SU1259218A1 - Linear-circular interpolator - Google Patents

Abstract

The invention relates to the field of automation and computer technology and can be used in numerical control systems. The purpose of the invention is to enhance the functionality and simplify programming. The linear-circular interpolator contains the estimator sign driver, switching unit, control units for reversible counters, coordinate registers-counters, code comparison blocks, reversible counters, AND units, accumulator, increment calculation units, I. The essence of the invention is that in a linear-circular interpolator, works according to the method of the evaluation function, a switching block, control blocks for reversible coordinate counters are additionally added, or ph-counters of coordinates of coordinates point, blocks of comparison of codes, blocks of the year of increments of coordinates and element I. These blocks with the appropriate connections switch in the device when the current point of the arc moves during circular interpolation from quadrant to quadrant and ensure preservation of one-step interpolation accuracy at multi-quadrant development of a circular arc. Due to the automatic modification of the evaluation function at the boundaries of the quadrants, the main interpolation unit, as compared with the prototype, is not complicated. The invention can also be used in other areas where it is necessary to specify the movement of the working bodies along a linear or circular path. 5 il. (Ls

Description

The invention relates to the field of automation and computer technology and can be used in numerical control systems.

The purpose of the invention is to expand the functionality of the device and simplify programming.

Introduced additional blocks allow switching reversible counters of coordinate channels at the boundaries of quadrants during arc interpolation, changing the direction of increments of coordinates at the device outputs, preserving the accuracy of circular interpolation in one step with multi-square arc processing and with minimal switchings. from circular interpolation to linear interpolation.

This solution allows to interpolate an arc of a circle in unlimited limits according to a single program frame, which simplifies programming, reduces the length of the original program carrier, saves the memory of the device when the control program is stored in it, improves the program parameters, reduces the complexity of the postprocessors and improves the quality of manufacturing 1X on the machine parts.

FIG. I shows the scheme of the proposed interpolator; in fig. 2 is a diagram of a sign maker of the evaluation function i in FIG. 3 is a diagram of a switching unit; in fig. 4 is a diagram of the control unit of the reversible counter j on

ten

five

Switching unit 2 contains an RS trigger. 20, four elements AND 21-24, elements OR 25 and 26.

Blocks 3 and 4 of the control of reversible meters are identical and each

of them contains the element OR 27, the inverter 28, the 1K-trigger 29 with the possibility of presetting on the S and R inputs, the elements And 30 and 31.

The increment calculation blocks 14 and 15 are identical. Each of them contains K, 8-trigger 32, element OR 33, divider 34 into four, element AND 35, inverter 36, IK trigger 37 with the possibility of presetting on the S- and R-inputs, elements 38 and 39.

20

The functional communications of the device are carried out along the following lines: the 4P input of the 1 sign maker of the evaluation function is the clock input, the outputs 41 and 42 of the 1 sign maker of the evaluation function, 25 outputs 43-47 of the switching unit 2, the first 48 (51) and the second 49 (52) the outputs of the reversible counter control unit 3 (4), the output 50 (53) of the block 3 (4), the inputs 54 and 55 of the comparison code blocks 7 and 8, respectively, the outputs 56 and 57 of the reversible counter loads 9 and 10, respectively device inputs and connectors to the program block; inputs 58 and 59 of load of register-counters 5 and 6, respectively, are connected to the program block, outputs 60 and 61 overflow of reversible counters 9 and 10, respectively, output 62 pezo

35

Fig. 5 is a block diagram of the calculation of the increment of the highest bit of accumulations. storage accumulator 13, inputs 63 and 64 of the interpolator contains 2 switching formations for resetting or the 1 digit mark of the evaluation function, switching unit 2, reversible counter control blocks 3 and 4, registers-, counters 5 and 6 coordinates, blocks 7 and 8 code comparisons, reversible counters 9 and 10 with the possibility of parallel writing and reading codes, PI blocks 12 And elements, accumulator 13, Calculation Blocks 14 and 15

The settings of the trigger 20 of this block are connected to the unit of pro- linear commands by linear or circular interpolation.

grams, inputs 65 and 66 of the initial setup of triggers 29. blocks 3 and 4, respectively, inputs 67 and 68 of the initial setup of triggers 37 blocks 14 and 15 of the increment calculation

50, respectively, are connected to the program block, input 69 of the trigger setup 32 blocks 14 and 15 are connected to the program block; outputs 70 (72), 71 (73) devices by coordinates

increments, element and 16.

