# Патент USA US2404294

код для вставкиJuly 16, 1946. 2,404,294 w. B. JORDAN INTEGRATOR Filed Sept. 18, 1944 m/ AHf \\ 5 M. f . à / l \\\\\\\\ f *Y /l- Inventor* William B. JoT' dan , by yv/Máîâwßq His Attorneg. Patented July 16, 1946 2,404,294 UNITED STATES PATENT OFFICE 2,404,294 IN TEGRATOR William B. Jordan, Scotia, N. Y., assigner to Gen eral Electric Company, a corporation of New York Application September 18, 1944, Serial No. 554,661 4 Claims. (Cl. 23S-61) 1 2 This invention relates to integrators, and it has for its object the provision of an improved integrator which is positive and accurate in its grator comprising a variable o1' integration input shaft I0, an integrand input shaft II, and a final integral output shaft I2. The specific ein bodiment of the invention illustrated integrates operation. More specifically, this invention contemplates with respect to time (t) the magnitude of a variable rate of change (œ), which may be the rate of change of range to a target. Thus, the the provision of a mechanical integrator which computes its integral by the trapezoídal rule; variable of integration (t) is introduced by the shaft I0, the integrand (œ) is introduced by the series of trapezoids; computing the area of each 10 shaft Il, while the final output of the integral shaft I2 is (y), (y) being related to a: and t-by trapezoid by multiplying one-half the sum of the the equation: y=lfxdt. lengths of two sides thereof by the base length; The shaft I0 operates a first reversing mecha and finally by adding the calculated areas of the that is, it mechanically computes the desired area under a curve by sub-dividing the area into a trapezoids together. nism I3; as shown, the shaft I0 is geared to In accordance with this invention, there is pro 15 drive an input gear I4 of the reverser I3 by means of a shaft I5 to which the shaft I0 is geared by vided an integrand input shaft and a variable bevel gears I6, and by a shaft I'I to which the of integration input shaft. Means are provided gear I4 is secured and which shaft is geared to for sub-dividing the total variable of integration shaft I5 by bevel gears I8. The gear I4 is in input to determine the interval of integration. And also means are provided for determining the 20 mesh with gears I9 and 2U which it rotates in opposite directions and which are mounted on product of this interval and the values of the a shaft 2I to rotate freely with reference to it. integrand introduced by the integrand input A shuttle 22, which is slidably mounted on the shaft so as to determine the integral of the shaft 2I but which is arranged to rotate it, as integrand with reference to the variable of in tegration, 25 by means of a splined connection (not shown), is arranged to be operated selectively by the two More specifically, a first reverser is provided reversely rotating gears I9 and 20; for this pur which is operated by the variable of integration pose, the shuttle is provided on its opposite ends input shaft; it periodically reverses the direction with clutch teeth 23 and 24 which are adapted of rotation of the input thereto, and thereby sub divides the total of the variable of integration 30 to mesh with sets of teeth 23a and 24a. `formed on the gears I9 and 20, respectively. The shuttle input in order to determine the interval of in is shown in its neutral position in Fig. 1, and tegration. This interval is multiplied by the when moved upwardly to cause its tooth 23 to integrand values fed in by the integrand input engage gear tooth 23a it causes the shaft 2| to shaft by a suitable multiplying mechanism in order to determine the areas of the various sub 35 rotate in one direction, and when moved down divisions. The output of the multiplier is fed to an output shaft which, because of the reversals of the reversing mechanism ,is driven first in one di rection and then in the other, and the total motion of the shaft is imparted to a final and integral 40 output shaft by means of a second reverser. This second reverser always operates the final shaft in one direction, until the integrand changes sign, so that the total movement of the shaft is the combined forward and backward movements of the multiplier output shaft. For a more complete understanding of this invention, reference should be had to the accom wardly to cause its tooth 24 to mesh with the gear teeth 24a it causes the shaft 2| to rotate in the opposite direction. The shuttle is moved to its upper and lower driving means periodically by means of a cam 25 which operates between- a pair of spaced collars 25a and 25D on the shuttle. This cam 25 is peri odically operated by the input shaft I0. This is accomplished through a Geneva gear train 26 having three stages 26a, 2Gb, and 26e. This gear train is, in effect, a revolution counter, and every time the shaft l0 turns over a predetermined number of revolutions the cam 25 is operated to move the shuttle to reverse the output of the re panying drawing in which Fig. 1 is a perspective view illustrating an integrator arranged in ac 50 verser mechanism; as shown, the output of the gear 21 of the Geneva train meshes with a gear cordance