US3177423A - Trigonometric store - Google Patents

Trigonometric store Download PDF

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Publication number
US3177423A
US3177423A US52992A US5299260A US3177423A US 3177423 A US3177423 A US 3177423A US 52992 A US52992 A US 52992A US 5299260 A US5299260 A US 5299260A US 3177423 A US3177423 A US 3177423A
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US
United States
Prior art keywords
winding
voltage
sine
taps
cosine
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Expired - Lifetime
Application number
US52992A
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English (en)
Inventor
Herbert M Fuldner
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Milacron Inc
Original Assignee
Cincinnati Milling Machine Co
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Priority to NL267022D priority Critical patent/NL267022A/xx
Application filed by Cincinnati Milling Machine Co filed Critical Cincinnati Milling Machine Co
Priority to US52992A priority patent/US3177423A/en
Priority to GB23197/61A priority patent/GB913977A/en
Application granted granted Critical
Publication of US3177423A publication Critical patent/US3177423A/en
Anticipated expiration legal-status Critical
Expired - Lifetime legal-status Critical Current

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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
    • G05D3/00—Control of position or direction
    • G05D3/12—Control of position or direction using feedback
    • G05D3/14—Control of position or direction using feedback using an analogue comparing device
    • G05D3/1472—Control of position or direction using feedback using an analogue comparing device with potentiometer
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B19/00—Programme-control systems
    • G05B19/02—Programme-control systems electric
    • G05B19/18—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form
    • G05B19/408—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form characterised by data handling or data format, e.g. reading, buffering or conversion of data
    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
    • H03M1/00—Analogue/digital conversion; Digital/analogue conversion
    • H03M1/12—Analogue/digital converters
    • H03M1/48—Servo-type converters
    • H03M1/485—Servo-type converters for position encoding, e.g. using resolvers or synchros

