Apparatus and method in which a plurality of detectors generating signals with different periods are used to detect the absolute position of a moving member

An apparatus and a process for detecting an absolute positional value relating to mechanical movement of a member to be measured from a reference point. The apparatus includes a detecting means with a plurality of detectors having periods which are different from one another. Each detector generates an electric signal having a period corresponding to the movement of the member. The signals are stored in a memory. Then, the absolute value of mechanical movement between one of the detectors and the member is specified by using two values. The first value is derived by multiplying the period of the signal corresponding to the one detector by an integer N. The second value is stored in the memory and corresponds to the one detector's partial movement which is less than one period thereof. The value of the integer is decided by using periods and stored values corresponding to other detectors.

BACKGROUND OF THE INVENTION 
This invention relates to an apparatus and process for detecting an 
absolute position of an element, and more particularly to an apparatus and 
process for determining an absolute value by use of signals from a 
plurality of detectors. 
In the prior art, for example, as disclosed in Japanese Kokai Tokkyo Koho 
No. 53-53350, a detector detecting an absolute position of an element on a 
machine tool, obtains an absolute value as follows. First, the number of 
rotations of the element in a direction of a coordinate axis, i.e. the X 
axis, is derived from a driving unit for the X axis direction and that 
number is supplied to a reduction train with two (2) stages or three (3) 
stages. A rotary detector is provided on a rotatable axle of each 
reduction stage so that a value within one revolution of the rotary 
detector is read out to obtain an absolute value from the combination of 
values detected by the rotary detectors. The combination of values above 
is performed as follows. 
Suppose that a table of a machine tool is moved in the X axis direction. 
The number of revolutions derived from the X axis driving unit is reduced 
to 1/10 between the first axis and second axis of an X axis absolute 
position detecting unit. Further, the reduced number of revolutions is 
again reduced to 1/10 between the second axis and third axis thereof. 
Furthermore, the reduced number of revolutions is reduced to 1/10 between 
the third axis and fourth axis thereof. In this instance, the fourth axis 
rotates less than one revolution over all the length of all the measuring 
range in the X axis direction. 
For example, suppose that the first axis rotates one revolution per 2 mm 
which is the movement of the table in the X axis direction. The movement 
of the table corresponding to each revolution of the fourth axis is as 
follows. 
EQU 2.times.10.times.10.times.10=2000 (mm) 
Therefore, the effective detecting range is 2 meters. 
One revolution of the third axis corresponds to 200 mm in the movement of 
the table while one revolution of the second axis corresponds to 20 mm in 
the movement of the table. 
Thus, in this case, an absolute value within 2000 mm of the table movement 
can be calculated from the sum of each value of the rotating angles within 
one revolution of the first, second, third and fourth axes. 
However, the disadvantages concerning the above are: 
(a) The reduction train becomes larger in size and its inertial moment 
increases as the effective measuring range is enlarged. 
(b) The weighting factor for each value of the axes are different from each 
other. Thus, errors over one graduated scale on the fourth axis will be 
1000 times greater in the first stage. 
Accordingly, mechanical accuracy must always be maintained at a high degree 
even if vibration or wear occurrs in the machine tool during operation 
thereof. 
SUMMARY OF THE INVENTION 
It is a principal object of the present invention to provide an apparatus 
for detecting an absolute position in which a plurality of detectors each 
produces periodical electric signals in response to a predetermined 
mechanical movement of the member, the detectors having periods which are 
different from each other. Electric signals are obtained from the 
detecting means, which correspond to less than one period when the member 
is mechanically stopped. The signals thus obtained are digitally stored 
and an integral value is determined wherein a relative position between 
one of the detectors and the member is specified by a value multiplied by 
a value of integer N of the period corresponding to the one detector and a 
value of the less one period, and the integral value N is determined by 
using at least a period corresponding to another detector of the detecting 
means and the digital quantity stored in the storing means. 
It is another object of the present invention to provide a process for 
detecting an absolute position which comprises the steps of preparing a 
detecting means with a plurality of detectors which provide periodical 
electric signals corresponding to predtermined mechanicl movements which 
are different from each other, to a member to be measured, generating the 
mechanical movement between the detecting means and the member, storing 
the electric signals corresponding to each the period of the detecting 
means, specifying a relative position involved in the mechanical movement 
between one of detectors of the detecting means and the member by using 
the value, multiplied by integer N, of the period corresponding to the one 
of detectors and the value which is less than the period, and choosing the 
integral value N by using a period corresponding to another detector of 
the detecting means and the stored value which is from another detector. 
