Improved feed rate generator for machine tool control
United States Patent Sindelar Apr. 15, 1975 DOC  4ND CMTROL SPIIIOL E EEO RAE GEM&#39;RIM 3.725.654 4/1973 Tripp 235/1511] Primary Examiner-J0seph F. Ruggiero [57] ABSTRACT A control for controlling movement of a machine tool along a path in accordance with commanded departure distances along mutually perpendicular first and second axes and at a velocity in accordance with a commanded vectorial velocity. A calculating circuit receives signals having vlaues which are functions of the commanded departure distances and calculates therefrom the value of the square root of the sum of the squares of these signals. A ratio calculator operates to provide a signal having a value corresponding with the ratio of a function of the vectorial velocity to that of a function of the vectorial summation of the commanded departures. This signal is employed as a modifying factor in reducing the pulse rate of a pulse train to provide feed rate pulses for use in controlling movement of the machine tool.  
 22 Claims, 13 Drawing Figures PUL SE X DORO CONTROL BI-MECT/ML COUNTER MOTOR PHENTEDAPR 1 51975 SHEET 2 BF 9 PMENTEBAPR 1 51% 3. 878 372 SHEET 9 n5 9 IMPROVED FEED RATE GENERATOR FOR MACHINE TOOL CONTROL This invention relates to the art of machine tool control and more particularly to improvements in providing feed rate pulses for use in controlling movement of a machine tool.  
  The present invention is particularly applicable for use in calculating the feed rate number FRN in a machine tool control system from the programmed feed rate velocity F and the programmed slide departure distances along mutually perpendicular axes. In the example presented herein. the control is discussed in conjunction with a two axes movement ofa cutting tool relative to a workpiece with the two axes being mutually perpendicular and referred to hereinafter as axes X and Z. The invention may be employed in other applications, such as for controlling movement of a machine tool along three mutually perpendicular axes.  
  It has been known in the art to provide a programmed feed rate number FRN which represents the ratio of the desired vectorial velocity to the vectorial summation of the intended departure distances along mutually perpendicular X and Z axes. This requires a precalculation of the vectorial summation. More recently. it has been proposed in the art that the feed rate number should not be programmed. Instead. the programmed information includes the desired vectorial velocity along with the desired departure distances. Since the feed rate number is not precalculated. some means must be provided for determining its value. This requires knowledge of the vectorial summation of the programmed departure distances. For a two axis con trol system. this may be referred to as the hypotenuse H. where H is the square root of the sum of the squares of the programmed departure distances along the X and Z axes. Since the feed rate number FRN is expressed as a ratio of the desired vectorial velocity. or feed rate F. to the hypotenuse H. the value of the ratio F/H must be determined. This ratio is the feed rate number FRN and is used to modify a pulse train to a lower pulse rate to provide feed rate pulses used in controlling movement of the machine tool.  
  Previous proposals in the art for determining the feed rate number FRN from the programmed vectorial velocity F and the programmed departure distances have not directly calculated the square root of the sum of the squares ofthe programmed distances. Instead. the vectorial summation. or hypotenuse H. has been obtained from a look up table. such as a read only memory. for  
 providing values of the vectorial summation based on given values of the programmed departure distances. Other proposals have included employing separate digital computing means for computing the vector summation based upon a computer program. Still other pr o&#39; posals have provided estimates of the vectorial summation wherein certain constraints are employed. such as where at least one of the programmed departure distances is always equal to or greater than the other. In addition. these previous proposals have not provided means for directly calculating the value of the ratio of the vectorial velocity to the hypotenuse to obtain the feed rate number. Instead. they have employed multistage circuits wherein the complement or inverted value of one of these factors has been used to modify a pulse train which is then further modified by the other factor.  
  It is an object of the present invention to provide an improved feed rate generator for controlling a machine tool wherein the feed rate generator employs circuitry for directly calculating a function of the vectorial summation from the programmed departure distances.  
  It is a still further object of the present invention to provide an improved feed rate generator having circuitry for directly calculating the ratio of a function of the vectorial velocity to that of a function of the vectorial summation.  
  It is a still further object of the present invention to provide a machine tool control system employing hypotenuse calculating circuitry for directly calculating the value of the sum of the squares of signals having values which are functions of the programmed departure distances.  
  It is a still further object of the present invention to provide a machine tool control having a feed rate generator employing circuitry for normalizing the programmed departure distances and then calculating the value ofthe square root ofthe sum of the squares of the normalized departure distances to provide an output representation of the normalized vectorial summation.  
  It is a still further object of the present invention to provide a ratio calculator for receiving a signal representing the programmed vectorial velocity and a signal representing the normalized vectorial summation ofthe programmed departure distances and directly calculating therefrom the value of the ratio of the normalized vectorial velocity to the normalized hypotenuse.  
  In accordance with one aspect of the present invention. it is contemplated that programmed or commanded departure distances be presented calling for movement ofa machine tool along mutually perpendicular first and second axes at a velocity in accordance with a commanded vectorial velocity. First and second signals are generated exhibiting values which are respectively a function, such as the normalized value. of the commanded departure distance along the first axis and of the commanded departure distance along the second axis. The value of the square root of the sum of the squares of the first and second signals is calculated and a third signal is provided having a value in accordance with this calculation. A fourth signal is then provided having a value corresponding to the ratio of a function. such as the normalized value of the commanded vectorial velocity to the third signal. This fourth signal is employed for purposes of varying the pulse rate of a pulse train to provide a train of pulses for use in controlling movement of the tool.  
  In accordance with another aspect of the present invention. a ratio calculator serves to directly calculate the ratio of the value of a function of the commanded vectorial velocity to the value of a function of the square root of the sum of the squares of the commanded departure distances and provide an output signal having a value in accordance with that of the ratio.  
  This output signal is utilized in modifying the pulse rate of the train of pulses for use in controlling movement of the tool.  
 DESCRIPTION OF THE DRAWINGS The foregoing and other objects and advantages of the invention will become more readily apparent from the following description of the preferred embodiments of the invention as taken in conjunction with the accompanying drawings which are a part hereof and wherein:  
  FIG. 1 is a block diagram illustration of one application of the present invention to a machine tool control system;  
 FIG. 2 is a schematic-block diagram illustration of the interpolator control circuitry constructed in accordance with the present invention .FIG. 3 is a simplified block diagram of the hypotenuse calculator;  
  FIG. 4 is a graphical illustration used in explaining the operation of the hypotenuse calculator;  
  FIG. 5 is a schematic-block diagram illustration of the hypotenuse calculator;  
  FIG. 6 is a schematic-block diagram illustration of the ratio calculator;  
  FIG. 7 is a flow diagram illustration of the operation of the ratio calculator;  
 FIG. 8 is a block diagram illustration of an adder rate vmultiplier circuit employed in the function generator;  
  FIG. 9 presents graphical illustrations of wave forms used in illustrating the operation of the adder rate multiplier of FIG. 8;  
  FIG. 10 is a schematic-block diagram illustration of the circuitry employed in the function generator;  
  FIG. 11 is a schematic-block diagram illustration of the arc gating control circuitry employed in the function generator;  
  FIG. 12 is a graphical illustration showing quadrants of a circle used in describing the operation of the function generator; and,  
  FIG. I3 is a graphical illustration showing an arc of a circle and which is used in describing the circular interpolation operation of the function generator.  
