US3064899A - Function generator - Google Patents

Description

Nov- 20, 1962 J. A. HERNDoN FUNCTION GENERATOR 3 Sheets-Sheet l Filed Oct. 25, 1960 Nov. 20, 1962 Filed Oct. 25, 1960 VOLTAGE AMPLITUDE J. A. HERNDON 3,064,899

FUNCTION GENERATOR 3 Sheets-Sheet 2 360 SHAFT PosmoN (e) //`-ee l l l i I \I kl TlME E j INVENTOR.

JAMES A, HERNDON.

ATTORNEYS.

NOV- 20, 1962 J. A. HERNDON FUNCTION GENERATOR 5 Sheets-Sheet 3 Filed OCt. 25, 1960 United States Patent fifice Bdigg Patented Nov. 20, 1962 3,064,399 FUNCTEON GENERATOR James A. Herndon, Cincinnati, Ghia, assigner to Aveo Corperation, Cincinnati, (Ehio, a carpet-atten of Deia- Wa'e Enea on. 2s, rasa, ser. Ne. saaie ri claims. (ci. 23s-i97 The present invention relates to function generators, and it provides an improved function generator in which the output, which is the resultant of the combination of a modifiable function having a discontinuity and a modifier or command, is free from limitations imposed by the approach of the modifiable function to its discontinuity.

In accordance with the invention there are provided means for generating a pair of phase-displaced modifiable functions, each having a given time to go (before reaching a discontinuity at zero amplitude); means for arbitrarily producing a command or modifier having a maximum value between zero and the maximum amplitude differential between the aforesaid phase-displaced functions; means for selecting that one of the modifiable functions which, when combined with the modifier, has sufiicient time to go to produce the desired resultant function; and means for applying the selected modifiable function and the modifier to an adder to produce that resultant.

To define the objects of the invention graphically, let an example of a problem that it solves be stated. The problem here is to produce, at any instant, a resultant or output sawtooth wave form having any desired amplitude between approximately Zero and an arbitrary selected voltage VR. Assuming a fixed slope, the duration of the sawtooth will be entirely determined by its initial starting amplitude. Now, if it be assumed that a modifiable sawtooth wave form having a maximum amplitude VR can be initiated at a given time, obviously a sawtooth wave form having a maximum amplitude of VR-l/zVR or any other arbitrarily selected maximum can be produced by applying to an adder the modiable sawtooth and a subtractive modifier or constant voltage. The time to go of the resultant, if the constant is zero, will be full duration of the resultant sawtooth whose initial amplitude is VR. On the other hand, if the constant is 1/2VR, then the time to go (to zero value) of the resultant sawtooth will be reduced by one half. The modifying value of 1/zVR takes away half the amplitude of the modifiable sawtooth.

The point is that at any predetermined starting instant it is possible to apply to a sawtooth wave form a modifier which will reduce the time to go by any desired amount, and it is feasible by such an expedient to produce a sawtooth wave form (the same slope being assumed here) of such initial amplitude that it will reach Zero value (i.e., its discontinuity) in one minute, five minutes, ten minutes, or fifteen minutes, to give arbitrary examples. However, an approach of this kind suffers from two serious limitations. One of them is that the command to start the generation of the desired function must correspond in time with the beginning of the so-called modifiable sawtooth wave form. The other limitation resides in the fact that the time to go of the resultant sawtooth wave form is limited by the time to go of the single modifiable sawtooth that is available to work with. True it is that, by repeating the modifiable sawtooth, the supposititious system is improved at least to the extent that the production of a resultant sawtooth can be commanded at the start of each successive modifiable sawtooth. Although this reflects some improvement, it is not enough.

It is desirable to provide a resultant sawtooth generator which is not pegged to the initiation of a modifiable sawtooth, but which can be commanded at any time and to any degree, whether the modifiable sawtooth is beginning or at any time point in its trace. I-t is further desirable to provide a resultant sawtooth generator which is not susceptible to the time to go limitation imposed on a single modifiable sawtooth by the approach of the modifiable sawtooth to its discontinuity.

These considerations and objectives are applicable not only to a generator the ultimate function of which is to produce a sawtooth, but to any generator which produces its output by a mathematical operation performed on a modifiable function which approaches a discontinuity.

It has been stated above that, in accordance with the invention, two modifiable functions are rendered available, and that the modifier is combined with that one of the modifiable functions which has sufficient time to go to provide the desired resultant, An important object of the present invention, therefore, is to provide a pair of synchronized function generators which produce continuous phase-displaced functions of a repetitive nature.

Another object of the invention is to provide, in combination with such synchronized function generators, means for producing any desired modifier, selecting the discontinuous function desired to be modified, and combining the modifier with the selected discontinuous function to produce the desired resultant function.

Stated in most simple terms, as applied to one specific embodiment, the primary object of the invention is to provide an arrangement which will generate, beginning at any desired instant (called the instant of command), a resultant sawtooth of any desired amplitude or duration. If one is scheduling the arrival of a train, notes that it passes a reference point at any instant, and desires to reserve a track in the station for that train for a period of fifteen minutes, the reservation could be indicated and suitable track-availability-control equipment set up by initiating the generation of a sawtooth function of fifteen inutes duration at the time of observation of the trains passing the observation point. Similarly, if at another instant an observer noted another train passing the observation point, and he desired to reserve another track for such other train for a period of five minutes, that could be accomplished by commanding a function generator to generate a sawtooth of live minutes duration and using that sawtooth to control suitable track-availability equipment. Thus the utility of a device which can, at any arbitrarily selected instant, produce a sawtooth of any desired magnitude or duration becomes quite apparent.

For a better understanding of the present invention, together with other and further objects, advantages, and capabilities thereof, reference is made to the following description of the appended drawings, in which:

FIG. 1 is a circuit schematic, partly in block diagram form, of a complete resultant function generator in accordance with the invention;

FIG. 2 is a series of curves employed as an aid in describing the operation of the synchronized linear function generator portion of the invention; and

FIGS. 3, 5 and 4 are sets of curves exploited in describing the operations of the entire system when responding to commands for resultant wave forms of short, medium, and long duration, respectively, and furnishing resultant functions as ordered by said commands.

Referring now to FIG. l, the resultant function produced by this invention may be represented by the general equation f(t)-f(k)=f(t).