It is a further object of the present invention to provide a process for 
detecting an absolute position which comprises the steps of preparing a 
transmitting means of rotary type which includes a plurality of rotary 
detectors generating electric signals of which the period is due to a 
rotary angle range based on one revolution or equally-divided revolution 
thereof and axes rotating the detectors respectively at a predetermined 
ratio, connecting the rotary transmitting means to the member to be 
measured for mechanical movement thereof, supplying mechanical movement 
between the rotary detector and member to be measured under specified 
conditions, storing the electric signals corresponding to the respective 
period out of each detector, specifying a relative positional relationship 
between the member and one of the detectors involved in mechanical 
movement by using the value multiplied by integer N of the period 
corresponding to the one of the detector and the value which is less than 
one period thereof, and deciding the integral value N by using the period 
corresponding to another detector of the detectors and the stored value 
from the another detector.

DETAILED DESCRIPTION OF THE INVENTION 
Referring to FIG. 1, reference numerals 21, 22 and 23 indicate one part of 
a detecting means, i.e. scales which are provided in parallel, 
respectively, in the X axis direction. The period of scale 21 is P1 which 
consists of five (5) graduated scales as one unit in the X axis direction. 
The period of scale 22 is P2 which consists of six (6) graduated scales as 
one unit in the X axis direction and the period of scale 23 is P3 which 
consists of seven (7) graduated scales as one unit in the X axis 
direction. A distance L.sub.ABS indicates an effective detecting range 
from the starting point O.sub.ABS. In FIG. 1, all the periods of scales 
21, 22 and 23 are consistent with each other at the point L.sub.abs1 which 
is the next consistent point from the starting point O.sub.ABS. 
A detecting means 24 can move in the X axis direction, and supports 
detectors 25, 26 and 27. The detectors 25, 26 and 27 output electric 
signals as the waveforms 25a, 26a and 27a shown in FIG. 2. These waves 
correspond to the wave forms from a potentiometer of the rotary type as 
one example of an ideal detector. 
Suppose that the central position of the detecting means 24 is at the point 
L(X) and each detector 25, 26 and 27 outputs values .DELTA.P1, .DELTA.P2 
and .DELTA.P3, respectively, each of which values is less than one period 
of P1, P2 and P3. In FIG. 1, the distance L(X) is obtained by the 
following expressions. 
EQU L(X)=N1.times.P1+.DELTA.P1 (1) 
EQU L(X)=N2.times.P2+.DELTA.P2 (2) 
EQU L(X)=N3.times.P3+.DELTA.P3 (3) 
In the expressions, the values P1, P2 and P3 are known amounts and the 
values .DELTA.P1, .DELTA.P2 and .DELTA.P3 are also measured values, i.e. 
known amounts. Thus, the corresponding value L(X) will be obtained where 
the value of integer 1, 2, 3, . . . n is substituted for N1 in the 
expression (1), successively. After that, the values L(X) will be 
substituted into the expressions (2) and (3) in order to obtain the values 
j equal to the values N1. For instance, as shown in FIGS. 1 and 2, P1 is 
equal to five (5). P2 is equal to six (6) and P3 is equal to seven (7). On 
the other hand, the value .DELTA.P1 is equal to three (3), .DELTA.P2 is 
equal to five (5) and .DELTA.P3 is equal to two (2). The numerals 1,2,3,4 
. . . n are substituted for N1 successively in the expression (1). 
Suppose that N1 is equal to the numeral 1, 
EQU (LX)=1.times.5+3=8 (4) 
EQU 8=N2.times.6+5 (5) 
EQU 8=N3.times.7+2 (6) 
No integral numbers including zero (0), which are substituted for N2 and 
N3, can solve the expressions (5) and (6). 
Thus, the value N1 cannot be 1. 