 DESCRIPTION OF THE PREFERRED EMBODIMENTS General Description ;Rcference is nowmade to the drawings wherein the showings are for purposes of illustrating preferred embodiments of the invention only and not for purposes of limiting same. FIG. 1 is a block diagram illustrating a machine tool control system embodying the present invention for purposes of controlling movement of a machine tool along mutually perpendicular axes X and Z. This is known as a two axis machine tool control system. One application for such a control system is in conjunction with controlling a two axis turning machine. Whereas the invention is described with respect to such a two axis machine, it is to be appreciated that the various features may be employed in other applications, such as for controlling a three axis machine.  
  It is contemplated that the machine to be controlled includes a cross slide 10 having a longitudinal slide 12 mounted thereon for respective movement along X and Z mutually perpendicular axes. As is conventional.  
 these slides are driven simultaneously in response to servo motor is drivingly connected to a lead screw 14,  
 threaded to slide 10, for d&#39;rivi ng the slide at&#39;a velocity dependent upon the value of &#39;ia digital error signal provided by a bidirectional counter BC-l. This digital error signal&#39; re&#39; &#39;presents a pulse count and is converted into an analog representation thereof by means of a conventional digital-to-analog converter D-l. The magnitude of the analogs&#39;ignal controls the energization of the servo motor and hence. the angular velocity, neglecting load conditions. This&#39;cause&#39;s&#39; a corresponding angular velocity of&#39;lead screw l4,-The movement of slide 10 is&#39;at a linear velocity dependent upon the angular velocity of the lead screw and its pitch length.  
  A rotary pulse generator PG-l may be connected to the lead screw 14, so as to be driven thereby. for purposes of providing a pulse train having a fixed number of output pulses for each revolution of the lead screw. Whereas the pulse generator PG-I is illustrated herein as being a rotary pulse generator, other pulse generators may be employed. such as the linear feedback laser interfero-meter disclosed in the U.S. Pat. to Ralph H. Schuman. No. 3,648,276 assigned to the same assignee as the present invention.  
  The pulse generator PG-l preferably includes two tracks in quadrature so as to provide two trains of feedback pulses which are applied to a digitizer Dl-I. The digitizer Dl-I serves to combine the two pulse trains and determine therefrom the direction of angular rotation of the lead screw. The digitizer provides an output feedback pulse train having a fixed number of pulses per revolution of the lead screw and these feedback pulses are applied to oneinput of an anticoincidence circuit AC-l. Command pulses F are also applied to the anticoincidence circuit and these areobtained from a function generator FG. to be discussed in greater detail hereinafter. These command pulses exhibit a pulse rate which dictates the velocity of slide 10. The command pulses F and the feedback pulses from digitizer Dl-l are applied by the anticoincidence circuit AC-l,  
 to the up/down bidirectional counter BC-I. The anti coincidence circuit AC-l serves to prevent either a command pulse or a feedback pulse from being lost in the event that the two pulses occur simultaneously or overlap.  
  The up/down bidirectional counter BC-l serves as an accumulating register to produce a digital position error signal. This is a function of the number of pulses applied to the up input and thenumber of pulses applied to the down input of the counter. The bidirectional counter provides a digital position error signal which is converted into an analog signal by the digitalto-analog converter D-land is then amplified by amplifier A-l and supplied to control the servo motor SM-l. The slide 10 is then driven at a linear velocity along the X axis in dependence upon the magnitude of the error signal.  
  The digital control loop ZL for controlling movement of slide 12 along the Z axis by a lead screw 16, is structured and operates in the same manner as that discussed hereinabove with respect to the X axis control loop XL. Consequently. similar components in the two loops are identified with similar&#39;reference charactersto simplify the description of the invention herein. The  
 command pulses F for the Z axis control loop are 0b-&#39; tained from the function generator PG and the pulse rate dictates the linear velocity-of slide 12 along the Z Each feedback pulse represents a basic incremental distance. such as 0.000] inches. Similarly, each command pulse represents a basic incremental desired distance of movement. such as 0.000] inches. For linear operation then. if the programmed departure distance for the X axis is representative of 3 inches. the X axis servo control loop XL will receive exactly thirty thousand command pulses from an X displacement control circuit XDC. As will be discussed hereinafter. this control circuit may take the form of a down counter which receives a displacement command for the programmed X departure distance and then meters the appropriate number of command pulses F to the X axis control loop. A similar 2 displacement control circuit ZDC meters command pulses F to the Z axis control loop.  
 lnterpolator Circuitry With reference to FIG. I. the interpolator generally includes a feed rate generator FRG and a function gen erator FG. This is a pulse rate control system in that each command pulse F or F commands a specific length oftravel of a tool. For example. each command pulse may represent a commanded displacement of 0.000l inch along an associated axis. The pulse rate of the command pulses commands a certain axis velocity.  
 . For example. one KHz pulse rate may represent a rate of 6 inches per minute. Although. in the preferred embodiment. the information is coded in binary format, it is to be appreciated that the circuitry employed may be used with binary coded decimal or straight decimal coded information.  
  The intcrpolator control circuit functions to reduce a high frequency input clock signal by programmed inputs to an output pulse rate proportional to the programmed inputs and to distribute these pulses to the X axis control loop XL and the Z axis control loop ZL to generate a programmed path. The high frequency input signal originates from one of two sources. The source depends upon whether the programmed operation is to be in terms of tool velocity as a function of time or tool velocity as a function of spindle speed. If the programmed operation is to be dependent on spindle speed in inches per revolution. then this will normally be referred to herein as an lPR operation mode. In the lPR mode. the basic pulse rate F applied to the feed rate generator FRG will be obtained from a suitable spindle generator 50. On the other hand. if the programmed operation requires that tool velocity be a function of time. then this will normally be referred to hereinafter as an lPM operation mode. In the IPM mode. the basic pulse rate F will be based on clock pulses obtained from a high frequency clock source CS.  
  The interpolator control circuitry reduces the basic pulse rate F,, to a lower pulse rate in accordance with programmed inputs obtained from a data distribution and control circuit DDC and then distributes the command pulses F and F to the X control loop XL and the Z axis control loop ZL.  
  The data distribution and control circuit DDC receives instructions from a conventional tape reader TR and then distributes commands to the interpolator control circuitry. The program itself may be recorded upon a suitable tape such as a multitrack. punched paper tape T which is read by a conventional tape reader TR. It is contemplated that the program will include blocks of information for various cutting operations. Each block may include a programmed desired vectorial velocity F which may be expressed in terms of inches per revolution lPR or in terms of inches per minute IPM.  