There are disclosed in FIG. 1 a pair of linear potentiometers 15 and 16. The f(l') of the above equation is generated by one of the potentiometers 15 or 16, depending on which modifiable function-Le., linear potentiometer output wave form--is continuous over the period of duration of the desired function. For the output wave forms of FIGS. 3 and 5, the f(.t) is generated by potentiometer 16. For the output Wave form of FIG. 4, the f(t) is generated by potentiometer 15. rl`hese two linear potentiometers 15 and 16 provide offset functions, one of which will always be continuous over a particular interval of interest and will accordingly be selected for further operations. In FIGS. 3 and 5, wave form or modifiable function 2717 is continuous during the period of interest. 'in FiG. 4, wave form 26a, 26b is continuous during the period of interest. The expression f(t) in the aforementioned equation is referred to as the modifiable function. In the particular embodiment illustrated, it is one of the sawtooth outputs of the potentiometers 15 or 16.

The expression f( k) in the above equation is the modifier. It is the amount subtracted from the selected modifiable function, upon the rendering of a command, in ordering the production of the desired resultant function. The expression f(t") represents the resultant function; t is the commanded duration of that function. Since f(t") is a sawtooth of the same slope as f(z), the magnitude of the modifier determines the initial amplitude of the resultant sawtooth and therefore its duration.

The modifier f(k) represents the output of the potentiometer 56 illustrated in FIG. 1, upon the attainment of the position to which its rotary arm d5 is ordered when a command is introduced into the system (i.e., when the system departs from idling conditions and generates an output function). Now, what the specific embodiment of the invention here shown does is to take one of these sawtooth wave forms, hereinafter referred to as a selected modifiable function or wave form, and also the modifier or output of potentiometer 56, at any desired instant (the instant of command), and to perform such operations with these data as to process the elected modifiable sawtooth and to generate a resultant output sawtooth function of any desired amplitude and duration, having `a maximum possible amplitude of VR and a maximum duration equal to the time of one half turn of shaft 2:1. The command determines the time at which the resultant sawtooth will start, together with its initial starting amplitude and duration. The command is rendered by causing arm 65 of potentiometer 56 to move some predetermined amount to supply the ingredient f(k The potentiometers and 16 are so operated and their outputs so cycled that, at the time of rendering a command, two modiable functions or sawtoo-th wave forms are available. The invention features switching arrangements `by which the desired modifiable sawtooth is automatically selected. The data corresponding to the first two terms of the equation discussed above are applied to adder 69, which furnishes the desired resultant function on output line 70.

Referring now to FIG. 1, attention is first invited to a pair of linear potentiometers 15 and 16, the function of which is to generate sawtooth wave forms Z6 and 27, respectively (FIG. 2), these wave forms being phasedisplaced by 180 degrees in space and therefore in time. This pair of linear potentiometers comprises means for generating modifiable offset wave `form functions. The potentiometers 15 and 16 have rotary contact arms 17 and 18, respectively, and circularly arranged uniform resistance portions 19 and 20, respectively. The contact arms are synchronously driven by a common shaft indicated symbolically by the reference numeral .21, at the rate of,` say, one revolution per hour. This rate and all parameters herein mentioned are set forth for purposes of illustration and not of limitation.

The body portions of the potentiometers are connected in parallel between a grounded terminal 22 and the positive terminal 23 of a source of voltage, the voltage at terminal 23 having a value of -i-2VR.

The rotating arms 17 and 18 are angularly displaced from each other by 180 degrees. As they turn clockwise through 360 degrees, arm 17 beginning at the high voltage point 24 on resistor 19 and ending at the low voltage point 25 on that resistor, potentiometer 1S gencrates a sawtooth Wave form 26 (FIG. 2), the first half of which is designated by the reference numeral 26a, land the second hal-f of which is designated by the reference numeral Zeb. lt will be understood that the use of the expression wave form 26 is intended to mean the complete wave form made up of the halves 26a and 26h. Similarly, the expression wave form 27 indicates a total wave form made up of halves 27a and 27b. While the potentiometer 15 is generating the first half 26a of a sawtooth wave form, potentiometer 16 generates the last half Zb of a similar sawtooth wave form. That is because the potentiometers are so synchronized that arm 18 leads arm 17 by 18C degrees, and reaches the half-Way point on resistor 20 as arm 17, moving clockwise, touches point 24 on resistor 19. While potentiometer 15 is generating the last half 26h of its wave form, the potentiometer 16 is generating the first half 27a of a similar sawtooth wave form.

This action is repeated over and over, once for each revolution of shaft 21i.e., once per hour. Thus it will be seen that the potentiometers 15 and 16 constitute means for generating degrees phase-displaced sawtootli wave forms, each one hour in duration. At Zerodegree position of shaft 21, arm 17 touches 24.

One hour is an illustrative figure. The period involved for sawtooth wave forms is at least twice as long as the maximum duration of any output function to be generated by the invention.

During that part of the operation of the invention which will be referred to as idling the output wave forms of the two potentiometers are alternately switched between a first bus bar 33 and a second bus bar 36 by a doublepole, double-throw switch included in a. relay 30. The description now proceeds to the means by which this switching is accomplished.

Under the conditions illustrated in FlG. l, the sawtooth wave form 26a is available at switch-blade 29 of relay 3i, and the leading wave form 27 is available at blade 31, the blades 2.9 and 31 being conductively connected to the central output terminals of potentiometers 15 land 16, respectively.

It will be observed that each sawtooth Wave form in FIG. 2 reaches a Zero value, wave form 26 going through zero at the 360-degree position of shaft 21 (FIG. 2) when rotary arm 17 reaches point 25, and wave 27 (specifically 27h) going through zero when rotary arm 18 reaches the l80-degree position of shaft 21 (FIG. 2) at point 32. It should further be observed that, when either of the wave forms 26 or 27 is at zero Value, the other Wave form is at half maximum value. It will further be seen that the invention makes available at bus bar 36 the wave form which has at least half of its maximum value left to go, even though the other wave form is approaching its discontinuity of zero value. One of the contributions of the present invention is the fact that it overcomes the limitations imposed by the discontinuity of a single wave form, by making available always at the bus bars the choice of an alternate wave form which is further away from its discontinuity. To illustrate the last point, if wave form 27b were selected to be used or modified for the generation of some output function to begin at an instant fifteen minutes before arm 18 reaches point 32 (i.e., at the 90 degree position of shaft 21 in FIG. 2), that wave form would have only fifteen minutes to go before reaching its discontinuity (i.e., zero value), while wave form 26 would have a substantially longer time to go.