Suppose that N1 is equal to the numeral 2, 
EQU L(X)=2.times.5+3=13 (7) 
EQU 13=N2.times.6+5 (8) 
EQU 13=N3.times.7+2 (9) 
No integral numbers including zero (0), which are substituted for N2 and 
N3, can solve the expressions (8) and (9). Thus, the value N1 cannot be 2. 
Suppose that N1 is equal to the numeral 3, 
EQU L(X)=3.times.5+3=18 (10) 
EQU 18=N2.times.6+5 (11) 
EQU 18=N3.times.7+2 (12) 
No integrals N2 and N3 can solve the expressions (11) and (12). 
Suppose that N1 is equal to the numeral 4, 
EQU L(X)=4.times.5+3=23 (13) 
EQU 23=N2.times.6+5 (14) 
EQU 23=N3.times.7+2 (15) 
The expressions (14) and (15) are solved in this case, i.e. N2 is three (3) 
and N3 is three (3), as will be apparent from FIG. 1. Furthermore, the 
reason why only one group of N1, N2 and N3 exists for the combination of 
P1, P2 and P3 provided by the detecting means is illustrated below. 
FIGS. 1 and 2 show a detecting means of the linear type which moves 
linearly with respect to the scales 21, 22 and 23 whereas the rotary type 
thereof is illustrated in FIG. 3 as an preferred embodiment. In FIG. 3, a 
motor 31 activates a driven member 34 which moves through a feed screw 35 
in the X direction, shown as an arrow. An axle 36 extending from the 
driving motor 31 is connected with a rotary axle 38 of rotary detecting 
means Sn. The rotary axis 38 is connected to an axle 37 of a gear Gn in 
order to be rotated, gear Gn having Tn teeth. As illustrated in FIG. 3, 
the gears G1, G2, G3 . . . Gn . . . GN having teeth T1, T2, T3, . . . Tn, 
. . . TN, respectively, are engaged with each other to comprise a gear 
train. Detectors S1, S2, S3, . . . Sn, . . . SN output signals .theta.1, 
.theta.2, .theta.3, . . . .theta.n, . . . N, respectively, which 
correspond to the rotating positions of rotary axles 38 of each detector. 
Suppose, in FIG. 3, the driven member 34 stays at a point in the X axis 
direction after rotation of the motor 31. The absolute value Pn of the 
position thereof will be found as follows where the detector Sn outputs 
the position data .theta.n. 
EQU Pn=Rn.multidot..DELTA.+.theta.n (16) 
In the expression (16), the symbol .DELTA. indicates the moving degree of 
the driven member 34 in the X axis direction per revolution of the motor 
31, the symbol Rn indicates the number of revolutions of the detector Sn 
from the reference point, which number is an integer. The symbol .theta.n 
corresponds to the rotating angle position which is less than one 
revolution of the rotary axle 38 of the detector Sn, that is, which 
corresponds to the displacement of the driven member 34 in the X axis 
direction. The number of revolutions of the motor 31 is transmitted to 
each detector Si (i.noteq.n) as well as detector Sn through the gear train 
33. Thus, the following expression is solved. 
##EQU1## 
where iFix [A] is the integral portion of symbol A. Furthermore, the sum 
of the teeth to be rotated until each gear G1, G2, . . . GN reaches the 
same position is obtained by the following expression. 
EQU LCM{K} 
Where the symbol K is equal to {Tj:j=1, 2, . . . N} and the symbol LCM{K} 
means the least common multiple of K. 
The maximum number of effective revolutions Kn of detector Sn is defined by 
the following expression. 
##EQU2## 
Suppose that .rho.n is the solution of Rn in the expression (17), 
##EQU3## 
Only .rho.n exists in the above expression so that the value of .rho.n can 
be substituted into the following expression in order to obtain the 
absolute position Pn. That is, 
EQU Pn=.rho.n.multidot..DELTA.+.theta.n (20) 
Furthermore, the effective detecting range i.e. the maximum position for 
detecting Pn (max) is determined by the following expression. 
EQU Pn(max)=Kn.multidot..DELTA.+.theta.n(max) (21) 
In the expression, n(max) is the maximum value detected by detector Sn. The 
expression (21) means that the value will vary linearly with the position 
Pn(max) according to the number of revolutions of gear G(n). 