 If the program requires lPR operation, then control circuit DDC actuates a suitable circuit. represented by a single pole. double throw switch 20 to connect the output of the spindle generator to the feed rate generator FRG so that the basic pulse rate F is dependent upon spindle speed. On the other hand. if the operation commanded is IPM. then switch 20 is actuated to connect the clock source CS with the feed rate generator FRG so that the basic pulse F is dependent upon that of the clock source.  
  Each block of information also includes X and Z words which provide command information dictating the commanded displacement of the slides along the X and Z axes, respectively. This is the normal incremental programming for use in linear interpolation. However, for circular interpolation. the X word is referred to as the l word and the Z word is referred to as the K word. For circular interpolation, the incremental distance from the center of the arc to be traced to the beginning of the are as measured along the X and Z axes is programmed as the l and K words respectively. The arc center is the point about which the radius of the arc is rotated. Consequently then. the l word defines the address for the arc center offset as measured along the X axis and the K word represents the address for the arc center offset as measured along the Z axis.  
  In addition, each block includes a G word which serves a preparatory command coded to call for such functional operations as linear interpolation. circular interpolation in a clockwise direction. and circular interpolation in counterclockwise direction. The G word along with an X sign and a Z sign are applied to the function generator PG for use in controlling circular interpolator operation. The structure and operation of the feed rate generator and function generator will be described hereinafter in greater detail.  
 lnterpolator Control (FIG. 2)  
  Referring now to FIG. 2, the interpolator control circuit is illustrated in greater detail than that shown in FIG. 1. More specifically. the feed rate generator FRG includes a feed rate override control circuit FC which serves to receive pulses at the basic rate F and reduce the pulse rate in manually selectable 10% steps from 0 to I207: of the programmed rate. The output pulse rate is referred to as F This pulse train is then further reduced by a scaling circuit SC which serves to reduce the pulse rate by a factor for purposes of compensating for normalization techniques employed at a later point. The pulse rate of pulses obtained from the scaling circuit SC is referred to as pulse rate F Pulse rate F is further reduced by a ratio rate multiplier RMF in dependence upon a modifier obtained from a ratio calculating circuit RC. The purpose of normalization and circuitry involved will be discussed in greater detail hereinafter. The ratio is the normalized vectorial velocity number /F/ to the normalized hypotenuse number /H/. The hypotenuse is the vectorial summation of the programmed X and Z displacements and is equal to the square root of the sum of the squares of the programmed departure distances. in linear interpolation. the X displacement word is treated as the l word and the Z displacement is treated as the K word. The hypotenuse calculator circuit HC receives the l word and the K word and then develops an output signal which is equal to the normalized hypotenuse /H/ which is a function of the actual hypotenuse H. The ratio calculator RC receives the F word and the normalized hypotenuse word /H/. The F word is normalized in the ratio calculator scaling circuit so that the output signal from the ratio calculator is proportional to the ratio of the normalized /F/ word to the normalized hypotenuse word /H/. This ratio is employed as amodifier by the rate multiplier RMF to reduce the pulse rate F to a pulse rate F Pulse rate F serves as the cutter velocity pulse rate and is fed to the function generator F0.  
  The function generator F0, to be described in detail hereinafter. serves to receive pulses at the cutter velocity pulse rate F and distribute command pulses F and F to the X control loop XL and the Z control loop ZL. The function generator FG includes an 1 counter 1C and a K counter KC which provide modifiers to an 1 rate multiplier lRM and to a K rate multiplier KRM. The 1 counter 1C serves in linear interpolation as a means for storing the X word and similarly. the K counter serves in a linear interpolation for storing the Z word. In circular interpolation these counters operate as counters for generating an arc in accordance with the programmed arc center offset l word and K word. The l (or X) word is normalized so that the F pulse rate is proportional to the product of a constant, the pulse rate F and the normalized /l/ word. Similarly, the K (or Z) word is normalized and used as a modifier for the K rate multiplier KRM such that the output pulse rate F; is proportional to the constant. the cutter velocity pulse rate F and the normalized lK/ word.  
  The output pulse rate FX or F is an unnormalized pulse rate. This follows since, as will be appreciated from the discussion of normalization hereinafter, that the output of the scaling circuit SC is a pulse rate F which, when multiplied by the ratio (/F/)/(/H/), provides an output pulse rate F which is proportional to the ratio of the unnormalized F word and the normalized hypotenuse /H/. When this pulse rate is multiplied by the normalized /l/ word at the rate multiplier lRM, the output pulse rate F, is proportional to the programmed vectorial velocity F and the ratio of the normalized /l/ word to the normalized /H/ word. The ratio of the normalized /l/ word to the normalized /H/ word is equal to the ratio of the unnormalized 1 word to the unnormalized H word and consequently. the output pulse rate F is the unnormalized pulse rate. The same is true for pulse rate F For linear interpolation. the X displacement control XDC and the Z displacement control ZDC respectively receive an X word and a Z word. These controls may take the form of prcsettable down counters which are preset in accordance with the programmed displacement distances represented by the X word and the Z word. These circuits serve to meter the appropriate number of pulses at the pulse rate F of F to the respectively associated digital control loops XL and ZL.  
  1n circular interpolation the l and K words represent the incremental distance from the center of the arc to the beginning of the are, as measured along the X and Z axes. The are center is the point about which the radius of the arc is located. The function generator is provided with a G word (see FIG. 1) which serves to command either clockwise or counterclockwise and the 1 counter serves as a counter and the K counter serves as a counter rather than storage registers, as in the linear mode of operation. The output from the K rate multiplier KRM is supplied as an input to the 1 counter and similarly the output of the 1 rate multiplier lRM is supplied as an input to the K counter. This circuitry serves to effectively trace an arc and its mode of operation and circuitry will be described in detail hereinafter;  
  Having provided a general description of the circuitry and mode of operation of the interpolator circuitry. attention is now directed to the following description which deals in greater detail with the specific circuitry employed and the operation involved.  
 Normalization All of the data provided to the interpolator control circuitry is processed in the natural binary form in the embodiment of the invention illustrated herein. The F, 1 and K words may be obtained from the tape reader in BCD format. 1f so, it is contemplated that the words be converted to a natural binary form for use by the sealing circuitry in scaling the basic pulse rate F to a lower pulse rate. These words are also normalized. This is done by shifting the binary numbers in registers such that the results fall within a fixed range of values. This is done for two reasons; namely, to reduce the amount of electronics required and yet maintain the required velocity accuracy, and to reduce the clock rates within the interpolator control. The normalized values are compensated for in the feed rate generator FRG andin the function generator FG.  
  1n the feed rate generator FRG. the inputs i.e. the X. Z, l, and K words are normalized such that the larger number is between 1 and 2. In terms of 1PM operation then, the calculated hypotenuse will be normalized between 1 and 2.828 inches. The hypotenuse is calculated each time displacement information is read into the interpolator control. The F word is also normalized with the use of a register such that it is shifted to a normalized value between 1 and 2. The ratio of the normalized /F/ word to the normalized hypotenuse word /H/ is calculated with the use of the ratio calculating circuit RC.  
