Method and apparatus for determining velocity of a moving member

• US 4,100,599 A
• Filed: 12/22/1976
• Issued: 07/11/1978
• Est. Priority Date: 12/22/1976
• Status: Expired due to Term

• Current Assignee: NCR Corporation
• Original Assignee: NCR Corporation
• Inventors: Nally, Robert B.
• Primary Examiner(s): Wise, Edward J.
• Application Number:
  US05/753,044
• Time in Patent Office: 566 Days
• Field of Search: 235/151.32, 356/28, 356/27, 324/160, 324/175, 364/565
• US Class Current: 702/149
• CPC Class Codes: G01P 3/489 Digital circuits therefor
• CPC Class Codes: G01P 3/68 using optical means, i.e. using infrared, visible, or ultraviolet light G01P3/80 takes precedence ; by reflection of waves G01S17/58

Abstract

A method and apparatus is disclosed for determining the velocity of a document over a fixed distance of travel. Sensing means are provided for generating signals which are used in determining the value of the time the document requires to move over the fixed distance. Using terms of a Taylor series expansion of the velocity equation, a value of the velocity is determined utilizing digital elements requiring only multiplication and addition operations. The elements include a digital multiplier and accumulator together with a plurality of storage devices which utilize the value of the time together with a plurality of predetermined constants to determine and output the value of the velocity to a display which displays the velocity in numerical form.

Claims

1. A method of maximizing a computer for determining the velocity of a moving member over a predetermined distance comprising the steps of

(a) storing the value of the time required for the member to travel through said predetermined distance and the values of a plurality of constants representing the velocity and the successive derivatives of the velocity at the mean value of the time of travel through said predetermined distance in a plurality of storage units;

(b) multiplying the value of time and a first constant stored in said plurality of storage units to derive a first product;

(c) storing the value of the first product in another of said storage units;

(d) adding a second constant stored in said plurality of storage units to the first product stored in said another of said storage units to derive a first sum in said another of said storage units;

(e) multiplying the value of time and the first sum to produce a second product;

(f) storing the second product in said another of said storage units;

(g) and repeating steps (d), (e) and (f) until the last of the constants stored in said plurality of storage units has been added to the product stored in said another of said storage units to produce a sum which is the value of the velocity of the moving member.

2. The method of claim 1 which further includes the step of displaying the value of the sum upon the addition of the last constant.

3. A method of maximizing a digital processor in determining the velocity of a moving document comprising the steps of

(a) storing the value of the time required for a document to move through a predetermined distance in a first storage unit;

(b) storing a plurality of constants representing the velocity and successive derivatives of the velocity of the mean value of a preselected time of movement of the document in a second storage unit;

(c) multiplying the value of time in said first storage unit with a first constant stored in said second storage unit;

(d) storing the value of the product derived in step (c) in a third storage unit;

(e) adding a second constant stored in said second storage unit to the product stored in said third storage unit to produce a first sum in said third storage unit;

(f) multiplying the value of time stored in said first storage unit with the sum stored in said third storage unit to produce a second product;

(g) storing the second product in said third storage unit;

(h) and repeating steps (e), (f) and (g) until the last constant stored in said second storage unit is added to the product stored in said third storage unit.

4. The method of claim 3 further comprising the steps of displaying the value of the sum stored in said third storage unit upon the addition of the last constant to the product stored in said third storage unit.

8. The system of claim 3 which further includes means responsive to the generation of the value of the velocity of the moving member to display the value of the velocity.

5. A method of maximizing a digital processor in determining the velocity of a moving member comprising the steps of

(a) storing the digital value of the time required for the member to travel over a predetermined distance in a latch member;

(b) storing a plurality of digital constants representing the velocity and the successive derivatives of the velocity of the mean value of a predetermined time range in a storage unit;

(c) multiply the digital value of the time in the latch member with one of the constants stored in said storage unit;

(d) storing the result of step (c) in an accumulator;

(e) adding another of said constants to the accumulator

(f) storing the digital sum of step (e) in a second latch member;

(g) multiplying the digital sum in a second latch member with the value stored in said first latch member;

(h) clearing the accumulator;

(i) repeating the steps (d) through (t) until the last constant is added to the accumulator;

(k) and displaying the digital sum found in the accumulator after step (i) has occurred.

6. The method of claim 5 further comprising the steps of

(a) decoding the digital value stored in said accumulator after the last constant has been added to the accumulator to generate a plurality of electrical signals;

(b) and operating a display in response to the generation of said electrical signals.