The shaper 1 of the evaluation function sign contains an RS flip-flop J7 and two elements AND 18 and 19. The S input of the trigger is connected to the input of the device, the R input to the overflow output of the high bit of the adder 13.

Switching unit 2 contains an RS trigger. 20, four elements AND 21-24, elements OR 25 and 26.

Blocks 3 and 4 of the control of reversible meters are identical and each

of them contains the element OR 27, the inverter 28, the 1K-trigger 29 with the possibility of presetting on the S and R inputs, the elements And 30 and 31.

The increment calculation blocks 14 and 15 are identical. Each of them contains K, 8-trigger 32, element OR 33, divider 34 into four, element AND 35, inverter 36, IK trigger 37 with the possibility of presetting on the S- and R-inputs, elements 38 and 39.

Functional communications of the device are carried out on the following lines: 4P input of 1 sign maker of the evaluation function is the clock input, outputs 41 and 42 of 1 sign maker of the evaluation function, outputs 43-47 of the switching unit 2, the first 48 (51) and the second 49 (52) the outputs of block 3 (4) of the control of the reversible counter, the output 50 (53) of block 3 (4), the inputs 54 and 55 of the blocks 7 and 8 of the code comparison, respectively, the outputs 56 and 57 of the load of the reversible counters 9 and 10, respectively, are the inputs devices and connected with the program block; inputs 58 and 59 of load of register-counters 5 and 6, respectively, are connected to the program block, outputs 60 and 61 overflow of reversible counters 9 and 10, respectively, output 62 ne

 2 switches for reset or use

The settings of the trigger 20 of this block are connected to the unit of pro- linear commands by linear or circular interpolation.

grams, inputs 65 and 66 of the initial setup of triggers 29. blocks 3 and 4, respectively, inputs 67 and 68 of the initial setup of triggers 37 blocks 14 and 15 of the increment calculation

respectively connected to the program block, the input 69 of the installation of the trigger 32 blocks 14 and 15 is connected to the program block; outputs 70 (72), 71 (73) devices by coordinates

+ x (+ y), x (y), respectively, connect the outputs of the elements And 39 and 38 of block 14 (15) with the outputs of the device; at the exit 74 of the element And 16,

3

the output of the device drops the signal at the end of the area interpolation and frame change, and it is associated with the program block.

Interpolation in the device is conducted by the method of evaluation function. In linear interpolation, the estimated func tion has the form Ijjj yhu -4uh; where X; y are the coordinates of the current point of the interpolation trajectory, dx, and d are the increments of the x and y coordinates in the interpolation region; U ;; - value of O71enochny function in. point (x-, Yj) f

From FIG. 6 that if, then, in order to approximate a given straight line, a step should be made along the axis Y. If U is:; O, then the step is made along the length of the curve. X axis. On the straight U; j 0, and the direction of travel is determined by

arbitrarily. In the case of a hardware implementation of the algorithm, it is more convenient in this case to take a step along the X axis. When right along the X axis, a new value is estimated for the function: U ;, 4hu — lu (x; + 1) and –y. At a step along the Y axis, respectively, we obtain U; , yx (y | + i) -uyx; Ujj + UX. Thus, the strategy of linear interpolation looks like this. The sign of the evaluation function is analyzed. If, then the step is taken along the X axis and the value of d is subtracted from the previous value of the evaluation function; if U ;: сО, then the step is taken along the Y axis and to the previous value of the evaluation function. Their value is added. During the interpolation process, the steps are along the coordinates are counted. Interpolation is terminated when the current values of the coordinates X and y are compared with the magnitude of AX, respectively.

In circular interpolation, the evaluation function is usually

and. () -.

With this definition, the evaluation function for points lying outside the circle, for points lying inside the circle, and- 0, for points on the circle Ujj 0. The interpolation strategy depends on the position of the current trajectory point and the direction of the circumference of the circular arc. So, if the point (x ;, yj) is in the first quadrant and the movement goes counterclockwise (Fig. 7), then a step is taken along the Y axis and a new value of the evaluation function Uii., X; + (yj -1 f -Ro xt y; -Ro + 2yj -tI

25

59218. four

U; + 2y- + l (1), and the value of yj increases by one. If U; j O, then a step is taken along the X axis, and u, - „is calculated. (x; - I f + y | -R x + yJ-R - 5 -2x; + U; j -2x.- + l (2), and the value of X decreases by one. By such x, the rules will occur in numbers - when a point moves in the third quadrant in the same direction.