Definitions

  • This invention relates to a converter for transforming digital information into analog voltages which are representative of the desired positions to be assumed by the numerical controlled element of a machine tool. More particularly, the invention relates to a circuit for converting digital information into angular data corresponding to the rotation of a shaft, the converted data being in the form of quadrature voltages which are proportional to the sine and cosine of the angle of rotation.
  • Another object of the invention is to provide a trigonometric store having a tapped sine-cosine transformer of relatively few turns while'providing a high degree of accuracy in the synthesis of the sine and cosine voltages.
  • Another object of the invention is to provide a trigonometric store which utilizes split linear interpolation for the subdivision of the angles represented by the sine and cosine Voltages derived from t aps on a sine-cosine transformen
  • Another object of the invention is to proivde a digitalto-angular data converter which has all the advantages of a system employing 36 segments while affording the accuracy of a system employing 18 segments.
  • FIG. 1 is a diagram of the trigonometric store as incorporated in a servo system.
  • FIG. 2 is a diagram of the switching circuit used to I change'the connections from one pair of switch banks to another.
  • an AC. reference voltage is applied to terminals 10 and 11 which are connected by conductors to the end terminals 12 and 13 of a tapped autotransformer 14. Since, in the present apparatus, the autotransformer is required to serve as a low-impedance, precision voltage divider, it is preferably a toroidal type transformer designed for minimum flux leakage between turns.
  • the transformer is wound on an annular core 15 and is provided with a grounded center tap and eight intermediate taps 17, which are appropriately spaced to provide voltages which are proportional to the sine and cosine of 0, 18, 36, 54, 72, and 90 on either side of the center tap, the sine of 0 being equal to the cosine of 90, the sine of 18 being equal to the cosine of 72, the sine of 36 being equal to thecosine of 54, etc.
  • the primary winding 22 is excited from a winding 24 wound on the core 15 of the autotransformer.
  • the transformer 14 is provided with 252 turns, i.e., 126 turns on either side of the center tap 100, and the taps for sine 18, 36, 54 and 72 are tapped at 39, 74, 102 and turns respectively, on either side of the center tap.
  • the primary winding of transformer 20 is provided with 48 turns and the secondary windings connected to terminals E, D, C, B have 3, +3, -3 and -8 turns, respectively, as do also the secondary windings connected to terminals G, H, I, and K, respectively.
  • the signs as used above indicate that the secondary windings are poled to subtract their voltages from those provided by the transformer taps, while the sign indicates that this winding'is poled to add its voltage to that provided by the tap.
  • the winding 24 which excites the primary winding of transformer 20 is comprised of a single turn wound on the core 15. It will be appreciated that multiples of the given numbers of turns will provide the same voltages at the terminals AL but with a higher impedance.
  • terminals 10 and 11 when the terminals 10 and 11 are energized from a source of reference voltage, terminals 25, marked A-L will be supplied with voltages which are proportional to the plus and minus values of the sine and cosine of 0, 18, 36, 54 72 and 90.
  • each 36 of displacement of the unit will equal .01 inch movement of the slide.
  • 36 divisions of the transformer 14, such as between terminals F and D, D and B, etc. Will represent .01 inch of slide movement. Since, in the present ap enemas 1 In other words, the voltage between taps on the winding 29 is ten times as great as the voltage between taps on the winding 30. This is for the purpose of enabling the voltage between adjacent terminals A, B, C, D, etc.
  • the means for connecting the taps in the proper order to provide the desired resolution of voltages comprises three multi-bank switches 138, 258 and 3S8. These may be manually settable selector switches or, alternatively they may take the form of step ping switches controlled from a punched tape and tape reader in a well-known manner.
  • the switches are provided with multiple banks of contacts which are designated by letter suffixes such as C, B, E, etc.
  • the switch bank llSS-C has ten contacts numbered 9, inclusive, which contacts are connected to the terminals in the order indicated by the letter designations beside the contacts, namely, F, D, B, B, D, F, H, K, K, H. It will be noted that these are alternate terminals. in other'words, the wiper of bank lSS-C advances in 36 bites.
  • Bank D of switch 158 has its ten contacts 0-9 connect ed to the terminals 25 as indicated by the letter designation beside the contacts, namely, E, C, A, C, E,G, J, L, J, and G. These too it will be noted are alternate terminals on the transformer. However these terminals lie between the terminals to which the contacts of bank 1SS-C are connected, i.e., the order of connection has been advanced 18. terminals'D, B, B, D, F, H, K, K, H and B. These are the same terminals to which the contacts of banks lSS-C are connected but the order of connection has been advanced 36.
  • the approximate value of the cosine of 195.12" is derived in a similar fashion from the sine-cosine voltages 7 provided at the terminals A-L.
  • a wire 9 connected to the wiper of bank D will be supplied with a potential proportional to the sine of 18 and a wire 95 connected to the wiper of bank B will be supplied with a potential proportional to the sine of 36.
  • the wires 92', 9 2- and 95 are connected to a pair of wires '74 and 79 through the contacts of a I switching relay ZCR.
  • the taps of winding 29 are connected by wires 74 -725 to the contacts 0-9' of a switch bank LESS-D. As indicated on the drawing, wire 74 is connected to the contacts 0 and 5, wire '75 is connected to contacts 1 and 6, etc. '1 .e taps of winding 30 are connected to the contacts 0-9 of a switch bank dSS-C, and a wire 91 connects the wiper of this bank with the wiper of bank ZSS-D.
  • An output con ductor $1 is connected to the end of winding 3d which is connected to the 0 contacts of switch bank SSS-C and provides anoutput voltage which, referenced to ground,
  • a voltage 2 proportional to the sine of 18 will be supplied to the-up provided a second toroidal transformer 33 which may be identical to the trmsforrner 28 and, like this transformer, has a pair of linearly tapped windings Maud 35 wound on an annular core .36.