As to the preferable selection for the number of teeth, 
(a) Elements (the number of teeth) of the set K should not have any common 
factors, and 
(b) Pn(max) becomes larger where the number of teeth Tn of the gear G(n) 
connected to the detector Sn is the minimum in the set K. 
In view of the above (a) and (b), the expression (18) will be converted to 
the following expression. 
##EQU4## 
As the gears G(l) and G(m) are selected to have the relationship of a 
prime number to each other, the following expression is not solved. 
##EQU5## 
Furthermore, the reason why only .rho.n exists in the expression (19) is 
illustrated as follows. 
In FIG. 3, the effective rotating number En of detector Sn is solved by the 
following expression. 
##EQU6## 
Where En=Kn+1. 
That is, En effective rotating numbers exist which can satisfy the value 
.theta.n in the expression 16. 
In view of the expressions (16) and (17), suppose that Rn is, as a 
solution, equal to .rho..sub.n.sup.1 where i is equal to 1. The following 
expression will be established. 
##EQU7## 
Suppose that E.sub.n.sup.1 which corresponds to .rho..sub.n.sup.1 and 
Rn=.rho..sub.n.sup.1 +E.sub.n.sup.1 is substituted for the right portion 
of the expression (17). Thus, the right portion of the expression (17) is 
equal to the following expression. 
The right portion of expression (17)= 
##EQU8## 
where the element Tn/T1.multidot.E.sub.n.sup.1 is an integer and 
E.sub.n.sup.1 is equal to LCM{Tn, T1}/Tn. 
Thus, possible Rn's which can satisfy the expression (17) are 
1/E.sub.n.sup.1 in toto. Similarly, suppose, i is equal to 2, 3, . . . , 
n-1, n+1, . . . , N, respectively, 
##EQU9## 
From the above, for all the cases where i is equal to 1, 2, 3, . . . , 
n-1, n+1, . . . N, the capability to satisfy the expression (16) and (17) 
is indicated by the following expression. 
##EQU10## 
Thus, only one value .rho.n exists, which satisfies the following 
expression. 
##EQU11## 
FIG. 4 illustrates an embodiment derived from the process for detecting an 
absolute position shown in FIG. 3. For convenience of illustration, the 
numbers of teeth of the gear G(3), G(4) and G(5) are three (3), four (4) 
and five (5), respectively. A feed screw 67 for the X axis is directly 
connected to an output axle 66 of motor 49. A driven member 65 moves in 
the X direction shown by the arrow by rotation of the motor 49. An axle 52 
which rotates with an output axle 66 of motor 49 extends upwardly in order 
to rotate with a rotary axle 53 of a resolver 56. The gear G(3) is 
provided on an axle 53A which extends from the rotary axle 53. 
Furthermore, resolvers 47 and 48 are provided in parallel to the resolver 
46. A rotary axle 54 of resolver 47 is connected to an axle 54A of gear 
G(4) to rotate, which is engaged with the gear G(3). Similarly, a rotary 
axle 55 of resolver 48 is connected to an axle 55A of gear G(5) to rotate, 
which is in turn engaged with the gear G(4). The primary exciting coils of 
resolvers 46, 47 and 48 are connected to an exciting circuit 50 through 
lines 56, 57 and 58 to supply exciting current thereto, respectively. A 
selecting circuit 51 is connected to the exciting circuit 50 by lines 59 
and 60. The selecting circuit 51 selectively supplies exciting current to 
the resolvers 46, 47 and 48 by way of a combination of selected signals 
S.sub.EL0 and S.sub.EL1. The secondary outputs of the resolvers 46, 47 and 
48 are introduced into an isolator 45 through lines 62, 63 and 64, 
respectively. Output signal EN (enable signals) of the isolator 45 is 
introduced into a register 42 through a circuit including a filter and 
comparator 44. 
A counter 41 for 10,000 counts is connected to a central processing unit 
(CPU) 43 through register 42 so that the number counted by the counter 41 
at the time when the signal EN is produced is fed into the CPU 43 by lines 
65 and 66. The data fed into CPU 43 will be processed according to the 
following procedure as shown in FIG. 8. In the isolator 45, a terminal AG 
of the primary side indicates an analog ground whereas a terminal LG of 
the secondary side indicates a logic ground. 