The bus bars 33 and 36 are so arranged that the last halves 27b and 26b of the wave forms are alternately applied to the first bus bar 33, while the first halves 26a and 27a of the wave forms are alternately applied to the second bus bar 36. Accordingly, the first bus bar 33 is provided with two input contacts 34 and 35, contact 34 being touched by blade 31 to encircuit bar 33 with potentiometer 16 when blade 31 is thrown to the upper one of its two positions, and contact 35 being encircuited with potentiometer by blade 29 when blade 29 is thrown to its lower position. Likewise, bus bar 36 is provided with input contacts 37 and 38 so that contact 38 is touched by blade 29 to encircuit bus bar 36 with potentiometer 15 when blade 29 is thrown in one direction (upwardly), and so that contact 37 is touched by blade 31 to encircuit bus bar 36 with potentiometer 16 when blade 31 is thrown to its other (lower) position. The bus bars and the associated double-pole, doublethrow switch, including blades 29 and 31, are so arranged that bus bar 33 is encircuited with potentiometer 16 during the iirst half hour of rotation of shaft 21, and with potentiometer 15 during the second half hour, whereby the wave forms 27b and 26b successively appear on the rst bus bar 33. In other words, there alternately appear on the first bus bar 33 the last halves of the wave form outputs of potentiometers 16 and 15. Bus bar 36 is first encircuited with potentiometer 15 for one-half hour, and is then encircuited with potentiometer 16 for the remaining half hour, whereby wave form 26a appears on the second bus bar 36 for one-half hour, followed by the wave form 27a. Generalizing, there alternately appear on the second bus bar 36 the first halves of the wave form outputs of potentiometers 15 and 16. Again, what is being described now is the idling condition.

The switching action, whereby the outputs of the po tentiometers and the bus bars are alternately interchanged, is produced by the action of the blades 31 and 29, under the control of relay 30. That relay is provided with separate coils 47 and 53, one of which acts through appropriate eXpedients indicated by the dashed line 39 to throw the switch blades 29 and 31 in one direction, and the other of which actuates expedients 39 to cause the switch blades to be thrown in the other direction. In FIG. 1, coil 47 is shown as energized, thereby causing the outputs of potentiometers 15 and 16 to be applied to bus bars 36 and 33 respectively. When, on the other hand, coil 5.3 is energized, the switch blades 29 and 31 are thrown in the opposite direction and the outputs of the potentiometers 15 and 16 are connected to bus bars 33 and 36, respectively.

There will now be described the means by which the selection of the coils 47 and 53 for energization is accomplished. Attention is invited to a cam 48 which has 180-degree low and high cam surfaces and is rotatably mounted on shaft 21, in such a manner that when cam 48 presents in its low cam surface to element 42 (for the first 180 degrees of its rotation), the switch arms 31 and 29 are in the upper position illustrated in FIG. 1, and that when cam 43 presents its high cam surface, the blades 29 and 31 are thrown to the lower position. The reference numeral 40 designates one terminal of a power source (at 28 volts, direct current, for example). Between source 46 and ground there are provided separate selectable energizing circuits for the coils 47 and 53. A single-pole, double-throw switch comprising blade 41 is actuated by the cam 48 to connect source 46 either to coil 47 through an on- off switch 45, 46, or to coil 53 through on- oif switch 51, 52. To that end the singlepole, double-throw switch having cam-actuated blade 41 is provided with a contact 43 (for energization of coil 47) and a contact 49 (for energization of coil 53). It follows from the foregoing that the low surface of cam 48 throws blade 41 in one direction (as shown in FIG. 1), and the high surface of the cam 48 throws the blade 41 in the opposite direction so that coil 53 is energized. The description under way still relates to the idling condition.

The arrangement is such that cam 48 presents its low surface to element 42 during the first 180 degrees of rotation of rotary arms 17 and 18, and it presents its high surface to element 42 during the second 180 degrees of rotation of arms 17 and 18.

Each of these two energizing circuits for coils 47 and Cil 53 is provided with on-oif switches so that, when a command is given to the system, a starting relay 54, acting through suitable gauging expedients, throws blades 45 and 51 to disconnect both energizing circuits, leaving relay 30 in whatever condition it is at the time that the command is given. That is to say, if the command is given during the first 180 degrees of rotation of shaft 21, then the blades 31 and 29 will remain in the upper position illustrated in FIG. 1. On the other hand, if the command is given during the second 180 degrees of rotation of shaft 21, then the switch blades 31 and 29 will remain thrown to their lower position. The point is that, when the system goes from the idling condition into the generation of a resultant output function, in response to a command, the interchanging of connections between the bus bars and the linear potentiometers stops.

Reference is now made to the step-by-step potentiometer 56 illustrated in PEG. 1. This potentiometer, on command, produces the modifier k. This potentiometer comprises a rotary contact arm 65 and a series of fixed contacts, arranged in ya circular pattern and, say, ninety in number, of which a few are shown and designated by the reference numerals 1, 2, 3, 4, 3113, 39, and. 96 (counting clockwise beginning with 1). These contacts are connected to spaced taps on a resistance voltage divider 60, and the voltage divider is connected between ground land the negative terminal of a supply of direct current, the potential at end tap or terminal 57 having a value of -VR. Contact 1 is connected to end tap 57 and is therefore at a potential of li/R. Contact 2 is connected to the immediately adjacent tap 62, `and the potential at terminal 2 is therefore It will be understood from the foregoing that the voltage at terminal 911, which is connected to the tap 58, is

That is to say, as the rotary arm 65 sweeps through the fixed contacts, beginning with contact 1 and ending with contact 96, the voltage output on conductor 59 changes in equal steps from a maximum value -VR to a minimum value and the output voltage value drops to zero as arm 65 leaves contact 96 and approaches contact 1. The output voltage of this step-type potentiometer appears on output conductor 59, electrically connected to arm 65. Illustrative ones of the taps on the voltage divider 69 are given the reference numerals 62, 63, 64, and 66, tap 66 being connected to contact 89, tap 64 being connected to contact 88, tap 63 being connected to contact 3, and tap 62 being connected to contact 2. i

In the description of the operation of potentiometer 56 during idling conditions, it will first be supposed for purposes of discussion that the output of this potentiometer, as its arm 65 sweeps through 360 degrees, beginning at contact 1, is a linear sawtooth wave form which begins at a value -VR and continues with the usual slope (i.e., the same slope as functions 26 and 27) until it reaches a value of zero as arm 65 leaves contact 9?. Although the potentiometer output in fact is a step-by-step type sawtooth, it can reasonably be assumed to be a linear sawtooth for purposes of the description immediately ahead. This hypothetical linear sawtooth is illustrated in FIG. 3, and the reference numeral 67 is applied to it.

The idling condition operations of the potentiometers 15 and 16 and their immediately associated circuitry have been described. The idling condition of potentiometer 56 is such that the arm 65 moves from contact 90 to contact 1 at the precise time that arm 17 of potentiometer 15 reaches the midpoint ofaresistor 19;i.e., at'the shaft 21 position of 18() degrees, illustrated in FlG. 2. Now arm 65 of potentiometer 56 again passes from contact 9d to Contact 1 when arm 17 of potentiometer 15 moves from point 25 to point 24 on resistor 19 (FIG. l). In other words, the potentiometers 56, 1.5, and 1e are so synchronized that arm 65 operates at twice the angular rate of rotation of arms 17 and 1S. Now, assuming the output of potentiometer 56 to be linear, potentiometer 56 would produce a sawtooth wave form 67 having a maximum amplitude of -VR during the time that wave form Z7b is on bus bar 33, and it would produce a like sawtooth wave form 68 during the time that wave form Zeb is on bus bar 33 (see FIG. 2).