  • the winding 34 is divided into five sections of twenty turns each and the winding '35 is divided into ten sections of two turns each so that the voltage between taps on winding Ed is ten times as great i as the, voltage between taps on winding 35.
  • the data input meansfor the cosine system includes additional banks of contacts on the switches 13S, 23S and 388.
  • banks F, G, and H of switch 183 are connected to terminals A-L according to the same scheme as used for the sine functions but displaced to provide voltages which are proportional to the cosine of the angle.
  • wires 1% and 104 are connected to wires )6 and 1.02, which, in turn, are connected to the upper and lower ends of the winding 34.
  • a voltage proportional to the cosine value of the first 18 segment of a 36 bite wiil be impressed across the winding 34.
  • the five taps of this winding are connected by wires 96-101 to the contacts 09'of a switch bank ZSS- E, wire 96 being connected to contacts 0 and 5.
  • wire 97 being connected to contacts 1 and 6, etc.
  • the taps of winding 35 are connected to the contacts 09 of a switch bank ESS-D and a wire 116 connects the wiper of this bank with the wiper of bank ZSS-E.
  • An output conductor 1536 is connected to the 0 end of winding 35 and true sine and cosine values of the 3.6 and 36 angular 7 increments which correspond to the .001 inch and .0001 inch movements of the slide.
  • the sine and cosine voltages are applied to the guadrature windings 70, 71 of a resolver 72 which is also provided with a rotor winding 73.
  • the two leads 84 and 85 from this winding are connected to a pair of input terminals on a servo-amplifier 86.
  • the output of the servoamplifier is connected by leads 87 and 88 to the control winding 89 of a two-phase electric servomotor 90.
  • This motor also is provided with a reference voltage winding 91 and runs in one direction or the other depending on the phase of the voltage supplied to the winding 89 in a well-known manner.
  • the armature of the motor is drivingly connected, as indicated by the dashed line 107, to the slide 93 which is to be positioned in accordance with the input data supplied to the trigonometric store.
  • the rotor of the resolver is also arranged to be driven by the slide through an angle of 36 for each .01 inch movement of the slide as is indicated by the dashed line 108.
  • a trigonometric store for a positioning system comprising a function generating transformer including a plurality of voltage taps selected to provide a series of voltages proportional to the values of the sine and cosine of angles spaced at 18 intervals, an interpolating transformer having two linearly tapped windings each capable of dividing a voltage impressed thereacross into equal voltage increments, one of said windings having ten times as many turns between taps as the other winding, switch means for connecting a selected pair of adjacent taps on said function generating transformeracross said one winding, and additional switch means for connecting a selected tap on said one winding with a selected tap on said other winding to thereby cause a voltage to be impressed on one end of said other winding which is approximately proportional to the value of the sine or cosine of the angle represented by the setting of said switch means.
  • a trigonometric store comprising a function generating transformer having a plurality of voltage taps selected to provide a series of voltages approximately proportional to the value of the sine and cosine of a plurality of equally spaced angles, an injection transformer having a single primary winding and a plurality of secondary windings each having one end connected to a tap on said function generating transformer, a winding on said function generating transformer for energizing said primary winding, an interpolating transformer having a linearly tapped winding for dividing a voltage impressed thereacross into equal voltage increments, switch means for connecting the other ends of a selected pair of adjacent secondary windings across said linearly tapped winding, and additional switch means for selecting a voltage from any one of the taps of said linearly tapped winding to thereby provide a voltage which is approximately proportional to the value of the sine or cosine of the angle represented by the setting of said switch means.
  • a trigonometric store comprising an autotransformer of two hundred fifty-two turns with a center tap and first, second, third, and fourth taps at 39, 74, 102 and 120 turns on either side of the center tap, an injection transformer having a primary winding of forty-eight turns and first, second, and third and fourth secondary windings each having one end connected to a corresponding tap on said autotransformer and having -3, +3, -3 and -8 turns respectively, and a winding of one turn, or a multiple thereof, on said autotransformer connected to said primary Winding for energizing the same.
  • the trigonometric store of claim 3 including an interpolating transformer having a linearly tapped winding for dividing a voltage impressed thereacross into equal voltage increments, switch means for connecting the other ends of a selected pair of adjacent secondary windings across said linearly tapped winding, and additional switch means for selecting a voltage from anyone of the taps of said linearly tapped winding to thereby provide a voltage which is approximately proportional to the value of the sine or cosine of the angle represented by the setting of said switch means.
  • a trigonometric store comprising a function generating transformer having a plurality of voltage taps selected to provide -a series of voltages proportional to the values of the sine and cosine of angles spaced at 18 intervals from 0 to and from 0 to 90, an interpolating transformer having a linearly tapped winding capable of dividing a voltage impressed thereacross into equal voltage increments, switch means for selectively connecting either of two pairs of three adjacent taps on said function generating transformer across said linearly tapped winding, additional switch means cooperating with the taps on said linearly tapped winding, and means controlled by said additional switch means for causing said first mentioned switch means to disconnect one of said pairs of taps from across said linearly tapped winding and to connect the other of said pairs of taps thereacross.
  • said first mentioned switch means includes a switch having at least three banks of contacts with successive contacts on each of the three banks connected to alternate taps on said function generating transformer and with the corresponding contacts of each bank connected to taps spaced 18 apart.