FIGS. 5 through 7 illustrate transmission of signals from the resolvers 46, 
47 and 48 to the register 42. FIG. 5a shows waveforms of the secondary 
outputs Px1, Px2 and Px3 of resolvers 46, 47 and 48, respectively, when 
exciting signals consisting of sine waves and cosine waves are 
simultaneously supplied to the resolvers above. FIG. 5b shows wave forms 
in which three (3) wave forms are in phase with each other by adjustment 
of their mechanical angles. FIG. 6a shows wave forms which indicate 
repeating of counts from zero (0) through 9999 by the counter 41 which 
runs as a collating position counter and can count 5 KHZ. FIG. 6a shows 
setting up signals of the register 42 i.e. EN signals in FIG. 4 which are 
fed from the filter and comparator 44. FIG. 6a finally shows waveforms of 
the secondary outputs of resolvers 46, 47 and 48. It is apparent from FIG. 
6a that the setting up signals EN are formed at the time when the 
secondary output crosses the zero (0) level line in voltage. In FIG. 6a, 
the value counted by counter 41 is not zero (0) at the time when setting 
signal EN rises. However, the value counted by counter 41 shows zero (0) 
in the waveforms of FIG. 6b. That is, the value of collating position 
counter 41 i.e. zero (0) is set up in the register 42 at the rising point 
(or the falling point) of output signals (Px1, Px2, Px3) of resolver 46, 
47 and 48 which have been adjusted to be in phase. This is called zero 
cross adjustment. The position obtained by the above procedure becomes the 
absolute origin. 
FIG. 7 illustrates how to obtain the coordinates Po where the driven member 
65 is stopped at the absolute coordinates Po in the predetermined X 
direction by rotation of motor 49 shown in FIG. 4. As shown in the upper 
right side of FIG. 7, the secondary wave forms Px1, Px2 and Px3 of 
resolvers 46, 47 and 48 are shifted in phase with respect to each other 
because of gear trains G(3), G(4) and G(5). The zero cross position of 
each signal is indicated by the symbols X1, X2 and X3, respectively. Each 
saw tooth waveform corresponding to the waveforms Px1, Px2 or Px3 in FIG. 
7 corresponds to the top waveforms in FIGS. 6a and 6b, respectively. As 
shown by the waveform Px3, Px2 or Px1 in FIG. 7, the length of waveform 
Px3 is 3/5 of Px1 and the length of waveform Px2 is 4/5 of Px1. The height 
of each waveform indicates the count in register 42 so that one times the 
value of Px1, two times the value of Px2 and three times the value of Px3 
are supplied to the CPU 43. 
FIG. 8 illustrates a process for obtaining the absolute position based on 
the data X1, X2 and X3 supplied to the CPU 43 of FIG. 4. 
As illustrated in FIG. 7, the absolute position Po is expressed by the 
following expression. 
EQU Po=Rx.multidot.10,000+X3 (26) 
where Rx indicates the number of rotations, necessarily an integer, of the 
rotary axle of resolver 46, which is from the absolute origin to the 
position Po. The driven member 65 moves 10,000 .mu.m per each revolution 
of gear G(3). 
The data X2 obtained by the signal Px2 is determined by the following 
expression. 
EQU X2=3/4(RX.multidot.10,000+X3)-A (27) 
where 
EQU A=iFix[3/4(Rx.multidot.10,000+X3)/10,000].multidot.10,000 (28) 
and iFix [a] indicates an integer of a. The data X1 obtained by the signal 
Px1 is determined by the following expression. 
EQU X1=3/5(Rx.multidot.10,000+X3)-B (29) 
where 
EQU B=iFiX[3/5(RX.multidot.10,000+X3)/10,000].multidot.10,000 (30) 
In the first (I) part of FIG. 8, the numbers of RX which satisfy the 
measured values X3 and X2 simultaneously are determined with regard to the 
expression (27). In the second (II) part of FIG. 8, the value of Rx0 which 
satisfies the measured value X1 is selected from the numbers of RX. 
In the flow chart of FIG. 8, RX is set to be zero (0) in Step 1 (as 
abridged STP hereafter) and k is set to be one (1) in STP 2 in order to 
set up an initial condition where an operation starting signal is given 
after storing the measured data X1, X2 and X3 in the memory of CPU. In STP 
3, is determined whether or not the expression (27) is solved, which is 
obtained by calculation of the expression (28) since the value of RX is 
given to be zero. 