 About the second and fourth quadrants if U ;; -0, a step is taken along the X axis and it is calculated t iti.j b - + 2xj + j, x, x. J (3), if U; .0, then a step is made along the Y axis and 5 Ui, j ,, Ui | -2y are calculated. +1, () When moving clockwise, the strategy changes: in the first and third quadrants, the calculations are carried out by formulas (3) and (4), in the second and fourth volumes - by formulas (1) and (2).

In order to reduce hardware costs and unification, the proposed interpolator proposes, with a step along the X axis, a new value of the evaluation function always be EXTRACTED using the formula,; U, j + 2X; +.

+1 (5), and at a step along the Y axis, according to the formula Uj-, Ui -2yj + l (6), which, under the above definition, the estimated function corresponds to the motion in the first and third quadrants clockwise. It is also proposed to perform a step along the X axis, if 0, and along the Y axis, if U, j & 0.

5 Such a stretch requires a change in the definition of the evaluation function when moving to the fourth and second quadrants. For these quadrants we define Uij RO- (x; + Y p. Then outside the circle

0, inside the circle. When Ujj О, in order to approach the point to the circular arc, it is necessary to take a step along the X axis and calculate and, -, ,, j Rjj () - () + 2xi-Uu-. + 2x5-1 (7).

5 This differs from (5) by 2, which is easily obtained by the action 2 (x; -1) +1. In other words, if X decreases, then the current value of x should be reduced by

0 unit, then double the result and increase by one. If Uj :: P, then to approach the point to the arc of a circle, one should take a step along the axis Y and calculate Ujj, Ro t;

5 - (y; -1) (x + y) -2y. -1 and - (2u. +1 + 1) (8). This expression differs from (b) by -2 and is easy to obtain by the action of (y; -1) +. Otherwise, if y is increased, then the calculation of the next value of the evaluation function during the step along the axis of Y, the current value of y is taken reduced by one. After doubling the value, a unit is added to the result.

When interpolating counterclockwise in the first and third quadrants, expressions (7) and (8Y in the second and fourth - expressions (5) and (6) are used. Automatic modification of the evaluation function allows you to save without changing the structure of the communication and .

Thus, to implement multi-quadrangle; circular circular interpolation, the following are used: the coordinates of the starting point of the arc (Xd, Yjj) are given with signs; specifies the direction of the interpolation. The coordinates of the end point of the arc (xj ,,) are specified with signs. In the program block, by signs (Xd, Wo) and the direction of interpolation, initial signs of issuing increments of coordinates are set, defining the initial installation of triggers 37 in blocks 14 and 15 of increment calculation and the initial installation of triggers 29 in blocks 3 and 4. Reverse counters control . If the reversible counter 9 of the x coordinate is included in the subtraction, then when you enter the values, the unit is subtracted. In the reversible counter 10, the y coordinates, if it is included in the addition, the unit is not subtracted, since a negative number will be taken from It. Then, during the interpolation process, from the reversible counter 9, with each step along the X axis to the adder 13, the block 11 of the elements And is transmitted the direct code of the block 9 contents. The transfer is carried out with a shift by one bit to the left, which is equivalent to multiplying by two, after which for the low-order bit of the adder 13, one is added. With each step along the Y axis, to the adder 13 from block 10 through block 12 is transmitted from. by shifting by one bit, p d to the left, the reverse code of the contents of block 10, after which one is added to the lower bit of the adder I3, which gives the value 2 (yj -) +. In Sum 3, the current value of the estimated value is calculated and accumulated.

functions. Overflow of the adder means that the evaluation function becomes positive.

During the interpolation process, a sign of a quadrant border crossing is the achievement of one of the coordinates of a zero value. In this case, the reversible counter of the corresponding coordinate is overflowed. The overflow signal is used to switch the flip-flops 29 to the inverse of the previous state, whereby the reversible counter that worked on the addition switches to the subtraction mode, and

the second reversible counter is in add mode. The same signal changes to the inverse state of the trigger 37 of the output unit of the increments of another coordinate channel, and also changes the state of the sign trigger of the coordinate of its channel, since after passing through the zero value of the coordinate it changes the sign to the opposite one. The arc processing must end when the values and signs of the coordinates of the current and end points match.