  The interpolator data is processed in natural binary form. This may be accomplished, for example. by multiplying each X and Y commanded displacement by a factor of 10 in order to convert any real numbers to natural decimal numbers. The result is then converted into a natural binary number and normalized (con-&#39; verted to a real binary number) in the hypotenuse calculator. For example, if the programmed real number for the X axis displacement is 3.0, the natural decimal number would be 30,000. Similarly, if the programmed Z axis real number is 4.0 inches, the natural decimal number would be 40,000. When a natural decimal number of 30,000 is converted into a natural binary number, the binary number is 1 110101001 10000. This natural binary number when converted into a normalized (real) binary number is 0.11101010011. The rational decimal equivalent of this normalized binary number is the function 30,000/32,768 for a real decimal equivalent (approximately of 0916). If a natural decimal number of 40,000 be converted into a natural binary number, the number would be 1001 1 10001000000. The normalized real binary number would be 1.001 1 10001. The rational decimal equivalent then is the fraction 40,000/32,768 for a real decimal equivalent (approximately) of 1.221. The bypotenuse calculation for this triangle then is 1.526 inches (real decimal equivalent of the normalized binary hypotenuse).  
 The programmed F word in [PM is multiplied by 10 to convert it a natural decimal number. This is then converted into a natural binary number and the natural binary number is normalized to produce a real binary number between 1 and 2. Table 1 below illustrated the conversion of an F word of 10.0 in lPM.  
 TABLE] 5 Programmed F Word (IPM) lll.(l  
 Natural Decimal Number l()() &#39;0 Natural Binary Number 1 100100 Normalized (Real) Binary Number 1.100] Rational Decimal Equivalent l()() Real Decimal Equivalent 1.563  
  The output of the ratio calculator then is the ratio of 1.563 to 1.526 or 1.024. The pulse rate is reduced .in 1PM by a still further factor of4 so that the output frequency rate F.-.- FA l.024)/4).  
  In the function generator FG. the input pulse rate F 7 is divided into two output pulse rates F and F In the preferred form of the invention. the function generator does not employ counter rate multipliers for pulse rate modification. Instead. the function generator employs arithmetic circuits. to be described in detail hereinafter. to modify the pulse rates. Also. unlike the feed rate generator FRG. which normalizes by shifting the numbers the function generator preferably employs circ uitry normalization by adjusting the denominator of the transfer equation. Adjusting the denominator effectively adjusts the size of the function generator to the displacements or radius programmed. The function generator employs adder-accumulator registers for modifying input pulse rates. Carry signals from selected bits ofthe function generator adders are used as output pulses. By selection of the proper carry bit used for the function generator output. the size (denominator of the transfer equation) is adjusted. The selection of the carry hit is determined by the size (most significant bit) of the larger of the two modifier inputs (1 word and K word).  
  In the normalizing operation in the feed rate generator FRG. the decimal F word is always treated as.a full four digit number without a decimal point. The F word is normalized by dividing it by an even binary multiple equal to or just less than the F number so that the normalized /F/ word is less than 2 and equal to or greater than 1. The denominator (next even binary multiple) is referred as to 2&#34;. For example if the F word. when converted to a natural decimal number. is 1230. then the even binary multiple which is equal to or just less than the F number would be 1024. This is equal&#39;to 2&#34;&#34;&#39; where m equals 10. The normalized /F/ word then would be the ratio 1230/1024. which is equal to 1.201171875. if carried out to 10 decimal places. In order to determine the denormalized F word. the normalized /F/ word must be multiplied by 2&#39;&#34;; that is, F (/F/) 2&#34;. The sealing control circuit SC. as will be described hereinafter. multiplies the pulse train by 2&#34;. i 0 When this factor 2 is multiplied with the ratio (/F/l/(lHl). the output pulse rate F is proportional to the ratio of the unnormalized F word to the normalized hypotenuse word /H/. When this pulse rate multiplied by the normalized /l/ word in the function generator FG. the output pulse rate F is proportional to the ratio of the normalized /l/ word to the normalized /H/ word multiplied by the unnormalized F word. Consequently then. this is essentially the same thing as stating that the output pulse rate F is proportional to the ratio of the unnormalized l word to the unnormalized H word multiplied by the unnormalized F word.  
  1n the following sections. detailed descriptions are presented with respect to the circuitry employed in the feed rate generator and the function generator. These descriptions will further discuss the manner in which the circuitry achieves normalization.  
 Feed Rate Override Circuit Provisions are made for manual adjustment to achieve feed rate override in selectable 10% steps from 0 to 120% of the programmed rate. This is accomplished with the feed rate override circuit FC illustrated in FIG. 2. A feed rate override number FRO is supplied to a feed rate multiplier FRM for purposes of reducing the basic pulse rate F in selectable 10% steps of the programmed rate. The output frequency from the rate multiplier is referred to as frequency rate F The feed rate multiplier FRM may take any conventional form such as a 12 bit binary rate multiplier which basi cally is comprised ofa binary up counter. called a multiplier counter. that counts the input pulses and gating circuitry. called multiplier gates. that gate the counter with a modifier input and the input pulses to produce an output frequency. All of the rate multipliers employed in the feed rate generator FRG may take this form. The modifier for the feed rate multiplier FRM is the feed rate override number FRO X 100 (indicative of 100%) and divided by a factor of 2. Consequently then. the total modifier applied to the multiplying input of the rate multiplier is (FRO) 100/2.  
  The feed rate override rate multiplier FRM may be a six bit multiplier and in such case. the binary pattern of the FRO word is a six bit binary pattern. The binary pattern is representative of the percentage override desired in 10% steps. The pattern may be selected by an operator manipulating a switch to supply a selected binary number for a selected FRO word. This may be implemented in the manner as shown in FIG. 1 wherein a switch arm Zl is illustrated as being selectively engageable with one of a plurality of circuits each of which provides a binary FRO word for application to the feed rate multiplier FRM. It is to be appreciated that such FRO words would include modification so that the FRO word is in effect multiplied by l00&#39;and divided by a factor of 2. Consequently then. with a six bit feed rate override rate multiplier. the output frequency F is proportional to F0 (FRO)/(2 100.  