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  • Engineering & Computer Science (AREA)
  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Automation & Control Theory (AREA)
  • Human Computer Interaction (AREA)
  • Manufacturing & Machinery (AREA)
  • Theoretical Computer Science (AREA)
  • Ac-Ac Conversion (AREA)
  • Control Of Electrical Variables (AREA)
US52992A 1960-08-30 1960-08-30 Trigonometric store Expired - Lifetime US3177423A (en)

Priority Applications (3)

Application Number Priority Date Filing Date Title
NL267022D NL267022A (Direct) 1960-08-30
US52992A US3177423A (en) 1960-08-30 1960-08-30 Trigonometric store
GB23197/61A GB913977A (en) 1960-08-30 1961-06-27 Trigonometric store for converting digital entered angles into analog voltages

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
US52992A US3177423A (en) 1960-08-30 1960-08-30 Trigonometric store

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US3177423A true US3177423A (en) 1965-04-06

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GB (1) GB913977A (Direct)
NL (1) NL267022A (Direct)

Cited By (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US3493735A (en) * 1964-03-20 1970-02-03 North Atlantic Industries Computer circuits for processing trigonometric data
US3849774A (en) * 1972-09-14 1974-11-19 Astrosyst Inc Analog-to-digital converter employing an electromagnetic resolver
US3870938A (en) * 1971-04-20 1975-03-11 Elliott Brothers London Ltd Waveform generator and phase shifter
US3898568A (en) * 1972-09-14 1975-08-05 Astrosyst Inc Signal synthesizer employing an autotransformer having a tapped coil
US11736047B2 (en) * 2019-09-25 2023-08-22 Allegro Microsystems, Llc BLDC motor controller/driver

Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US1667752A (en) * 1924-08-27 1928-05-01 Percy H Thomas Regulating means for systems of electrical distribution
US2200979A (en) * 1939-06-22 1940-05-14 Gen Electric Transformer tap-changing system
US2201642A (en) * 1936-12-18 1940-05-21 Siemens Ag Inductive regulator for coarse and fine regulation
US2849668A (en) * 1955-10-14 1958-08-26 Inductosyn Corp Automatic machine control
US3042307A (en) * 1957-04-30 1962-07-03 Emi Ltd Trigonometric function generators

Patent Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US1667752A (en) * 1924-08-27 1928-05-01 Percy H Thomas Regulating means for systems of electrical distribution
US2201642A (en) * 1936-12-18 1940-05-21 Siemens Ag Inductive regulator for coarse and fine regulation
US2200979A (en) * 1939-06-22 1940-05-14 Gen Electric Transformer tap-changing system
US2849668A (en) * 1955-10-14 1958-08-26 Inductosyn Corp Automatic machine control
US3042307A (en) * 1957-04-30 1962-07-03 Emi Ltd Trigonometric function generators

Cited By (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US3493735A (en) * 1964-03-20 1970-02-03 North Atlantic Industries Computer circuits for processing trigonometric data
US3870938A (en) * 1971-04-20 1975-03-11 Elliott Brothers London Ltd Waveform generator and phase shifter
US3849774A (en) * 1972-09-14 1974-11-19 Astrosyst Inc Analog-to-digital converter employing an electromagnetic resolver
US3898568A (en) * 1972-09-14 1975-08-05 Astrosyst Inc Signal synthesizer employing an autotransformer having a tapped coil
US11736047B2 (en) * 2019-09-25 2023-08-22 Allegro Microsystems, Llc BLDC motor controller/driver

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Publication number Publication date
NL267022A (Direct) 1900-01-01
GB913977A (en) 1962-12-28

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