STP 4 sets Rx(k) where the judgment is YES in STP 3. Where the judgment is 
No therein, the process proceeds to STP 6. After STP 4, k is incremented 
by one in STP 5, and Rx is incremented by one in STP 6. Rx is checked to 
determine if it has reached its maximum number i.e. 20 which is given by 
the expression (24) and is the value obtained by the least common multiple 
60 of the numbers of teeth 3, 4 and 5 divided by the number of teeth 3. 
STP 3 through STP 6 is repeated until RX reaches 20, i.e. No is decided in 
STP 7. During this process, the value Rx(k) and k are defined through STP 
4 and STP 5, respectively, where the expression (27) is solved. STP 8 sets 
up N=1 as the initial value when YES is decided in STP 7. 
The value B is calculated by the expression (30) in STP 9 and, it is 
confirmed that the expression (29) is solved. STP 10 follows YES in STP 9. 
In STP 10, the value Rx(N) is set up as Rxo. An absolute position Po will 
now be obtained by substituting Rxo for Rx of the expression (26). FIG. 8 
shows only up to the choice of Rxo. 
STP 11 confirms that the value N is equal to the value K-1. The value k is 
the last i.e. the largest value which is defined in STP 5 of the first 
part (I) of the flow chart. STP 12 increments the value N by one following 
YES in STP 11. That is, the value Rx (1), Rx(2), . . . Rx(k), i.e. from a 
small value to a large value, all of which satisfy the value x3 and x2 of 
the expression (27) simultaneously, are designated in STP 9. STP 13 
follows YES in STP 11 to indicate existence of an error in the measuring 
system. This means that the expression (29) is still not solved even where 
the largest value Rx(k) is entered thereinto after checking the value Rx 
from N=1 in order in STP 9, i.e. it is not in a normal measuring 
condition. 
In the meanwhile, the above process for data processing is effective to 
work out an accurate absolute position where the expressions (27) and (29) 
are approximately solved. The reason for the above will be illustrated as 
follows. 
The embodiment in FIG. 4 shows the resolvers 46, 47 and 48 of which one 
revolution results in one cycle, respectively. Thus, the effective 
detecting range from the absolute origin will be determined by the 
following expression where K is set to be equal to 3, 4 and 5 and Tn is 
set to be equal to 3 in the expression (24). 
##EQU12## 
This means that the motor 49 in FIG. 4 rotates less than 20 revolutions. 
As illustrated above, one revolution of motor 49 corresponds to 10,000 
.mu.m so that twenty (20) revolutions thereof correspond to two hundred 
mm, since 
##EQU13## 
A preferred embodiment is illustrated in FIG. 9 in which the effective 
detecting range is two thousand (2000)mm. 
The configuration shown in FIG. 9 is similar to that of FIG. 4. However, 
the following differences exist between FIGS. 4 and 9. That is, the 
resolvers 103, 104 and 105 are of the type which include ten (10) poles 
and the counter 108 is for 200 counts. Further, the gears G(31), G(32) and 
G(33) include the number of teeth 31, 32 and 33, respectively. 
Furthermore, outputs of filter and comparator 112 are clocked into a flip 
flop circuit 113 by clock signal CK from a clock pulse generator 122 to 
become EN signals (enable signals) for a register 109 through a NAND gate 
114. 
Suppose that a driven member 102 moves 10,000 .mu.m in the X axis direction 
while a motor 101 rotates one revolution as in FIG. 4. As a result, the 
resolver 103 which includes ten (10) poles makes five (5) cycles of phase 
shift during its one revolution. Each period thereof corresponds to two 
thousand (2000).mu.m as illustrated in FIG. 10. Two thousand counts of 
counter 108 corresponds to one period of the resolver 103. FIG. 11(a) 
shows the waveforms before adjustment of absolute origin whereas FIG. 
11(b) shows them after adjustment. FIG. 11(a) shows the difference between 
the zero point of counter 108 and the zero cross point of the secondary 
output waveforms of the resolvers 103, 104 and 105, respectively, whereas 
FIG. 11(b) shows coincidence between the content of counter 108 and the 
zero cross point of the secondary output waveforms. In this case, a pulse 
signal EN is adopted as an instructing signal in order to feed the content 
of counter 108 to register 109. 