 Feed Rate Scaling Circuit The feed rate scaling circuit SC provides compensation for the F word normalization which takes place in the feed rate generator. As will be recalled from the discussion dealing with normalization. the normalized /F/ word may be denormalized by multiplying it by 2&#34; &#39;which is equal to the next lower even binary multiple ling rate multiplier serves to multiply pulse rate F by the ratio of 2&#39;&#34; to 2 or Fm (2&#34;&#39;)/(2&#34;-) The factor 2&#39;&#34; is found by using only the most significant bit of the binary F word. This is accomplished in the embodiment of the invention illustrated herein by applying the binary F word as a 12 bit word to a l2 bit. parallel to serial shift register FR-l. This shift register receives the F word as a parallel input and upon receipt of shift input pulses provides a bit serial output with the most significant bit being shifted first and the least significant bit being shifted last. ln shifting this binary number from the F register FR-l, the most significant bit 2&#39;&#34; is detected as the bits are shifted into a serial to parallel shift register FR-Z. This operation is commenced upon closure of a suitable load actuating switch represented herein by a normally open switch 30. Closing switch 30 causes a binary 1 signal to enable an AND gate 32. This permits AND gate 32 to pass clock pulses from a suitable clock source CK. Clock source CK may be associated with clock source CS or may be a separate source of clock pulses. These clock pulses from source CK are used as shift pulses for shifting the F word from register FR-l into register FR-Z. It is only necessary that the 12 bits of the F word be shifted and consequently. only l2 clock pulses need to be provided. This may be accomplished with the use of a presettable pulse counter 34 which serves to enable an AND gate 36 for a count of N. where N corresponds to 12 pulses. This permits AND gate 36 to pass twelve pulses. Thereafter, the N counter 34 disables AND gate 36. The output pulses from AND gate 36 are applied to a clock or shift input of register FR-2 so that a bit serial pulse train may be entered into this twelve bit register. The clock pulses are also applied to the shift input of register FR-l so the bit pattern stored in register FR-l is shifted one bit at a time with the most significant bit being shifted first. The output from the register FR-l is applied through a normally enabled AND gate 38 to register FR-Z.  
  As the bit pattern from register FR-l is being shifted into register FR-Z, a flip-flop 40 operates to detect the location of the most significant bit of the F word. This is accomplished by connecting the output of the least significant bit stage of register FR-2 to the reset input of flip-flop 40. Consequently then. when the first significant bit of the F word is shifted into register FR-Z, the flip-flop 40 will bercset to disable AND gate 38. The AND gate then will carry a binary 0 level signal at its output and this signal is applied to the input of register FR-2. Thereafter, each clock pulse applied to the clock input of register FR-Z, will shift abinary 0 level signal into the register. Only one bit position of register FR-2 will have a logic one level signal when the shift operation is completed. The l2 bit output pattern from register FR-2 provides a modifier binary number of 2&#39;&#34; and this is used in scaling the pulse rate F with the sealing rate multiplier SRM.  
 Hypotenuse Calculator The hypotenuse calculator serves to calculate the hypotenuse of the right triangle formed by the X and Z displacements in linear interpolation or the l and K are center offsets in circular interpolation. In the preferred embodiment of the invention, to be described in detail with reference to FIG. 5, the inputsto the hypotenuse calculator are normalized the larger number is between l and 2. However, before dealing with the spel2 cific circuitry employed in FIG. 5, reference is made to FIGS. 3 and 4 which respectively present a simplified block diagram illustration of the hypotenuse calculator together with a graphical illustration of the operation.  
  The hypotenuse. calculator includes a presettable down counter lDC which is initially set to count condition in accordance with the number represented by the programmed l word. The calculator also includes a presettable up counter KUC which is initially set to a count condition corresponding with the K word. As will be discussed hereinafter. these counters are preferably multistage binary counters, although for the purposes of this discussion. they may be considered as decimal counters. The down counter lDC has its output applied to a pulse rate multiplier RM-l for purposes of multiplying an input frequency signal F,-,, by the count in the down counter to obtain an output pulse rate F,,. Similarly. the up counter has its output applied to an associated rate multiplier RM-2 for purposes of multiplying the input frequency rate F,-, by a modifier in dependence upon the count in the up counter to obtain an output frequency rate F The output frequency F,, from the up counter rate multiplier RM-Z is applied to the count input of the presettable down counter whereas the output frequency F,,&#39; from the down rate multiplier RM-l is applied as an input to the. up counter KUC. During operation. the input frequency pulses F,-, are applied to both rate multipliers RM l and RM-2. The up counter KUC counts in an upward direction for each pulse in accordance with the pulse rate F,,. The down counter counts down one increment for each pulse applied thereto at a pulse rate F A zero detect circuit ZD serves to monitor the output of the down counter IDC and operates to stop clock pulses F, from being applied to the rate multipliers when the count condition of the down counter has reached a zero count status. At this point, the count status of the up counter KUC is a count representative of the value of the hypotenuse H. That is. once the zero detect circuit has detected a zero count condition of the down counter lDC. the count status of the up counter KUC is a value equal to the square root of the sum of the squares of the initial counts preset into the down counter and the up-counter.  
  This operation may be more readily understood from an examination of the graphical illustration of FIG. 4; If the initial count for the X axis be represented by X and that for the Z axis be represented by Z. then a right triangle having a hypotenuse H is defined. The vector representation of H describes a point X Z on an arc of the circle having a radius signal to H. As the down counter counts down and the up counter counts up. the point defined by the end of the vector traces an arc of a circle. When the down counter has reached a zero count. the value of X is zero. At this point, the hypotenuse H is equal to the final value of the Z count in the up counter.  
 Detailed Description of Hypotenuse Calculator Circuitry In the preceding discussions, the hypotenuse calcula-&#39; tor HC was discussed with reference &#39;to a simplified showing and did not include normalization of the information data. Preferably, the invention is practiced by employing a hypotenuse calculator which includes normalization and a preferred embodiment of the calculator is illustrated in FIG. 5. For purposes of simplifying an understanding of the invention. the comparable circuits in FIGS. 3 and 5 are labeled with like character references.  
  The l word and the K word obtained from the tape reader by means of the data distribution and control circuit may be stored in parallel to serial storage registers 50 and 52 of FIG. 5. The number of bit stages employed is dependent upon the accuracy of resolution required in the operation. For example. each storage register may take the form of a bit storage register. The l word and the K word stored in registers and 52 are stored as natural binary numbers. Each of these registers is operative as a shift register to shift the stored binary number in hit serial sequence with the most significant bit being shifted first and the least significant bit being shifted last in synchronism with shift pulses applied to the respective shift inputs of the registers. These shift inputs are clock pulses obtained from a clock source CKH. This clock source may be incorporated in a master clock that includes the clock source CS or the clock CK described herein with reference to FIG. 2. The pulse rate of the shift pulses from the clock source-CKH may be relatively high. such as on the order of 5.6 mHz. The shift pulses from clock source CKH are applied to the shift inputs of registers 50 and 52 through an AND gate 54 when this gate has been enabled by a flip-flop 56. This flip-flop is normally in its reset condition to maintain AND gate 54 disabled. However. when AND gate 54 is enabled to supply shift pulses to registers 50 and 52, the contents of these registers are shifted in bit serial fashion and loaded into serial to parallel shift registers 60 and 62 respectively. During this process as will be discussed below. the l word and the K word are normalized.  