7. A system for generating a value of the velocity of a moving member comprising:

(a) means for generating a signal representing the time (t) of movement of the member through a predetermined distance (d);

(b) means for storing the value of time;

(c) means for storing values representing the velocity and the successive derivatives of the velocity at a preselected mean value of the time (t_m) of movement through said distance;

(d) and means for adding and multiplying the value of time and the values representing the velocity and the successive derivatives of the velocity to derive a value of the velocity of the moving member in accordance with the terms of a Taylor series expansion of the equation d/t developed using the following equation;

space="preserve" listing-type="equation">V.sup.n (t.sub.n) = [d.sup.n V(t)/dt.sup.n ]

wherein t = t_m

n = n^th derivtive.

9. The system of claim 7 in which said generating means includes

(a) means for generating a predetermined number of clock signals in response to the movement of the member through a predetermined distance;

(b) and means responsive to the generation of said clock signals for generating a signal representing the time of movement through said distance.

10. The system of claim 7 wherein said means for computing the value of the velocity operates according to the formula

11. A system for determining the velocity of a moving document comprising:

(a) sensing means positioned adjacent the path of movement of the document for generating a first and second output signal upon sensing the document, said sensing means separated by a predetermind distance (d);

(b) means for generating a plurality of clock pulses at a predetermined frequency;

(c) means responsive to said first and second output signals for counting a number of clock pulses in accordance with the generation of said first and second output signals;

(d) first storage means for storing said number of clock pulses;

(e) second storage means for storing the reciprocal of said predetermined frequency and a plurality of values representing the velocity and the successive derivatives of the velocity at a pre-selected means value of the time of movement of the document through said predetermined distance;

(f) multiplying means;

(g) adding means;

(h) and control means for operating said multiplying means to generate a product of the number of clock pulses and the reciprocal of the frequency, said control means further operating said multiplying means and said adding means for alternately multiplying the product and adding the plurality of values representing the velocity and the successive derivative of the velocity to derive the value of the velocity of the moving document in accordance with the terms of a Taylor series expansion of the equation d/t developed using the following equation;

space="preserve" listing-type="equation">V.sup.n (t.sub.n) = [d.sup.n V(t)/dt.sup.n]

where

t = t_m

n = n^th derivative.

12. The system of claim 11 includes means responsive to the generation of the value of the velocity to display said value.

13. The system of claim 11 wherein said control means operates the multiplying and adding means in accordance with the formula

14. Apparatus for determining the velocity of a moving member comprising:

(a) first storage means for storing the time of movement of the member through a predetermined distance;

(b) second storage means for storing the velocity and successive derivatives of the velocity of the member at a preselected value of time;

(c) third storage means;

(d) first control means for sequentially transferring the contents of said second storage means to said third storage means;

(e) means for multiplying the contents of said first and third storage means deriving the product of the time and the contents of said third storage means;

(f) means for adding the product derived from said multiplying means to one of said successive derivatives;

(g) and second control means for alternately operating said multiplying means and said adding means until all of the derivatives stored in said second storage means has been added to the last product derived from the operation of said multiplying means.

15. The apparatus of claim 14 which further includes display means controlled to said adding means to display the sum of the last derivative stored in said second storage means and the last product.

16. Apparatus for determining the velocity of a moving document along a predetermined path comprising:

(a) a pair of sensing means positioned adjacent said path for generating a first and second output signal upon sensing the document as it moves along said path, said sensing means separated by a predetermined width;

(b) means for generating a plurality of clock pulses at a predetermined frequency;

(c) means connected to said generating means and responsive to said first and second output signal for counting a number of clock pulses in accordance with the generating of said first and second output signals;

(d) first storage means for storing said number of clock pulses;

(e) addressable storage means for storing data representing the reciprocal of the frequency of said clock pulses, and the velocity and successive derivatives of the velocity of the document at a preselected value of time;

(f) third storage means for storing the addresses of data stored in said addressable storage means, said third storage means connected to said addressable storage means;

(g) fourth storage means connected to said addressable storage means;

(h) multiplying means for multiplying the contents of said first storage means with the contents of said fourth storage means to derive a product;

(i) adding means connected to said multiplying means and said addressable and fourth storage means to add the data representing the velocity and the successive derivatives of the velocity to the product;

(j) first control means for operating said third storage means to effect transfer of the reciprocal of the frequency to said fourth storage means and to operate said multiplying mans to derive a value of time;

(k) second control means for storing the value of time in said first storage means;

(l) third control means for operating said third storage means to effect transfer of the data in said addressable storage means to said adding means;

(m) and fourth control means for alternately operating said multiplying means and said adding means wherein the sum in said adding means is multiplied by the value of time stored in said first storage means and the data in said addressable storage means is added to the product of said multiplying means.