FIG. 12 illustrates a measuring process for an absolute position detecting 
device as in FIG. 9. In FIG. 12, suppose that the driven member 102 is 
initially located at the absolute origin under the condition that the 
resolvers 103, 104 and 105 and counter 108 are adjusted and then driven 
member 102 moved to the point Po. Under this condition, the resolvers 103, 
104 and 105 output signals no, mo and lo, respectively. 
Thus, the absolute position P0 will be determined as follows, with 
reference to FIG. 12. 
EQU Po=2000.rho.+no (31) 
EQU .rho.=Rn.times.5 (32) 
where Rn indicates the revolution number (an integer) of the resolver 103. 
Regarding resolver 104, the following expression is solved. 
EQU G(31):G(32)=31:32 
Thus, the output mo of resolver 104 is as follows. 
##EQU14## 
Regarding resolver 105, the following expression is solved. 
EQU G(31):G(33)=31:33 
Thus, the output lo of resolver 105 is as follows. 
##EQU15## 
Accordingly, the value .rho. will be obtained by putting the figures 0, 1, 
2, . . . , (1056-1) successively into the expressions (33) and (34). After 
that, the only value of .rho. will be obtained as the value .rho..sub.0, 
which satisfies the expressions (35) and (36). Then, the value .rho.o is 
substituted into the expression (31) in order to obtain the absolute 
position Po. 
The flow chart shown in FIG. 13 is divided into two parts. The first part 
of FIG. 13 shows a process to select the values .rho., of which more than 
one will exist and satisfy the expressions (33) and (34) simultaneously, 
while the second part of FIG. 13 shows a process to select the value 
.rho..sub.0 out of the values .rho. which are obtained in the first part. 
The flow chart in FIG. 13 shows a process which is basically similar to 
that of FIG. 8. The differences between the two flow charts are as 
follows. That is, Rz.fwdarw..rho., X3.fwdarw.no, N.fwdarw.J, X2.fwdarw.mo, 
X1.fwdarw.lo, A.fwdarw.C, B.fwdarw.D, Rxo.fwdarw..rho.o, 
Rx(N).fwdarw..rho.(J). Thus, a detailed explanation of each step of the 
flow chart will be omitted. 
The following is an illustration of the effective detecting range. 
The expression below defines the range detected by the detecting device 
shown in FIG. 9. 
Suppose that any absolute position P is set up, 
##EQU16## 
where l, m and n indicate measured position data at any position P. 
Suppose that the values of data l, m and n are to be zero including the 
absolute origin, from the expressions (38) and (39), 
##EQU17## 
Accordingly, 
##EQU18## 
Functions F and G are introduced into the expressions (41) which will be 
changed as indicated below. 
##EQU19## 
F(.rho.) and G(.rho.) are shown in FIG. 14. Thus, with regard to FIG. 14, 
the solutions of F(.rho.)=0, G(.rho.)=0 are obtained as follows. 
EQU .rho.F=32 .alpha. (44) 
EQU .rho.G=33 .beta. (45) 
where, .alpha. and .beta. are zero (0) or a positive integer. Now, suppose 
that .rho.F is equal to .rho.G, 32 .alpha. is equal to 33.beta.. 
##EQU20## 
where .gamma. is zero (0) or a positive integer. 
Accordingly, 
EQU .rho.F=.rho.G==.multidot.33.gamma.=1056 .gamma. 
where the values .alpha. and .beta. are substituted into the expressions 
(44) and (45). That is, regarding .rho., the cases that position data 
become zero are as follows. 
##EQU21## 
Accordingly, the effective detecting range Pmax (=2000 .rho.max+nmax) is 
given by the expression below. 
##EQU22## 
Thus, 
EQU Pmax=2000.times.1055+1999=2,111,999 (.mu.m).congruent.2000(mm) 
where .gamma. is equal to zero. 
The following is an illustration for determining errors in measurement. 
The illustration above regarding FIG. 9 relates to a process in which 
errors for data lo, mo and no measured are excluded. However, in practice, 
these measured data lo, mo and no include errors due to quantization which 
are involved in electrical resolving power and mechanical errors from the 
gear train. Thus, the measured values are different from the theoretical 
values. 