  The loading of shift registers 60 and 62 is commenced by providing a suitable load signal represented herein by closure of a normally open switch 64. This actuates a suitable one shot circuit 66 which applies a binary 1 pulse to the clear input of each of the registers 60 and 62. This is conventional in the art and serves to effectively reset the registers so that all bit positions are occupied by binary 0 level signals. This binary 1 pulse from the one shot circuit 66 is inverted by an inverter 68 which applies a momentary binary 0 pulse to the C input of flip-flop 56. This pulse has a negative going transition which is then followed by a positive going transition. The positive edge serves to actuate the flipflop. This flip-flop may take various forms. Preferably. it takes the form known as a combined RS and D flipflop. This type of flipflop has a D input and a C input. The flip-flop also has a 0 output and a 0 output. In addition. the flip-flop is provided with a set input S and the reset input R. As is known. ifa binary 1 level signal is applied to the D input. then upon application of a positive going pulse to the C input. the flip-flop will be actuated to a state wherein the Q output terminal carries a binary 1 signal and the Q terminal carries a binary 0 signal. Consequently then. the one shot circuit provides a positive pulse for purposes of clearing the shift registers 60 and 62 and the trailing edge of that pulse is used by flip-flop 56 to provide a binary 1 signal to enable AND gate 54. There is a slight time delay before AND gate 54 is enabled and this time delay is sufficient to permit the shift register 60 and 62 to be cleared.  
  With AND gate 54 being enabled by flipflop 56, the shift clock pulses from clock source CKH are applied to the shift inputs of storage registers 50 and 52 as well as to the shift inputs of the l shift register and the K shift register 62. The data in registers 50 and 52 is then simultaneously shifted in bit serial sequence into registers 60 and 62 respectively.  
  Normalization of the l word data and the K word data is achieved by an operation which includes detecting the most significant bit of the larger of the two words. This is achieved by connecting an OR gate 70 to receive the binary level signal of the most significant bit position of each register 60 and 62. Consequently then, when the most significant bit of the larger of the two words is shifted into the most significant bit position of its associated register 60 or 62, this condition is detected by OR gate 70 which applies a binary 1 signal to the reset input R of flip-flop 56. This causes the output of flip-flop 56 to change state so that the Q output terminal carries a binary 0 signal to disable AND gate 54 and thereby prevent further shift pulses from clock source CKH from being applied to registers 50, 52, 60 and 62.  
  While shifting the data from registers 50 and 52 into registers 60 and 62., the data is also loaded into the l down counter IDC and the K up counter KUC. That is. shift register 60 is a serial input to parallel output shift register for loading the l down counter. The K shift register 62 is also a serial input to parallel output shift register for loading the K up counter KUC. When the most significant bit of the larger of the two words I and K has been detected. flip-flop 56 is reset. This causes a one shot circuit 72 to apply a load triggering pulse to the load inputs of the l down counter lDC and the K up counter KUC so that the normalized /l/ word is loaded into the l down counter and the normalized /K/ word is loaded into the K up counter. These counters are now preset to count conditions corresponding with the normalized /l/ count and the normalized /K/ count. Preferably. the 1 counter and the K counter have the same number of bit positions as the l shift register and the K shift register respectively. In the example being given. each counter is a 12 bit binary counter. The 12 bit binary pattern representing the count status of each counter is applied to an associated rate multiplier for purposes of reducing an input pulse rate to a lower pulse rate. In the case of the l down counter lDC. its output is applied to a twelve bit binary rate multiplier RM-l whereas the output of the K up counter is applied to an associated binary rate multiplier RM2. The output pulse rate from the rate multiplier RM-l is applied as input count pulses to the count input of the K up counter where the output pulse rate of rate multiplier RM-Z is applied as count pulses to the count input of the down counter.  
  The calculating operation is commenced after the l counter and the K counter have been loaded. One shot circuit 72 applies a positive pulse to cause this loading operation. This output pulse is inverted by an inverter &#39;74 so that a momentary binary 0 pulse is applied to the C input of a flip-flop 76. Since flipflop 56 is in its reset condition, it applies a binary 1 signal to the D input of flip-flop 76. Consequently then, on the trailing or positive going edge of the binary 0 signal pulse from inverter 74., flip-flop 76 is actuated. This causes a binary 1 signal to be applied by its 0 output to enable an AND gate 78. This AND gate then passes clock pulses from the clock source CKH which serve as the input frequency rate F,-,, to the rate multipliers RM-l and RM-2.  
  The down counter lDC will now count down in accordance with the pulse rate of the pulses obtained from the up counter rate multiplier RM-2 while the up counter KUC counts in an up direction in accordancce with the pulse rate of the pulses provided by the down rate multiplier RM-l. As discussed hereinbefore with reference to the showing in H0. 3, when the down counter has obtained a count condition of zero. the count provided by the up counter KUC is of a value corresponding with the normalized hypotenuse /H/. This condition is detected with zero detector ZD connected to the output of the down counter lDC. Once a zero count condition has been detected. the zero detector ZD applies a trigger pulse to reset flip-flop 76 and thereby disable AND gate 78 to prevent further pulses from being applied to the rate multipliers RM-l and RM-2. The output of the up counter KUC is a 12 bit binary signal and is of a value corresponding with the normalized hypotenuse /H/. This signal is now used by the ratio calculator RC for purposes of calculating the ratio of the normalized /F/ word to the normalized /H/ word.  
 Ratio Calculator The ratio calculator RC (FIG. 2) calculates the ratio of the normalized /F/ word to the normalized hypotenuse word /H/. The circuitry employed to perform this calculation preferably takes the form as that as illustrated in FIG. 6 to which attention is now directed.  
  The F word is stored in natural binary form in a parallel input to serial output storage register 80. The input supplied to the register may be supplied from the data distribution and control circuit DDC in accordance with information read by the tape reader TR. Register 80 may be a conventional 12 bit parallel input to serial output shift register which serves to provide an output in hit serial fashion as clock pulses are applied to the shift input of the register. The output pattern presents the most significant bit first and the least significant bit last. The F word stored in register 80 is shifted in bit serial sequence into an accumulator shift register 82 when the shift load input S/L receives a binary 1 signal. This accumulator shift register is conventional in the art and may receive a binary signal for storage with the signal being received in bit serial fashion or with the signal being received in hit parallel fashion. The mode of operation depends upon whether a binary 1 signal or a binary 0 signal is applied to the shift-load input S/L. When a binary 1 signal is applied to this input. one bit of information is shifted into the shift register in series fashion for each clock pulse applied to the clock input of the shift register. When a binary 0 signal is applied to this shift-load S/L. a multiple bit binary signal is shifted in parallel for storage when a clock pulse is ap plied to the clock input CLK.  