Another feature of multiquadrant circular interpolation by the estimation function method is associated with an implicit

specifying the radius of the interpolated circle and rounding the coordinates of the starting point of the arc. As a result, the starting point of the arc is located at the S node of the grid, whose pitch is

coincides with the interpolation step, and in the general case does not belong to the arc of radius R. The radius vector of this point is equal in modulus to l1x + V0 RO and in the general case is not integer

relative to the interpolation step. As a result, the arc interpolates with a radius of R. As the simulation of the interpolation process on a computer has shown when the quadrant border is reached, if R is integer, the current point has a modulus of (O, R, + I) or

; (, 0). If no special measures are taken, then in the long run an error will accumulate and at the border of the single quadrant the coordinates of the current point will take the value (Rg + 2.0) or

 0) etc. In addition, at the boundary of the quadrant, the value of the evaluation function is always positive. In connection with the change in the expression for the evaluation function at the boundary of the quadrant, the first step is done incorrectly, i.e. error compensation over the radius does not occur.

To eliminate this phenomenon in the proposed interpolator into blocks

9 and 10 reversible counters are entered with two additional bits, and divider 4 is added to blocks 15 and 14 for incrementing. The initial setting of divisors is 00. In the interpolator, the arc of radius 4R is processed, and at the output, by division by 4, the radius R is applied At the boundary of the quadrant, as in the case of interpolation of an arc of radius R, a point is reached with coordinates (0.4R-H or (4R + 1.0), the value of the evaluation function remains in the adder. Thanks to setting the dividers to 4 at the outputs the coordinates receive the exact number of steps. When the limit is reached, Vadranta, the overflow counter overflow signal resets the dividers in blocks 14 and 15, the first two bits of the reversible counters 9 and 10, and also the adder 13 are reset. Thus, the values corresponding to the exact position of the point on a circle of radius 4R are set in the interpolator. further movement will occur exactly.

The device operates in two modes.

In the linear interpolation mode from the program, the Linear interpolation command is entered into block 2, the reversible counter 9 is assigned the value of Dx along the X axis in the interpolation segment, and the reversible counter

10 is the value of do — movement along the Y axis in the interpolation section, counters 5 and 6 are reset, blocks 14 and 15 are entered into the initial settings corresponding to the direction of signal output required by the program on axes X and Y, dividers are reset

34 in blocks 14 and 15, the adder 13 and the trigger 17 of the sign maker of the evaluation function,

With the start-up of the device, line 69 sets the triggers 32 in blocks 14 and 15, and line 40 provides pulses fj, the frequency of which determines the interpolation rate. The first - a pulse passes through the element I 19 of the imager 1, the trigger 17 of the imaging device 1 is installed at the S-input, the element And 19 closes, and the element 18 opens. In addition, according to line 42, this impulse comes in

20

25

259218 8

These are the inputs of the AND 12 block, which transfers the additional code of the number DU from block 10 to the accumulator 13. In the adder 13 5, the current value of the evaluation function is added with the additional code of the number Y y, i.e. a value U is formed; U is Ay. The same clock pulse goes to the input.

10 of the switching unit 2, passes through the open element AND 24 of this block, via line 45 enters the counting input of the register-counter 5, and through the OR element 25 of block 2 via line 43 enters

t5 to the input of the divider 34 of the block 14 calculating the displacement along the axis x). The second clock pulse passes through the element AND 18 of the imaging unit 1 and, via line 41, enters the block 11 of the elements AND, transferring the content of the reversible counter 9 to the adder of the direct code. In the adder the new value of the evaluation function is calculated

25

ABOUT

0 5

five

0

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and,;, Jitij If the result of the addition is positive or zero, the adder overflows, from the output of its senior bit the overflow signal on line 62 resets the trigger 17 of the driver 1, closing the element And 18 and opening the element And 19. Then the next clock pulse will go on the way first.