The output of potentiometer 56 is connected through conductor 59 to an adder 69, and the output of the selected bus bar 33 or 36 is connected to the adder through switch blade 'ifi yand conductor S5. lt will be seen from an examination of FIG. 2 that, during the zero to 180- degree phase of rotation of shaft 21, wave form Z715 is applied from potentiometer 16 through the elements 33 and 55 to the adder. The actual wave form generated by potentiometer 56, idealized as 67, is likewise applied to the adder during this period. form 67 effectively cancels out Wave form 2,711, so that the resultant output on line 7i) is ideally zero. Considering now the lSO-degree to S60-degree phase of the shaft 21 rotation, when wave form 26h is present on bus bar 33 and is applied to the adder together with the actual wave form idealized as 62, again the efect of the opposingfunction produced by the potentiometer 56 is effectively to cancel out the wave form 26h. More signiiicant still, what the wave forms 67 and 63 do is suppress the appearance of any substantial resultant or output sawtooth function on line 7G until the command to generate such a function is introduced into the system. That is the reason why the invention can start to produce a desired resultant output function at any time and of any duration within the limitations of the system, such duration being determined by the magnitude of the command introduced into the system. Since wave forms 67, for example, normally subtract enough away from wave forms 271') at all times during idling conditions to reduce the resultant output to zero, this zero provides a base-line, as it were, for any desired output function. It will now be perceived that one of the keys to the production of any desired output function is to alter the generation of wave form 67 or 68 in a predetermined manner. ln HG. 3, for example, the generation of the wave form idealized as 67, and actually normally having steps la, etc., under idling conditions, is speeded up on command (per 163) so that the output of potentiometer 56 becomes a constant value k1, arm 65 being arrested at k1 output. lt is this value k1 which is subtracted from wave form 27 b to produce wave form vi), beginning substantially at T1.

Idealized wave forms 6'7 and 68 have been discussed so far. Actually, during the idling condition, the step potentiometer 56 produces step-type sawtooths which only approximate the linear sawtooth wave forms 67 and 63. Essentially, however, the action is such that the sum of the wave form 27h and the step sawtooth idealized as 67, as applied to adder 69, approximates zero. So, too, the sum of the step-type wave form shown ideally as 63 and 26b approximates zero.

Potentiometer S6 is a step-type device, and its actual output is not a linear trace 6'7 but is a series of ninety steps such as 1a, 2.a, etc. (FGS. 3, 4, and 5), the 1a and 2a designations indicating that arm 65 is on contact 1 and later on contact 2, and so forth. The steps 1a and 2a are greatly exaggerated in duration and size. Because the output of potentiometer 56 is in steps, that output and the linear wave form on bus bar 33, as differentially applied to the adder, cause the resultant output appearing under idling conditions on line "itl, ideally zero, to approximate a series of small triangular sawtooth wave In the adder, wave,

forms, to which the reference, numerals 1b, 2b, etc., arci applied (see FIGS. 3 and 5). Thesesresidual wave forms 4such as 1b and 2b are of no significance, can be reduced to as inconsequential values as may be desired, and therefore will not further bediscussed herein.

While the cooperative action of thek three potentiometers 15, 16, and 56, and the bus bars during idling conditions is that of repetitively generating sawtooth wave forms 27h and 26h, repetitively generating opposed sawtooth wave forms 67 and 68, and combining the two wave forms to produce an over-all output on line 70 which ideally approximates zero, the action of the system upon the introduction of a command is dilferent in several respects. On command, the amplitude of wave form 67 or 68 at the instant of command is suddenly decreased by an amount determined bythe magnitude of the command. The amount of this sudden decrease in amplitude determines the duration of the generation of the desired resultant function, because the decrease in amplitude of the voltage from potentiometer 56 changes the zero output on line 7d by a corresponding amount substantially at the moment a command is introduced into the system. 1n other words, on command arm 65 of potentiometer S6 is suddenly accelerated, displaced by an amount related to the durationof the desired resultant function, and then quickly arrested. ThatV is, on command potentiometer 56V produces an output voltage which is combined with one of the modifiable sawtooth wave forms to produce a resultant sawtooth output Wave form havinga magnitude depending'on such displacement. in FiG. 5, the arm 65 is displaced to a point between contacts 9i? and 1, beginning at time T2. Resultant 101 is of medium duration. 1n FiG. 3, the arm d5 is displaced kapproximately to the titty-ninth contact beyond 1, beginning at time T1, and the generated result-ant 10S is short.

Let it be supposed that, at any arbitrary instant hetween zero and the ISO-degree position of shaft 21, arm 65 be very rapidly accelerated and displaced by a predetermined number of contact steps. Suppose, for example, that arm 65 is on contact 2 shortly after shaft 21 passes the zero degrees position. Let it be supposed further that arm 65 is immediately substantially instantaneously displaced clockwise to a position between contacts il and 1, reducing the output voltage of potentiometer e6 to zero. Applying the potentiometer 56 output value of zero and the output of bus bar 33 to the adder causes to be generateda resultant function, appearing on line 70, which would be a wave form identical in shape and amplitude to that portion of wave form 27b between the time of command (very shortly after zero degrees) and the l-degree position. This illustrates the man* ner in which the invention can be made to start to generate, at any instant, a resultant wave form equal in duration to the remaining duration of wave form 27h (or 26h) at that instant. In the example just discussed,- k=0. This example is shown in FlG. 5.

Assuming now the same set of facts, except that the command is earlier (when arm 65 is on contact 1) and is of such a nature as suddenly to displace arm 65 to a position beyond contact 1 and two-thirds of the way to contact 9d, and immediately stop it. ln that event the resultant of the application of the wave form 27b and the output voltage of the potentiometer 56 to the adder 69 would be the generation of a wave form (such as 16?, FIG. 3) of substantially smaller amplitude and duration than wave form 27h. Under the conditions now discussed, k1=approximately /sVR (as shown in FG. 3). Thus it will be seen that, by reason of the rendering of commands involving the displacement of arm 65 clockwise, the device can be made to generate, at any instant, a sawtooth wave form ofany desired duration up to and inclusive of the maximum remaining duration of wave form 2712 at that instant (FIG. 5). Such resultant wave form (such as 16d, FIG. 5) can be of any starting amplitude between zero and the maximum amplitude of wave form 27b at the time that the command is given, neglecting in this discussion the time required for arm 65 to accomplish the required displacement.