  The operation of the ratio calculator may commence once the accumulator shift register 82 has been loaded with the F word and the hypotenuse calculator has completed its calculation. Information in the F shift register 80 may be shifted into register 82 on command from various sources. In the embodiment illustrated.  
  the tape reader TR serves to decode an end of block EOB designation by means of a decoder 84 and in response thereto. sets a flip-flop 86. This flip-flop then provides a load A signal which indicates that the accumulator shift register is to be loaded. The accumulator register will hereinafter be frequently referred to as the A register. The load A signal is applied as a binary l signal to the shift-load input S/L of the accumulator register 82 to condition the register to receive the F word in bit serial fashion. The load A signal also enables AND gates 88 and 89. This permits clock pulses from a suitable clock source CKR to be passed by AND gate 89 to register and by AND gate 88, through an OR gate 90 to register 82. Clock source CKR may be a portion of a master clock which also includes clock sources CS (HO. 1) or CK (FIG. 2) or CKH (FIG. 5). As the clock pulses are applied to registers 80 and 82, the F word is shifted in bit serial fashion from register 80 into register 82. The F word is normalized when shifted into register 82 by detecting when the most significant bit of the F word is located at a particular bit position of the 12 bit accumulator register 82. The selected bit position for this 12 bit register is bit position 10. Consequently, when this bit position is occupied by a binary 1 level signal. an output taken from this position of the accumulator register serves to reset flip-flop 86. This removes the load A signal to prevent further shift pulses from being applied to register 80. ln this manner. the F word from register 80 has been loaded into register 82 and normalized.  
  The calculating operation of the ratio calculator commences when a flip-flop is set. This may be accomplished in various ways. In the embodiment illustrated herein. when flip-flop 86 is in its set condition. its 0 output provides a load A signal. This is a binary 1 signal and is inverted by an inverter 102 to disable an AND gate 104 and thereby prevent flip-flop 100 from being set. Once the accumulator has been loaded. flipfiop 86 is reset and its output terminal 0 provides a binary 0 signal. This is inverted by inverter 102 to enable AND gate 104. This condition is indicative that the F word has been loaded in accumulator register 82. The ratio calculation also requires that the normalized hypotenuse word /H/ has been calculated (FIG. 5). Consequently. during the time that the hypotenuse calculator is performing its calculating operation. it is desirable that flip-flop 100 not be in its set condition to cause a ratio calculation. This may be accomplished by employing a switch which serves to disable AND gate 104 so long as the hypotenuse is being calculated. In the embodiment illustrated. this is illustrated by a simple normally open switch 106 which is actuated to a closed condition during the hypotenuse calculation operation to apply a binary 1 signal which is then inverted by an inverter 108 to disable AND gate 104. Once. however. the accumulator register 82 has been loaded and the hypotenuse calculation has been completed. both inputs to AND gate 104 are satisfied and flip-flop 100 is actuated to its set condition. When this flipfiop is in its set condition. its output terminal 0 carries a binary 1 signal indicative of a command for ratio calculate. This binary signal is applied by flip-flop 100 to enable an AND gate 110 to pass clock pulses from clock source CKR to the clock input CLK of accumulator shift register 82. Since flip-flop 86 is reset. a binary 0 signal is applied to the shift-load input S/L of register 82. Consequently then, in the absence of other instructions. each clock pulse will cause a parallel loading of information into the register of the binary information from the sum output of a full adder 112 to be discussed hcreinbelow.  
  When flip-flop 100 is set. it also enables an AND gate 114 to pass clock pulses from the clock source CKR through the AND gate and thence. through a succeeding OR gate 116 to the clock input of a ratio shift register 118. This register is constructed somewhat similar to that of the accumulator register 82 in that it includes provisions for receiving information shifted therein in series or in parallel. Thus. register 118 has a shift-load input S/L. When the signal level applied to this input is at a binary 1 level. the ratio register 118 will be loaded in parallel for each clock pulse applied by OR gate 116 to the clock input. The ratio register 118 is initially preset to place a binary 1 level signal in its least significant bit position. This may be implemented by permanently connecting the parallel input for the least significant bit stage to a binary 1 source. This may be accomplished. as illustrated in FlG. 6, wherein a simple normally open switch 124 is actuated to apply a binary 1 level signal to a one shot circuit 126. The one shot circuit then applies a momentary binary 1 signal pulse which is inverted by an inverter 128 to apply a binary signal pulse to the shift load input S/L of register 118. As will be appreciated from the following description. during the calculating operation. information bits are shifted from right to left in register 118, as viewed in FIG. 6, until the preset binary 1 bit has been shifted to the left to a position which is identified herein as output stage R This corresponds with the most significant bit stage. When the preset binary 1 signal has been shifted to position R a reset signal is applied to the reset input of flip-flop to indicate that the ratio calculation has been completed. The output obtained from the ratio shift register 118 at that point in time will correspond with the ratio of the normalized /F/ word to the normalized hypotenuse /H/. This is employed as a modifier for the feed number rate multiplier RMF for purposes of scaling the pulse rate F to a lower pulse rate F The full adder 112 is a conventional binary adder circuit and effectively provides a subtraction process wherein the value represented by the normalized /H/ word is subtracted from the value in the accumulator for each clock pulse. This is done with binary level signals and to accomplish the subtractive process. an addition process is carried out. The ones complement of the normalized /H/ word is applied to the X input of the full adder. The accumulator contents are applied to the Z input of the adder. A binary 1 carry in signal is applied to the carry in position by wiring the carry input to a binary 1 source. The carry output of the full adder is not employed in this operation. The summation output of the adder value of corresponding with A l /H This corresponds with the value ofA /H/. where A is the value of the binary contents of the accumulator 82. This summation signal is applied as a parallel input to the accumulator and its value is doubled by wiring each bit output to the next higher bit input of the accumulator.  
  Depending upon the results ofa comparison made by comparator 120 of the value of the normalized /H/ word and the value of the accumulator register contents. the output sum of the full adder is doubled and entered into the accumulator. or the contents in the accumulator register is doubled by shifting the contents by one position to the next most significant bit position.  
  To facilitate an understanding of the manner of operation of the ratio calculation circuitry RC. attention is now directed to FIG. 7 which presents a flow diagram illustrating the operation of the circuitry of FIG. 6. ln followingthe description. it will be useful to refer to both FIGS. 6 and 7 simultaneously. The ratio calculation commences once clock pulses are applied through AND gate 114 and OR gate 116 to the clock input of the ratio shift register 118. The ratio clock signal is also provided as a clock to the accumulator register through AND gate and OR gate 90. The information in the accumulator register is shifted one position to the left to double the value of its contents or the contents will be changed by supplying thereto in parallel format signal corresponding with twice the summation of the output of the full adder; that is. 2(A /H/).  
  For each clock pause. the comparator serves to compare the contents of the A register or accumulator 82 with the value represented by the normalized hypotenuse word /H/. obtained from the hypotenuse calculator (FIG. 5). lf the value of the contents of the A register is less than that of the normalized hypotenuse /H/. then comparator provides a binary 1 signal on its output. lf the comparison indicates that the value of the contents of the A register is equal to or greater than that of the value of the normalized hypotenuse /H/. the comparator provides a binary 0 signal. The binary level of this signal is applied to the shift/load input of the accumulator register 82 to control its mode of operation. When a binary 1 signal is applied to this input. a parallel load operation is instituted whereby a signal corresponding with 2(A /H/) is entered into the accumulator. lfa binary 0 signal is applied to this input S/L. then on the next clock pulse applied to the input of accumulator 82, its contents are shifted one place to the left to double its value.  