with this invention; and Fig. 2 is a diagrammatic view illustrating the principle of operation of the mechanism. Referring to the drawing, this invention has been shown in one form as applied to an inte 28 which is fixed to and drives a gear 29. The gear unit 28 and 29 rotates freely on the shaft I0. The gear 29 drives a gear 30 which in turn 55 operates the shuttle cam 25 through a shaft 3l, 2,404,294 a ¿i bevel gears 32, shaft 3f, bevel gears 34 and cam differential 63 by ring gear 6l. Differential 69 shaft In the specific embodiment of the invention illustrated where the input of the shaft is is time (t), the mechanism operates the shuttle everyT (it) seconds, and therefore, in effect, mechani cally sub-divides the total variable of integration also has an input gear 'il which is driven by shaft El 'to introduce elim; as shown, it is driven from shaft li by bevel gears l2, shaft "i3, spur gear 'M fixed to shaft ‘f3 and an idler gear lâ meshing with the gears 'El and lli. The gear ratio between shaft l i and gear ‘H is such that the rotation of the gear li measures the product ‘li-Kaz. This mi’ (t) in order to determine the interval of inte gration (ît). ' > The output of the reverser i3 is added to the input (r) of the integrand input shaft l l in a dif ferential 36. This differential, as shown, has an input gear 3l, which is driven by gear 38 attached to the shaft 2l; an input gear 39 driven by a gear ¿iii attached to the shaft il ; and a set of 15 planetary gears lli which drive the output shaft £2 of the differential, which output is the sum-` mation: t<of shaft 10) +r<of shaft 11) Another similar differential 43 subtracts the input (x) from input (t). This differential has an input gear fill- driven by the output gear-3B product is subtracted from the product 4MM-K) in the differential 6% so that the differential out put gear lâ measures 43st. It will be observed, in View of the foregoing, that the differentials ¿if and (ai, the two cam mechanisms and ff, and the two differentials and ¿it constitute a multiplier wherein the inputs thereto from the reverser i3 and the in put shaft il are multiplied so that the output becomes :the product 40st. The output ¿fait of the multiplier is fed to a shaft 'Il from gear it, which gear meshes with gear lla, fixed to the shaft 'Ví so that the motion of the shaft ‘il measures the product 496i. The shaft l? is utilized to drive the ñnal in of reverser i3 through the gear 3l; an input gear tegral output shaft l2. ¿l5 driven by the gear il@ of input shaft Il; and the reverser E3 in periodically reversing, the mo tion of the shaft ll is ñrst positive and then a planetary gear set e6 which drives the differ ential output shaft ¿il to measure the difference t-œ. The output shafts @2 and 4l of the two differ entials 36 and ¿i3 are fed into two cam mech anisms fill and ¿i9 respectively, which mechanisms generate quadratic functions of the inputs. The two mechanisms ¿i8 and i9 comprise cams 5!! and El respectively having formed therein a series of gear slots 52 and- 53 arranged in spiral paths, and with which toothed gear wheels 54 and 55 mesh respectively. The cam plate 50 has a pe ripheral gear 5t which meshes with gear El driven by shaft ¿i2 while cam 5l has a peripheral gear driven by gear 59 of shaft lll. Therefore, `the summation of t-|~5c is fed into gear cam 5&3, while the difference t-:r is fed into gear cam 5l. Because of the action of negative. It is desirable that the final output shaft if always be driven in the same direction, and that it add up the total motions of the shaft 'il in its two directions; therefore, the shaft 'Il drives `the final output shaft l2 through a second reverser TES. This reverser comprises input gears le and 88 which are driven in opposite directions by the shaft 'if-the gear l@ by means of gear 8l ñxed to the shaft il, and the gear 86 from the gear 8l through gear 32 fixed to a shaft 83, and a gear Sit also fixed to the shaft 83 and meshing with the gear 8f?, This reverser fur ther comprises a shuttle 85 with two sets of teeth 8l' and e3 which are arranged to mesh with sets of teeth 3S and 89 formed on the two input gears ‘F9 and e@ respectively~ The shuttle is splined to the shaft i2 and, therefore, when it rotates it ro In order to always keep positive the radii of tates this shaftl The position of the shuttle 85 is the two spiral paths of gear slots 52 and 53, a 45 controlled by means of a cam 9E! that operates be constant (K) is added to each input so that the tween the shuttle collars âìl and 92. The cam 90 input to the cam 50 becomes t-i-K-l-œ, while that is driven by the shaft 3i so that the reverser 'I8 to cam 5l becomes t-i-K-au It will be under operates to reverse periodically and simultane stood that this constant (K) is generated by off ously with the reversals of the reverser I3, where setting the Zero position between the outputs of by even though the output shaft l? of the mul the differentials 36 and ¿i3 and two cams 50 and tiplier moves first in one direction and then in fil respectively. the other in accordance with the product 43st, As pointed out above, the two mechanisms 43 