It will be noted that, in what has just been said, the remaining duration of 27b at the time of rendering the command limits the amplitude and duration of the wave form proposed to be generated, the limitation being faced by reason of the fact that the wave form 27b is approaching its discontinuity or zero value. One of the principal features of the invention resides in the elimination of this limitation. That is to say, it has been shown that, by issuing a command which reduces the output of the potentiometer to some magnitude between the contemporaneous value of 27b and zero, there can be produced a resultant sawtooth wave form having any desired duration short of the remaining duration of wave form 27b.

in accordance with the invention, even greater resalts are obtained. Let it be assumed for purposes of discussion that the command given accelerates arm 65 beyond contact 9b, bearing in mind that the larger the duration of the desired sawtooth to be generated by the adder, the larger the displacement of arm 65 occasioned by a command. Expressing the matter another way, let us assume that arm 65 is accelerated and displaced beyond contact l to contact 2 or some later contact, and then arrested. Now, in that event, the output of potentiometer 56 would attain a value such that, if it were subtracted from 27b, the resultant would be a sawtooth smaller than the remaining duration of 27b. But what is desired is a sawtooth larger than the remaining duration of 27b, and therefore the output of potentiometer 56 is subtracted from, not the wave form 27b, but the wave form 26a, 26h (see FIG. 4). This is accomplished by a relay 6i which moves switch arm 74 from contact 76 to contact 30 whenever, following the issuance of a command, arm 65 passes from contact 9@ to contact 1 in other words, whenever the issuance of a command causes the output voltage of the potentiometer to go through zero and jump to a maximum; alternately expressed, whenever it is desired that there be produced a wave form greater in duration than the remaining duration of the smaller sawtooth on the bus bar 33.

Stating the matter another way, if one subtracts a quantity from 27b, one can produce a smaller-amplitude wave form (FIG. 3). If one reduces that quantity and subtracts less from wave form 27b, one can produce a longer wave form (FIG. 5). lf the quantity subtracted reaches zero, one cannot produce any larger resultant wave form from 27b (FIG. 5). However, the invention further teaches that one can space wave form 27b by VR, an amount equal to the maximum subtractable quantity, from a greater amplitude wave form 26a. When the maximum subtractable quantity is taken away from 26a, the resultant is 27b, from which it follows that a wave form having a maximum amplitude equal to VR is the largest wave form function that the illustrative embodiment is capable of producing at any and all instants of command.

In accordance with the invention, the modiable function having the larger amplitude or time to go is automatically selected if a command is of such magnitude as to cause arm 65 of potentiometer 56 to move clockwise beyond contact 90 and on to contact 1. The reason for this is that, when the desired resultant output function (such as 162, FIG. 4) is of longer duration than the smaller-amplitude modifiable function, it can be produced by the subtraction of the output of potentiometer 56 from the larger-amplitude modifiable function. In this manner the limitations imposed by the approach of the smaller-amplitude function to its discontinuity are overcome.

It will be understood that the invention starts to work on the smaller-amplitude function (as in FIG. 3). The

larger the resultant output function desire-d, the more arm 65 is displaced by a command, and the less is the voltage value subtracted from the smaller-amplitude modifiable function; but, when the command has such a value that it displaces arm 65 beyond the zero voltage position (between contacts and l), then the quantity to be subtracted (i.e., k) is large, and the larger-amplitude modifiable function (26a, FIG. 4) is automatically chosen as the minuend. Assuming the choice of the larger amplitude function as the minuend, it will be seen that, for still longer output functions, the arm 65 is displaced more clockwise beyond Contact 1, so that the subtrahend diminishes, However, a resultant wave form of one-half hours duration is the maximum that can be commanded at any and all instants. While FIG. 4 indicates that a resultant wave form longer than one-half hour could be commanded at times between the zero and ISO-degree position of shaft 2li, it is obvious that at the 180-degree position a resultant having a maximum amplitude of VR, and a maximum duration of one-half hour is the largest resultan wave form that can be commanded.

Now, we have shown that during idling conditions the relay 3ft causes connections between the linear potentiometers l5 and 16 and the bus bars 3.3 and 36 to be interchanged every degrees of rotation of shaft 21. When a command is given to the system, control by relay 30 is removed from relay 3i); At the instant that a command is rendered, blade 74 is on contact 76, and that blade remains in that position to put Wave form 27b or 26h on line 55, dependent on the shaft position of element 21 at the time that thel command is given, unless the command causes arm 65 of potentiometer 56 to move from contact 90 to contact ll, in which event relay 61 causes blade 74 to move to contact Si) and to select either wave form 26a or 27a. Once the selection of either 26 or 27 occurs, that wave form will continue to be applied to the adder from bus bar 36 (because the cycling action of relay 36 ceases on the issuance of a command) until the desired resultant wave form has been generated.

Reference is made to FIGS. 3, 4, and 5 in describing how typical output functions are generated. In FIG. 3 a command is given at time T1, and the arm 65 of potentiometer 56 is displaced clockwise by approximately fifty-nine steps, until the output of that potentiometer reaches a value of k1. This value is subtracted from wave form 27b to generate the resultant sawtooth function indicated by the reference numeral 100. It will be seen that the effect of the rendering of the command is to upset the normally balanced relationship of wave form 27b and the wave form idealized as 67.

Now consider the conditions illustrated in FIG. 5, in which the command, initiated at time T2, displaces arm 65 by such an amount as to bring the output of potentiometer 56 to zero (just beyond contact 90). In that case the resultant wave form 191 is generated.. Since the value subtracted from the modifiable function 27b is reduced to zero (i.e., k=0), the resultant wave form 101 has substantially the same initial amplitude as wave form 27b at the instant of command.

Now assume that a wave form larger than and of longer duration than wave form 161 is desired to be initiated at time T2. Note that wave form 162 (FIG. 4) is of such long duration that a subtractive operation on Wave form 27b would not provide it, wave form 27b being of insuicient duration. Also note that the command displaces arm 65 beyond the Zero output of potentiometer 56 and beyond contact 1, so that the subtrahend reaches a value k2. Under these conditions, as arm 65 touches contact l, modiable wave form 26 is selected, by the operation of the relay 61. Wave form 26, being further from its discontinuity than wave form 27 is, at time T2, provides an adequate minuend for the generation of the desire-d output function 102. Thus it will be seen that the invention will generate an output function of any 1 1 duration up to one-half hour, beginning at any instant of command.

