

Abstract: A meter driving system receives pulse signals from a sensor, counting frequencies or periods of the input signals. The counted results are weight-averaged to determine an output value and a value to be indicated. In a weight-averaging process, a weight is varied in response to the frequencies of the input signal. Thus, the meter can give a precise indication regardless of varying input frequencies.

Abstract: An apparatus for driving a gauge having coils in quadrature to generate a resultant magnetic field in accordance with currents applied thereto and having a pointer angularly swept by the field, the apparatus having a memory to store a first data defining a relationship between a first level, indicative of the current applied to one of the coils, and an angle of the pointer. The first level has a continous waveform varying in isoceles trapezoid form over an angle range of 0.degree. to 180.degree.. The first data varies symmetrically with the isoceles trapezoid wave at the 180.degree. pointer angle over an angle range of 180.degree. to 360.degree.. The memory is arranged to store second data defining a relationship between a second level indicative of the current applied to the other coil and the pointer angle. The second level has a continuous waveform phase shifted by 90.degree. from the continuous waveform of the first data.

Abstract: A method of producing an input variable for a cross-coil indicating instrument from a measurement signal is disclosed in which the frequency of the measurement signal is converted into a frequency-proportional input current for the cross-coil indicating instrument (11). Furthermore, a circuit is disclosed in which an input terminal for the measurement signal is connected to a period measuring device (3, 4, 5) the output of which is connected to a divider (6). The output of the divider feeds a control variable which is proportional to the frequency of the measurement signal (f.sub.M) to an input (13) of a processing circuit (8, 10). The known method and the known circuit have the disadvantage that, in case of a low frequency of the measurement signal, a jerky movement of the pointer of the indicating instrument (11) can be observed.

Abstract: An apparatus for tranmitting signals that can be broken down into at least one AC voltage component between a rotor and a stator from a sender unit to a receiver unit, with the help of annular coils, the coil windings of which form components of the sender or receiver unit, and which are arranged coaxially to the axis of rotation of the rotor and inductively coupled is to be developed so as to generate measured values that are associated with the rotational speed.

Abstract: A meter driving device for indicating angular positions corresponding to input values. The device includes a memory for storing previously given input values, angular directions corresponding to the input values, and coefficients representative of the grades of change in angular direction depending on the change between adjacent two input values, as parameters. Based on these parameters and the frequency of input pulse signal giving the input values, the angular direction corresponding thereto is calculated. The angular direction signal receives PWM process and then supplies to a pair of crossed exciting coils via a driver. During a predetermined time period from the turning ON and OFF of the power source, the transference of the angular direction signals to the driver is shut out by logic gates, thereby inhibiting malfunctional meter indication.

Abstract: A cross coil type instrument includes a plurality of coils cross-arranged around a movable permanent magnet, a needle fastened to the movable permanent magnet through a shaft projecting from the movable permanent magnet and penetrating the coils, a reset-to-zero permanent magnet arranged in the vicinity of the movable permanent magnet, and a stopper so as to make contact with the needle at a reference indication position when the movable permanent magnet is driven only by the reset-to-zero permanent magnet.

Abstract: A drive apparatus for a cross-coil type meter has cross-coils formed of a first and a second coil disposed intersecting at the center thereof. A magnet rotor is disposed in a magnetic field set up by the cross coils, and a measurement is represented in terms of a rotational angle of the magnet rotor. The drive apparatus comprises a first supply means for supplying the first coil with a first square wave current having a duty cycle of a% in accordance with the measurement; a second supply means for supplying the second coil with a second square wave current having a duty cycle of (100-a)% complementary to the first square wave current; and a polarity setting means for setting in accordance with the measurement polarities of the first square wave current and the second square wave current.

Abstract: An air-core gauge comprising two coils in quadrature has a driving system with switches on a junction terminal and end terminals of the two coils, and a drive circuit controlling the switches so that each terminal is selectively at either of two signal levels, with one terminal being connected alternately to the two signal levels with variable duty cycle depending upon the angle through which the pointer of the gauge is to be turned. For any given angle, one terminal is held at one level, another at the other level and the third is alternated between the two levels with appropriate duty cycle. Any angle of pointer deflection from 0.degree.-360.degree. can be achieved with just the two voltage levels and calculating the duty cycle from an appropriate function of tangent values of angles in the range 0.degree. to 45.degree..