the ñnal output shaft i2 always moves in the and itâ generate quadratic functions of their in same direction and measures the total motions puts; in the speciñc embodiment of the invention 55 of the shaft l1. illustrated, they generate the squares of their in And this ñnal output of the shaft l2 is puts; thus, the mechanism ¿i8 generates and its g/:fœdt output shaft ‘dfi measures (t-l-K-i-œ)2, and the The theory of operation of this integrator may mechanism £9 generates and its output shaft 5l be better understood by reference to Fig. 2. The measures (t+K-;c)2. These two outputs are 60 total area under the curve, which represents the subtracted in a differential Gla. equation x=î<t), is equal to the sum of 'the sub This differential lila, as shown, has an input divided areas of the trapezoids S1, S2, etc. The gear 62 driven by gear h3 fixed to shaft 60; an area of input gear Se driven by gear 65 fixed to shaft el, and a planetary gear system 66 having a that of ring ge‘ar Gl, which measures the aforemen S2=1/2(x1-}-$2)h tioned difference (t-i-K-Hw 2-(t-{-K-«x)2; this difference equals: ext-PMK or 4MM-K) . The constant K is deleted in a differential 68. and so on. Now at the instant of time tu the instantane by subtracting ¿1Km from ¿HUH-K) so that the 70 ous position of the output shaft 2l of the reverser output of the differential 68 is the product ext. i3 is -l/gh and the reverser has just thrown As shown, the differential 63 has a planetary gear system e9 which includes a ring gear 70 which meshes with output ring gear 6l of differential over to its forward position; and at the instant of time t1, the instantaneous position the out put shaft 2l is -l-l/ah and the reverser throws to te; in other’words, 4r(t-|-.K)_is introduced into 75 its reverse position and reverses its output; the .2,404,294 5 6 be calculated by this integrator using the trape zero position of the shaft 2| corresponds to the zoidal rule. It is also possible, however, to use time point exactly mid-way between to and t1 i11 it for computing integrals by Simpson’s one dicated by the vertical dotted line in Fig. 2. third rule or by other well-known mechanical When the shaft 2| is at position -1/2h, the :n input shaft I I is at its position œo, and the output 'ci quadrature formulas by an adjustment of the Zero position of the multiplier. For example, if shaft 'I'I of the multiplying mechanism is at its the shaft 2I is at position -l?gh when the .7: in position èl/zhxo. put shaft II is at its position ro, and the re Then at the end of one-half of an operating versers I3 and 'I8 have just thrown to their for _cycle of the mechanism, that is, at the end of the ward driving positions at this instant, then the time interval h=t1-îo, the position of shaft 2i integrator will calculate the integral fœdt based is +1/„>h, that of shaft II is an, and that of shaft on Simpson’s one-third rule. » 'I1 is -i-l/ghsci. While I have shown a particular embodiment The net rotation of the shaft ‘I7 at the end of of my invention, it will be understood, of course, the first half cycle, that is, at the end of time that I do not wish to be limited thereto since t1-to, is the difference betweenits position at many modifications may be made, and I, there the end of the first half cycle and its position at fore, contemplate by the appended claims to the beginning of the ñrst half cycle, or cover any such modifications as fall within the true spirit and scope of my invention. 20 Thus, during the first half cycle, the shaft 2I moves from its initial forward position corre sponding to »Mah to its extremefposition in its forward motion corresponding to -i-ï/gh, and as a result the movement of shaft 'I'I is 1/2(œo-|-sci)h. What I claim as new and desire to secure by Letters Patent of the United States, is: ' 1. An integrator comprising variable of integra tion input means, integrand input means, revers ing mechanism operable in accordance with the operation of said variable of integration input means for periodically reversing the direction of the input, means for multiplying the output of said reversing mechanism by the input of said in tegrand input means, and means for periodically position +1/2h, back to its position -1/271, and the reversing the direction of the output of said mul position of input shaft a: changes from :ci to x2. tiplying means simultaneously with the reversals The position of output shaft 'I'I at the start cf of said ñrst reversing mechanism. the second half cycle is -I-ï/ghœi and at the end 2. An integrator comprising a variable of inte thereof is -l/ghœz, and the net change in the po gration input shaft, a reversing mechanism op sition of the shaft 11 during the second half cy 35 erated by said input shaft constructed and ar cle is: ranged to reverse periodically the direction of ro tation of its output with reference to the input thereto, an integrand input shaft, a multiplier operated by the output of said reversing mecha During all of this time, the final output shaft 40 nism and the input of said integrand input shaft I2 is operated by the shaft 'I'I through the re operating to multiply said output and input to verser 18, this reverser always functioning to gether, a final integral output shaft, and a sec add the total forward and backward movements ond reversing mechanism operating said final out of the shaft 'I'I and imparting the sum te' the put shaft and controlled to reverse periodically shaft I2. Therefore, during the first half cycle 45 and simultaneously with said first reverser so as when the reverser I3 is in its forward motion, to periodically reverse the output of said multi the change in position of shaft I2 is the same plier to impart its motions to »said ñnal output as that of shaft 11, that is, it is equal to shaft. 