The curves 103, 194, and 195 in FIGS. 3, 5, and 4, respectively, show the behavior of the output Voltage of potentiometer 56 under the conditions pertinent to these figures. The vertical steps are greatly exaggerated in length and minimized in number for purposes of illustration. While only three steps are shown in 163, for example, the arm of potentiometer 56 would actually have to move approximately from contact 1 to contact 61B (59 steps) to be arrested at an output value of k1. This assumes that the arm 65 is on contact 1 at the instant of command, and it further assumes that k1 is approximately equal to in which case thev maximum amplitude of wave form 11)@ would approximate ZVR Consider now the events which occur upon the completion of the generation of the desired function. When a wave form 101B reaches zero value, the start relay 54 is reset to the FIG. 1 position, and those portions of the smallerand larger-amplitude modifiable functions which remain are applied to bus bars 33 and 36, respectively. Arm 65 of potentiometer 56 starts its clockwise rotation, beginning at approximately the fifty-ninth contact away from contact 1 (assuming operation per FIG. 3), and the wave form outputs of the potentiometers 16 and 56 continue to zero value at the lSO-degree position of shaft 21, whereupon the connections between the linear potentiometers 16 and 15 and the bus bars 33 and 36 are interchanged, relay 54- having been reset upon the fulfillment of the command so that the circuits to the coils 47 and 53 of relay 3d are again set up for energization. Potentiometer 56 resumes its idling condition because the command transmitter 82 gives to the clutch and braking device 96 a reset order which again coordinates the angular motions of that potentiometer with the other two po` tentiometers for idling conditions.

The same simple events occur upon the completion of the generation of resultant output function 101 (FIG. the bus bar switching occurring at the ISO-degree position of shaft 21 so that, as idling conditions are resumed, wave form 26b is on bus bar 33 and the larger modifiable function 27a is on bus bar 36. The step potentiometer 56resumes idling by passing to contact 1 between contacts 9i? and 1 at the ISO-degree position of shaft 21.

Referring now to FIG. 4, idling conditions are resumed at the conclusion of the generation of output function 1621, the step potentiometer arm 65 starting from contact 2. At the time output function 1192 is completed, wave form 26b is on bus bar 36. In this case relay 61 is immediately de-energized, and simultaneously the switching device 30 is energized to put 26h on bar 33, and blade 74 is encircuited with bar 33 to apply wave form 26]? to the adder. Wave forms 26h and 68 then continue to approach zero at the S60-degree position of shaft 21.

At this point it is in order to describe the means by which a command is given to the system. This means comprises thev command transmitter 82 and associated elements. The command transmitter causes the following operations to be performed:

First, it is coupled by order and reset circuits to start relay 54, so that, in rendering a command, it causes relay 54 to break the circuits of coils 417 and 53, thereby to leave the bus bars 33 and 36 in circuit with the linear potentiometers to which they were connected at the moment of command.

Second, the command transmitter sends pulses of current through a coil 98, magetizing a core 99 and causing arm 65 to speed up-i.c., to advance clockwise by the desired amount, dependent on the magnitude of the command. Thearm 65, due to the action of a known prior art expedient 121, advances or is displaced `by one Contact for each pulse. As indicated, the extent of the advance depends upon the magnitude of the command-ie., the number of pulses from the transmitter 82.

Third, the command transmitter is coupled by order and reset circuits to a clutch and braking device 96, which causes arm 65 to stop when it has been displaced by the desired commanded amount.

When the desired resultant function has been generated, the command transmitter resets the starting relay 54 and the clutch and braking device 96, so that idling conditions are resumed.

It has been pointed out that, if, in obeying a command, arm 65 of potentiometer 56 moves to contact 1, relay 61 is energized to change the position of blade 74-i.e., to move it from contact 76 to contact 80. That is to say, when response to a command moves arm 65 of potentiometer 56 through its zero output point and onto its maximum output point, selector means 61, which normally applies the output of bus bar 33 as a modifiable wave form to the adder, then operates to cause to be applied to the adder the output of the bus bar 36. What is said here is simply that the largeramplitude modifiable function is selected (FIG. 4) if a resultant wave form of longer duration than the remaining duration (at the instant of command) of the smaller-amplitude modifiable function is desired.

Reference is now made to the means by which the relay 61 is energized. An arm 111 of rotary switch 111) is ganged and coordinated with arm 65. Switch is provided with contacts 112 and 113 which correspond in position to contacts 9i) and 1. When arm 111 attains a position of contact with Contact 113, it sets up an energizing circuit via ground, the coil of relay 61, conductor 85, elements 113 and 111, contact 84, blade 83, conductor 114, contacts 78 and 79 of relay 54, and terminal 77 of a voltage source. Upon the rendering of the command and the actuation of the start relay 54, contacts 78 and 79 are closed. The issuance of a command and magnetizing of core 99 closes blade 83 on contact 34, so that, at the time arm 65 reaches contact 1, arm 111 touches contact 113 and causes relay 61 to be energized. Relay 61 is provided with a holding circuit comprising blade 94, contact 95, conductor 93, contact 92, blade 87, conductor 86, and direct current voltage terminal 40, the operation being such that the start relay 54 Closes contacts 87 and 92 on the giving of a command and breaks those contacts upon the fulfillment of the command. Contacts 94 and 95 are kept in contact by the coil of relay 61 so long as the contacts 87 and 92 are made.

It Will be understood that the blades 51, 87, and 78 are controlled in unison by the start relay, the conditions represented in FIG. 1 being idling conditions and the blades being thrown downwardly by the start relay on command.

The description of the events geometrically expressed by the wave forms in FIGS. 3, 4, and 5 has postulated that a command is introduced into the system at some instant between the zero-degree position of shaft 21 and the IBO-degree position of that shaft-i.e., during the half-hour period represented by the first degrees of rotation of shaft 21. It has been shown that at any instant during this period either the wave form Zb or the wave form 26a is available for selection as the minuend for the mathematical operation performed by the invention. The invention works in an equally effective manner if a command is given during the halfhour period between the instant when shaft 21 reaches its l80-degree position and its 360-degree position, either of the modifiable functions 26b and 27a then being available for Selection as the minuend. The invention has the advantage, therefore, that at any and all instants there is available for selection a minuend Wave form more remote from its discontinuity than the maximum duration of any resultant function to be produced. The invention accomplishes these results with relatively few electrical and mechanical components. The true scope of the invention includes means, in combination, for performing the various operations, and novel combinations of such means, and is not limited to the particular application shown, nor is it restricted to the specific illustrative means for performing such operations as herein described in the detail requisite to the disclosure of what is presently deemed to -be the preferred embodiment.

The invention includes, inter alia, the method of generating a resultant function (such as 106) which comprises the steps of repetitively generating a function (such as 27h), repetitively generating an opposing function (such as the wave form idealized as 67), normally combiningT the two functions (in adder 69) to produce an output approximating zero, disturbing the generation of the opposing function and arresting it at an assigned arbitrary value (such as k1 in 'Fl'G. 3), whereby the resultant function (such as ffii?) becomes a modified form of the first-mentioned function.