The second clock pulse is also fed to block 2, passes through AND 23, passes through line 46 to the counting input of register-counter 6, and through OR 26 through line 44 goes to divider 34 of block 15 for outputting along the U axis. these paths are in accordance with the sign of the evaluation function, with every fourth pulse entering the output block 14 or 15 appearing at the output of the device, passing through the element 35 and then 38 and 38 or 39.

The interpolation process continues until the counters-registers 5 and 6 have the numbers Dx and yu, respectively, i.e. when the contents of the counters are compared with the contents of blocks 9 and 10, respectively, this is fixed by blocks 7 and 8 of the code comparison. The signal of the corresponding comparison unit on line 54 or 55 resets the trigger 32 in block 14 or 15, AND element 35 of block 14 or 15 is closed, closing the increment channel 5

Research Institute on the X axis ipi y. If there are signals from both comparison blocks, a signal appears at the output of AND 16, which is fed to a program block to enter information of the next program frame.

In the circular interpolation mode from the program, the Krugov interpolation command is entered into block 2, the trigger 20 of block 2 is established by opening the elements 21 and 22, and the line 47 receives the enabling signal to the third inputs of the elements 30 and 31 of the reverse control blocks 3 and 4 counters. In blocks 3 and 4, along lines 65 and 66, the initial setting of trigger 29 is made, corresponding to the specified operating mode of the reversible counters 9 and 10. In these, coordinates of the initial point of the circular arc (XQ, Od) with signs are entered. In the register-registers 5 and 6, the coordinates of the end point of the arc (Xc, Y () with signs) are entered. In blocks 14 and 15 along lines 67 and 68, the initial setting of the trigger 37 is performed, corresponding to the specified directions for issuing increments on the X axis. and Y, respectively, dividers 34 are reset.

With the start-up of the device, the triggers 32 are installed in blocks 14 and 15 and the clock pulses are applied to the driver 1.

The first pulse passes through the element I 19, sets the trigger 17 of this block and on line 42 enters the second inputs of the block 12 elements I. The forwarding code is sent with a shift to the left of the reverse code of the content of the reversible counter 10 to the accumulator 13, then the low-order bit of the adder is one. Thus, the la adder sends the number (2ud + 1), which is added to the current value of the evaluation function. The same impulse from line 42 enters the BTopbte inputs of elements AND 30 and 31 of control reversible counter control unit 4 10. Depending on the state of the trigger 29 of this block, one of elements 30 and 31 is open, the second is closed. The passage through the open element I, the impulse goes to the input of or - the reversible counter 10, increasing or decreasing its contents by one or two units.

5921810

On line 42, the first pulse also enters block 2, where it passes through elements 22, RHH 26, and via line 44 is fed to the input of a divider

5 34 units 15 of the calculation of the increment of the y coordinate. The signal flow through the circuit of block 15 remains the same as AND in the linear interpolation mode. The second clock pulse passes

 through the element 18 of the imaging unit 1, via line 41 through the block I1 performs a jumper shifted by one bit to the left of the contents of the reversible counter 9 into the adder 13 with the subsequent 5 addition of one unit to the least significant bit of the adder. Further, through the elements 30 and 31 of the control unit of the reversible counter 9, the content of the reversible is changed.

20 counters per unit. In addition, a clock pulse from line 4 goes to AND 21 of block 2, passes through it and the OR 25 element, and via line 43 is fed to calculation block 14 when it grows along the X axis. Signal flow through block 14 remains the same as in the linear interpolation mode.

After 3 links to the adder 13, the number 30 of the 2X | j-t-l in the adder is calculated

the next value of the evaluation function, if the totalizer overflows, i.e. U, jjO., The overflow signal on line 62 resets trigger 17

35 block I, then the next pulse of tact will go the way of p.rvogo. If there is no overflow, then the next impulse goes, on the way of the second. If a given arc of a circle lies within the limits of one quadrant, then the interpolator works in a similar way before comparing the codes of numbers in blocks 9, 5 and 10, 6, respectively. Achieving equality of numbers is fixed

45 by blocks 7 and 8 comparison of codes whose signals perform the same operations as in the linear interpolation mode.