1/2(:vo+œi)h; however, the change in position of 3. An integrator comprising a variable of inte the final shaft I2 during the second half cycle 60 gration input shaft, an integrand input shaft, an when the reverser 'I8 has reversed its operation integral output shaft, a first reverser having an is the negative of the change in position of the output shaft, said reverser being operated by said shaft 'I'I during the second half cycle, that is, it variable of integration input shaft so that said is the negative of -1/2h(:r1-I-:rz) , which, of course, output shaft is periodically reversed with refer 55 ence to said variable of integration input shaft, the is +1/2h(:r1-I-œ2). Therefore, the total change in the position of output shaft thereby measuring the interval of the final output shaft I2 from time to to time t2 is integration, first mechanism for adding the out put of said output shaft with the input of said integrand input shaft and for squaring said sum 60 mation, second mechanism for subtracting from the output of said output shaft from the input of Immediately upon the completion of the first said integrand input shaft and for squaring the cycle, both reversers I3 and 18 operate to reverse difference, means for subtracting the output of and the complete cycle is repeated. And in this said second mechanism from that of said first During the next half cycle the shaft 2I moves in the reverse direction, and it moves from its way the mechanism adds up the areas of all of 65 mechanism so as to obtain the product of the the trapezoids under the curve. In other Words, variable of integration input and the integrand the total motion of the final output shaft I2 input, an output shaft driven first in one direc measures the areas of all the trapezoids under the tion and then in the other by the output of said curve, and consequently measures the desired in last-named means, and a second reverser for op tegral. 70 erating said integral output shaft operated by said variable of integration input shaft to reverse pe It will be understood that this integrator will riodically and simultaneously with said first re operate to calculate the integral of x regardless verser so that the total motion of said last-named of whether :c is positive or negative. output shaft in both directions is combined as a The description of this integrator and of its operation given above show how integrals may 75 motion in said final integral output shaft. nu 2,404,294 4. An integrator comprising a variable of `inte gration rinput shaft, an integrand input shaft, an integral output shaft, a first reverser having an output shaft, said reverser being operated by said variable of integration input shaft so that said output shaf t is periodically reversed with reference to said variable of integration input shaft, the out put shaft thereby measuring the interval of inte 8 operated by the output of said first differential for generating the square of said summation, a second cam mechanism operated by the output of said second differential for generating the square of said difference, a third differential op erated by said two cam mechanisms having' an output which generates the difference between the outputs of said first and second cam mech gration, a differential having an input driven by anisrns to thereby generate the product of the in said output shaft of said reverser, a second dif 10 tegrand input and the variable of integration in ferential having an input driven by said output put, a'shaft driven by the output of said third dif shaft of said reverser, said two differentials also ferential, a second reverser controlled by the op eration of said variable of integration input shaft having inputs operated by said integrand input shaft, and the two differentials also having out so as to reverse periodically and simultaneously put shafts, the first diñerential however gener 15 with the reversals of said first reverser, and a driv ating and delivering to its output shaft the sum ing connection between said second reverser and mation of the reverser output and the input of said integral output shaft so that said shaft moves said integrand shaft, while the second generates through the total distance that said last-named and delivers to its output shaft the difference be shaft is driven by said third differential. tween the output of said reverser and the input 20 of said integrand shaft, a first cam mechanism WILLIAM B, JORDAN.

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