The invention further provides the combination of a first function generator ,t6 for generating a function 27 having a discontinuity, a second function generator 15 for generating a second function 26 having a discontinuity, means 2l for synchronizing said generators so that their outputs are phase-displaced, a first bus bar 33, a second bus bar 36, and means (including 43 and 3%) for interchangeably connecting the function generators to the bus bars whenever either function reaches its discontinuity, whereby there is always made available on one of the bus bars a function substantially removed from its discontinuity.

The invention also provides switching mean 61 for selecting either of the aforesaid functions, generally referred to as modifiable functions. While this switching means 6l is so arranged that the smaller-amplitude function is normally selected, it automatically selects the larger-amplitude function if the subtrahend (in response to a command) is of such magnitude as to modify the smaller-amplitude function down to zero.

The invention additionally provides means 56 adjustable on command to subtract from the selected modifiable function any value up to and including the instantaneous amplitude of that function. For example, in FG. 3 the step-type potentiometer 56 subtracts the value k1 from the wave form 271;. The means 39 for interchangeably connecting the function generators to the bus bars is associated with a starting relay 54 and switch contacts which stop, on command, the interchanging action of relay 3?. The means adjustable to perform the subtracting operation further comprises an adder 69, to which the selected modifiable function is applied as a mintiend. The potentiometer du is essentially a third function generator which normally generates an opposing function (idealized as o7 or o3), which is applied to the adder as a subtrahend to reduce the selected function substantially to zero. it has been shown that the potentiometer 56 is adjustable on command to provide a constant value subtraliend.

Viewing the specific embodiment shown in a narrow aspect, it is a resultant function generator comprising, in combination, first linear potentiometer means td for generating a series of hrst sawtooth wave forms 27a, 2712 of a predetermined slope each beginning with a maximum amplitude having a voltage value of ZVR; second linear potentiometer means f5 for generating a series of second sawtooth wave forms 26a, 2615 of said predetermined slope each beginning with a maximum amplitude having a voltage value of ZVR; each of said linear potentiometer means having a rotary Contact arm f7 or i8, the arm 1S of the first potentiometer being angularly displaced by 'ifi 18() degrees from the arm Il? of the second; shaft means 21 for driving the contact arms of said linear potentiometers in synchronism; a iirst bus bar 33; a second bus bar 36; said linear potentiometers having outputs; relay means 3u for normally switching the outputs of said potentiometers twice per rotation of the shaft means so that the last halves 27b, 261) of the first and second wave forms are alternately applied to the first bus bar 33, and the first halves Zea, 27a of the second and next succeeding first wave forms are alternately applied to the second bus bar 36, thereby making available at the first and second bus bars a choice between phase-displaced sawtooth wave forms, one of said wave forms having an instantaneous amplitude of VR at each instant when the instantaneous amplitude of the other wave form is zero; a third potentiometer means S6 for generating in steps a third approximately sawtooth wave form of said predetermined slope with a maximum ampltude having a voltage value of VR; said third potentiometer means having fixed contacts 1 4, etc. for its steps and a rotary contact arm 65; means for normally so synchronizing the last-mentioned arm with the rotary arms of Athe linear potentiometers that the instantaneous `values of the third sav/tooth wave forrn 67 are normally substantially equal in amplitude to the wave form output of the first bus bar; adder 69; means :39 for applying the output of the third potentiometer to said adder; selector means el normally applying the output of said first bus bar as a modifiable wave form to said adder but operable to apply to the adder the output of either bus bar as a modifiable wave form; the third or modifying wave form 67 from the third potentiometer combining in the adder with the modifiable wave form 27h or Zeb on the first bus bar, under normal conditions, to produce a resultant function approximating zero output; means 54 subject to a command for disabling the relay means 30 to leave the bus bars connected to the linear potentiometers they were encireuited with at the instant of command; means 121i, 9S, 99 subject to a command for accelerating the third rotary arm to displace it by an ordered amount to a position in contact with one of its fixed contacts and to arrest the third arm thereat; means lli, M3, 35, 77, 755, 79, lll, etc. subject to a command for actuating the selector means to apply to the adder the output of the second bus bar 36 in the event that the third rotary arm 65 passes through its own zero-output position to its maximum output position while being displaced, whereby, in such event, the 4output of the linear potentiometer generating the larger-amplitude sawtooth is combined in the adder 69 with the subtractive voltage output of the third potentiometer to produce a resultant sawtooth wave form having a duration determined by the magnitude of the cornmand and a starting point determined by the instant of the command; and command means S2 for controlling the three last-mentioned means.

For purposes of clarity in explanation, it has been assumed that the step potentiometer S6 generates an ideal wave form 67 and that the output of that potentiometer actually falls to zero when arm 65 moves from contact 9i) to contact 1. A supposititious zero output point between these two contacts has been assumed for purposes of discussion, and the petty difference between an ideal wave form such as 67 and a wave form approximately the same but having ninety steps has been disregarded for purposes of clarity in explanation. it will be observed, however, that tlie step voltage output of potentiometer 56, under idling conditions, never actually reaches zero but has a minimum residual value of this for the reason that the arm 65 does not in actual practice attain an open-circuit condition between contacts 90 and 1. If the number of steps were infinity rather than ninety, then indeed the output of potentiometer 56 would reach zero, under idling conditions. it will be seen from an inspection of FiG. 4 that the curve 185 reaches a theoretical value of zero, and then, as arm 65 moves from contact @il to `contact 2, attains a value of k2. in -view of the fact that there are ninety discrete steps instead of an infinity of steps, the wave form tl will not in practice actuall go to zero value, hut its minimum value will be Since, by increasing the denominator of this fraction this residual value can be made to approach zero, the theoretical zero assumed for purposes of explanation is believed to be in order and in the interests of clarity. This comment is directed to the operation under command conditions or idling conditions.

While there has been shown and described what is at present considered to be the preferred embodiment of the present invention, in detail, further definition of the word command is in order. rfhe word command indicates the amount by which the arm 5S is suddenly displaced when the system is actuated to produce an output function. The duration of the resultant output function depends only on the magnitude of the command and is independent of the instant of command. This is true because the command causes a disturbance of a normally approximately balanced relationship-as, for example, that between wave forms o7' and 27h in FIG. 3. This substantially balanced relationship prevails until a command is rendered, and the magnitude of the command, as illustrated in PEG. 3, is the amount of the sudden displacement of arm 65, or the difference between the k1 voltage output position (of potentiometer S6) which the ar .i suddenly assumes and the contact position on which it was at the time the command was rendered.