If a given arc of a circle passes through several quadrants, then when the boundary of the quadrant is reached, the following occurs. The reversible counter, which worked on the subtraction, when reaching O overflows, 55 An overflow signal on line 60 (or 61) through the OR 27 element of blocks 3 and 4 of the reversible counter control changes the state of the flip-flops 29 of these

blocks to inverse by switching counters 9 and 10 to the opposite counting mode. The same switchings are made in the trigger 37 of block 14 or 15 (only the trigger in the block of its coordinate channel is switched). In addition, on line 60 (or 61), dividers 34 of blocks 14 and 15 are reset, the adder 13 is zeroed, the first (lower) two bits of the reversing counters 9 and 10 are reset through the OR element 27 and the invert state of the sign trigger is reversed your channel counter. The interpolator is ready for processing the arc in the next quadrant.

 invention formula

Linear-circular interpolator containing the estimator sign driver, accumulator connected with the output to the first input of the sign block of the evaluation function, and in the second coordinate channel, a successively connected reversible counter and block of AND elements, connected by the second inputs to the output of the estimated sign block functions, and outputs to the bit inputs of the accumulator adder, characterized in that, in order to expand the functionality and simplify programming, a switching unit has been introduced therein, the inputs of which associated with the outputs of the sign maker of the evaluation function, the element And and in each coordinate channel are entered a control unit by a reversible counter and serially connected register-counter, a code comparison unit and an increment calculation unit, the first input of which is connected to the corresponding input of the element And, the second input - with the first outputs of the switching unit, the third - with the output of the reversible counter, with the second input of the adder-tO of the accumulator, with the first input of the control unit with the reversible counter of each channel, with the fourth input the unit for calculating increments of the adjacent channel, the outputs of the unit for calculating the increments of t5 are connected to the first outputs of the linear-circular interpolator, the second output of the switching unit is connected to the first input of the register-counter, and the third output to the third input of the control unit by the reversible counter, the fourth input which is connected to the corresponding output of the sign maker of the evaluation function, and the outputs are connected to the reversible inputs

The 25th counter, the output of the AND element is connected to the second output of the linear-circular interpolator, the first input of which is connected to the second input of the sign maker of the evaluation function30, the second inputs - with the second inputs of the switching unit, the third - with the 1st inputs of the increment calculator, the fourth input - with the second input of the register-counter a n -

The 5th input is with the second input of the reversible counter, the second outputs of which are connected to the second inputs of the code comparison unit.

ifQ

Fsch.Ts

7f (73)

jomr

Compiled by I.Ivets Editor I.Derbak Tehred L.Oleinik

Order 511.9 / 44 Circulation 836 Subscription

VNIIPI USSR State Committee

for inventions and discoveries 113035, Moscow, Zh-35, Raushsk iab., d. 4/5

Production and printing company, Uzhgorod, st. Project, 4

.five

Proofreader A. Obruchar

Claims (1)

Claim A linear-circular interpolator, 20 containing a shaper of the sign of the evaluation function, an accumulator-drive connected by the output to the first input of the sign block of the evaluation function, and in each coordinate channel, the reverse counter and the block of elements And connected to the output of the block by second inputs sign of the evaluation function, and the outputs to the discharge inputs of the accumulator-accumulator 30, characterized in that, with a circuit for expanding functional capabilities and simplifying programming, a switching unit, input cat They are associated with: the outputs of the sign generator of the evaluation function, the And element, and a reverse counter control unit and series-connected register counter, a code comparison unit and an increment calculation unit, the first input of which is connected to the corresponding input of the And element, are introduced into each coordinate channel, the second input - with the first outputs of the switching unit, the third - with the output of the reversing counter, with the second input of the accumulator-accumulator, with the first input of the control unit of the reversing counter of each channel, with the fourth input of the block The calculation of the increments of the adjacent channel, the outputs of the increment calculation unit are connected to the first outputs of the linear-circular interpolator, the second output of the switching unit is connected to the first input of the counter, and the third output is connected to the third input of the reversing counter control unit, the fourth input of which is connected to the corresponding output of the sign former evaluation function, and the outputs with the inputs of the reversible counter, the output of the element And is connected to the second output of the linear circular interpolator, the first input of which is connected n with the second input of the evaluator of the sign of the evaluation function, the second inputs with the second inputs of the switching unit, the third with (the fifth inputs of the increment calculation unit, the fourth input with the second input of the register counter, and the fifth input with the second input of the reversing counter, second outputs kb-o are connected to the second inputs of the code comparison unit. 51 59 Figure 1