  If the first comparison indicates that the value of the contents of the A register is less than that of the normalized hypotenuse /H/. comparator 120 applies a binary 1 signal to cause the accumulator to be parallel loaded and have its contents updated to the value of 2(A /H/). At the same time the binary 1 signal from comparator 120 is inverted by an inverter so that a binary 0 signal is shifted into the first bit position of the ratio shift register 118 (the previously preset binary 1 signal is shifted one position to the left).  
  When the value of the contents of the accumulator is equal to or greater than the value of the normalized hypotenuse. then the comparator 120 provides a binary 0 signal. This commands the accumulator to double its contents on the next pulse applied to its clock input by shifting the bit pattern therein one position to the left. 1n addition. the binary 0 signal provided by the comparator 120 is inverted by inverter 130 so that a binary 1 signal is shifted into the first bit position of the ratio shift register 118.  
  This ratio calculation is continued until the most significant bit position R, of the ratio register 118 is at a binary 1 level. This indicates that the initially preset binary 1 signal at the least significant bit position has been shifted through the register. At this point. the  
 value of the contents in the ratio shift register corresponds with the value of the ratio of the normalized /F/ word to the value of the normalized /H/ word. The operation now stops since a binary 1 signal is applied from the R. output of ratio register 118 to reset flip-flop 100 and thereby prevent further clock pulses from being applied to the registers. This ratio is used as a modifier in scaling down the pulse rate from F,- to F As will be recalled from the previous description dealing with the scaling circuit SC. the output frequency F is proportional to 2&#39;&#34; (F Consequently then, the output frequency F of the feed rate number rate multiplier RMF is proportional to the ratio of the unnormalized F word to the normalized hypotenuse word /H/. This pulse train is applied to the function generator FG which interpolates the pulse train to provide the F command pulses and the F command pulses.  
 Function Generator (In General) The function generator FG divides the incoming pulse rate F into two output pulse rates which are supplied to the X and Z axes in the proper ratio to produce the programmed slope or radius. As illustrated in FIGIZ, the function generator employs an I rate multiplier IRM and a K rate multiplier KRM. These rate multipliers differ from those employed in the feed rate generator FRG. The rate multipliers in the feed rate generator FRG may be considered as being counter rate multipliers whereas those employed in the function generator FG may be considered as adder rate multipliers.  
  The input pulse rate to the function generator FG is the tool velocity rate F The modifier for the I rate multiplier is the number stored in the I counter and is the normalized /I/ word. Similarly. the modifier for the K rate multiplier KRM is the normalized /K/ word. The scaling, however, is further divided by 2 Thus, the X axis pulse rate F equals F (/I/)/4. In circular interpolation. the values of the normalized /I/ word and the normalized /K/ word will change as the control generates an arc. Consequently, the output pulse rates F and F will not be constant in circular interpolation. For linear operation, the programmed X word is applied to the X displacement control counter XDC as a prcsettable count andthen the counter counts down at the rate of F to meter the proper number of pulses to the X axis control loop XL. Similarly. the count represented by the Z word is used to preset the Z displacement control down counter ZDC which then meters the proper number of pulses at the rate of F to the Z axis control loop ZL.  
  Having now briefly reviewed the overall operation of the function generator, attention is now directed to the circuitry, employed.  
 I Function Generator Rate Multiplier Before describing the specific circuitry employed in the function generator illustrated in FIG. 10, attention is first directed to the adder rate multiplier illustrated in FIG. 8 and the accompanying wave forms of FIG. 9. The adder rate multiplier of FIG. 8 is illustrated as a 4 bit adder rate multiplier. In the description with reference to FIG. 9, the adder rate multiplier is described as a 20 bit adder rate multiplier.  
  As shown in FIG. 8, the adder rate multiplier includes a 4 bit binary adder 150 and a 4 bit accumulator register 152. Such a 4 bit adder and accumulator are, in themselves, conventional in the art. The 4 bit output pattern of the accumulator is applied as a 4 bit input to the adder along with a 4 bit modifier input M The 4 bit sum output of the adder is applied as a parallel input to the accumulator register I52. Pulses at an input clock rate of F,-,. are applied to the clock input of the accumulator and out pulses at a rate F,,,,, are obtained from the carry output of the adder. Each time the adder overflows, a carry output is provided as an output fre- LII quency pulse. Table II below illustrates the binary numbers present atthe various locations of the 4 bit adder I50 of FIG. 8 with a modifier M of 3 and fora pulse train of 32 input pulses at the input frequency F,-,,.  
 TABLE II 4 Bit Adder Rate Multiplier With M=3z F,,,,,=F,-,, 3/l6 Ac- Sum cum- Number of ulator Modifier B A Number of F Pulses Output (M) or or oul m) (A) (Z) (carry out) l 3 3 6 2 6 3 9 3 9 3 l2 4 l2 3 l5 5 l5 3 2 l 6 2 3 5 7 5 3 8 X X 3 l l 9 l l 3 l4 l0 l4 3 l I l l l 3 4 l2 4 3 7 l3 7 3 III l4 l0 3 l3 l5 l3 3 (l 3 I6 I) 3 3 l7 3 3 6 lb 6 3 9 l9 9 3 ll 20 ll 3 l5 ll l5 3 2 4 22 2 3 5 23 5 3 X 24 8 3 l l 15 l l 3 l4 :6 l4 3 l 5 27 l 3 4 28 4 3 7 29 7 3 ll) 30 ll) 3 l3 3l l3 3 (l b 32 U 3 3 Examination of the table shows that a multiplier of 3/16 is obtained for this rate multiplier arrangement. Consequently then. three output pulses are obtained for every l6 input pulses or 6 output pulses are obtained for a pulse train of 32 input pulses. Normalization in the function generator is obtained by selecting a carry output signal depending on the magnitude of the larger of the l or K words. However, there is only one carry output obtained from a conventional four bit integrated circuit adder, such as the four bit adder illustrated in FIG. 8. Carries between bit stages are internal to the typical integrated circuits available and consequently. these carry outputs. if selected. must be generated from the sum outputs. Reference is now made to the wave forms illustrated in FIG. 9. These wave forms are presented for a four bit binary adder and accumulator as interconnected in FIG. 8 with a modifier having a decimal weight of 3. The sum outputs are employed to generate the carry signals. Specifically, an internal carry exists between sum output 4 and sum output 8 on&#34; each change in binary level at sum output 8, as either a rising edge or a falling edge. Ifa pulse is generated on the rising edge as well as on the falling edge of the signal level changes at sum output 8, then these pulses will represent the internal carry output of the adder between sum outputs 4 and 8. Thus. a carry signal, other than the carry from the last stage. may be generated by selection of the proper sum output of an adder employed in an adder accumulator arrangement as shown in FIG. 8. As will be brought out in detail hereinafter, the function generator provides normalization by se-