1t will be understood by those skilled in the art that various changes and modications may be made in the preferred embodiment without departing from the true scope of the invention as defined in the appended claims. For example, it is known that the various modifiable functions here involved can be generated mechanically, hydraulically, or electrically. It is also know that algebraic combination or subtraction likewise can be accomplished electrically, mechanically, or hydraulically. The same is true with reference to the generation of the subtrahend. Therefore, it is not intended, in the presentation of the preferred embodiment above described in detail, to limit the invention to the particular electrical and mechanical means chosen as the function generators and operators. It is intended to cover a proper range of equivalents.

I claim:

1. The combination of a first function generator for generating a function having a discontinuity, a second function generator for generating a second and similar function having a discontinuity, means for synchronizing said generators so that their outputs are phasedisplaced by an amount equal to half the duration of either function, a first terminal, a second terminal, and means for interchangeably connecting the function generators to the terminals whenever either function reaches its discontinuity, whereby there is always made available a choice between functions, the last-mentioned means comprising a timer having two alternating states each of which is equal in duration to half the duration of either function, and a switch controlled by the timer for interchanging the connections between the function generators and the terminals whenever the timer changes its state.

2. The combination of first and second sawtooth generating potentiometers, each having a rotary arm, the arm of the first potentiometer leading the arm of the second potentiometer by 180 degrees, first and second bus bars, and double-pole, double-throw encircuiting means for connecting the outputs of the first and second potentiometers to the rst and second bus bars, respectively, during the first,l80. degrees of angular movement of said arms, starting with the second potentiometer at its maximum output, and for connecting the second and first potentiometers to the first and second bus bars, respectively, during the second degrees of angular movement of said arms, means for driving said arms in synchronism, and means including a cam synchronized with the driving means for actuating the double-throw encircuiting means.

3. The combination of claim 2 and a step-type potentiometer having a plurality of fixed contacts arranged in a circular pattern together with a rotary arm, a tapped voltage divider connected to said fixed contacts in a sequence such that the step-type potentiometer generates effectively a stepped sawtooth wave form, the last-mentioned rotary arm being operated at twice the angular rate of the rotary arms of the first and second potentiometers and so coordinated therewith that the step-potentiometer output of VR is at a maximum when the sawtooth appearing on the first bus bar is at its maximum of VR, and means for differentially combining the sawtooth appearing on the first bus bar and the step-sawtooth output of said step-type potentiometer.

4. The combination of a first function generator for generating a function having a discontinuity, a second function generator for generating a second function having a discontinuity, means for synchronizing said generators so that their outputs are phase-displaced, a first terminal, a second terminal, means for interchangeably connecting the function generators to the terminals whenever either function reaches its discontinuity, vwhereby there is always made available a choice between functions, selector switching means for selecting either of said functions as a modifiable function, and means adjustable on command to subtract from the selected function any value up to and including its instantaneous amplitude at the instant of command, but not to exceed half of the maximum amplitude of said function.

5. The combination in accordance with claim 4, and means for stopping, on command, the means interchangeably connecting the generators to the bus bars.

6. The combination in accordance with claim 5 in which the selector switching means normally selects the smaller-amplitude one of said functions but operates on command to select the larger-amplitude function as a modifiable function whenever said value exceeds the instantaneous amplitude of the smaller-amplitude function.

7. The combination in accordance with claim 6 in which the means adjustable to perform a subtracting operation includes an adder coupled to the selector switching means, to which adder the selected modifiable function is applied as a minuend, and further includes a third function generator coupled to said adder, which third function generator normally generates an opposing function applied to the adder as a subtrahend to reduce the selected function substantially to zero, but which includes an arm adjustable on command to provide a constant-value subtrahend.

8. The combination in accordance with claim 7 in which the first and second function generators generate sawtooth wave forms of identical slope.

9. The combination in accordance with claim 8 in which the third function generator is a step-type potentiometer which includes said arm and generates a steptype sawtooth.

10. The combination of a rst function generator for generating a function ZVR-s (t9-180 degrees), a second function generator for generating the function ZVR-s (6), first and second bus bars, switch means for interchangeably connecting the first and second generators to the bus bars every 180 degrees, so that the last half of each function is applied to the first bus bar and the 17 first half of each function is applied to the second bus bar, a third generator for generating a step function having half the duration and maximum amplitude of the two aforementioned functions, means for differentially combining the step function and the function applied to a selected one of said bus bars, wherein ZVR is the maximum amplitude in voltage of each of the rst-mentioned functions, n is the maximum number of steps in the step function, m is the number of steps through which the step function has passed at any instant, and s is the slope; means for stopping, on command, the interchangeably connecting means; means for instantaneously accelerating the third generator on command and arresting it at any step having a constant output value such as to provide a resultant output sawtooth of desired duration; and selector means for selecting the output of either the first or the second function generator as a modifiable function, said selector means normally selecting the smaller-amplitude one of said functions but operable on command to select the larger-amplitude one whenever said constant value exceeds the instantaneous amplitude of the smaller-amplitude function.

11. Means for repetitively generating a rst sawtooth Wave-form function of 360 degrees duration, means for repetitively generating a like second sawtooth waveform function of 360 degrees duration lbut phase-displaced from the first function by 18() degrees, means for repetitively generating a third similar sawtooth function of half the amplitude and twice the frequency of the aforementioned two functions, first and second terminals, means for alternately coupling the first two generating means to the first terminal normally to present the last halves of said two functions at said first terminal, said means alternately coupling the first two generating means to the second terminal normally to present the first halves of said two functions at said second terminal, means for disturbing the generating of the third function and arresting it on command at some arbitrary value, means for stopping the alternate action of the coupling means on command, means normally connected to said first terminal for subtracting that arbitrary value from the wave form on the first terminal if that Wave form is at least equal in amplitude to said arbitrary value at the instant of command, and means responsive to command for switching the connection of the subtracting means to said second terminal in the event that the amplitude of the wave form on the first terminal is less than said arbitrary value at the instant of command.

References Cited in the file of this patent UNITED STATES PATENTS UNITED STATES PATENT OEETCE CEBTEFICATE 0F C0 RECH November 2Ou 1962 James A7 Herndon lt is hereby certified that error appears in the above numbered patent requiring correction and that Jche said Letters Patent should read as corrected below..

Column l line ll before "full" insert m the mg column 5 line L8v strike out; "i1/11"; column ll line '50 strike out to Contact 1"; line 741 for "magetzing" read magnetizing w; column l3 line 37V for "mean" read means -f-D Signed and sealed this 28th day of May 1963,

(SEAL) Attest DAVID L. LADD Commissioner of Patents ERNEST W. SWIDER A esting @fficer

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