The following illustrates the range of errors. 
Positioning data l, m and n which are measured corresponding to the 
absolute position P from each of resolvers 103, 104 and 105 of FIG. 9, are 
indicated as follows, 
EQU l=lT+.DELTA.l (46) 
EQU m=mT+.DELTA.m (47) 
EQU n=nT+.DELTA.n (48) 
where lT, mT and nT indicate accurate values, while .DELTA.l, .DELTA.m and 
.DELTA.n indicate errors, respectively. 
Thus, the expressions (33) and (34) are modified as follows. 
##EQU23## 
where mT is determined as follows. 
##EQU24## 
Accordingly, the error .DELTA.m obtained by substituting the value mT of 
the expression (51) for the value mT of the expression (49) is calculated 
by the expression below. 
##EQU25## 
Thus, the value e is equal to 0 or 2000. 
##EQU26## 
Similarly, 
##EQU27## 
Suppose that the error due to quantization is .epsilon., which value is 
1(.mu.m/pulse), the mechanical error is .delta., which value is 2(82 
m/pulse) and .DELTA.n includes the value .epsilon. and .delta., all of 
which are substituted in the expressions (54) and (55), then 
##EQU28## 
suppose that [n] is .+-.1, then 
EQU [.DELTA.m]*=.+-.1.866(.mu.m) (56) 
EQU [.DELTA.l]*=.+-.1.809(.mu.m) (57) 
where [.DELTA.Q] is defined as the actual error pulse number and 
[.DELTA.Q]* is defined as the actual error quantity. 
Corresponding to the value .rho.o which is determined by successive steps 
of the flow chart shown in FIG. 13, 
EQU [.DELTA.n]=.+-.1, 
and the following conditions are necessary. 
Regarding the value mo, 
EQU &lt;mT-1.866&gt;.ltoreq.mo.ltoreq.1999 (58) 
or 
EQU &lt;mT+1.866&gt;.gtoreq.mo.gtoreq.0 (59) 
or 
EQU mT-1.866.ltoreq.mo.ltoreq.mT+1.866 (60) 
Regarding the value lo, 
EQU &lt;lT-1.809&gt;.ltoreq.lo.ltoreq.1999 (61) 
or 
EQU &lt;lT+1.809&gt;.gtoreq.lo.gtoreq.0 (62) 
or 
EQU lT-1.809.ltoreq.lo.ltoreq.lT+1.809 (63) 
where 
&lt;S&gt; is defined, when S.gtoreq.0, as 
EQU S-iFiX[s/2000].multidot.2000 
or 
&lt;S&gt; is defined, when S&lt;0, as 
EQU 2000+S 
Each of the expressions (58) through (60) will be selected corresponding to 
the measured value mo which is in the range from zero (0) to 1999. For 
example, the expression (58) will be selected where the value mo is close 
to and less than the value 1999. The expression (59) will be chosen where 
the value mo is close to zero (0). Furthermore, the expression (60) will 
be selected where the value mo is in the middle of the values zero (0) and 
1999. Similarly, one of the expressions (61), (62) and (63) is chosen 
corresponding to the value lo. Briefly speaking, the expressions (58) 
through (60) and the expressions (61) through (63) will not be solved 
where each of the measured data mo and lo include a value greater than the 
errors (.epsilon.+.delta.) in the detecting device shown in FIG. 9, which 
is given in the form of a numeral. 
Further, for instance, the value mT is necessary in order to solve the 
expression (58) which is an inequality. The value mT will be calculated by 
the expression (51) under the condition that nT is determined to be nearly 
equal to no (nT no) in the expression (51) and .rho.o, which is determined 
in the flow chart of FIG. 13, is substituted for .rho.. Furthermore, the 
following inequalities (58A) through (63A) can be adopted since all of the 
values lo, mo and no are integers. 
That is, the expression (58) corresponds to the following. 
EQU iFiX[&lt;mT-1.866&gt;].ltoreq.mo.ltoreq.1999 (58A) 
The expression (59) corresponds to the following. 
EQU iFiX[&lt;mT-1.866&gt;].gtoreq.mo.gtoreq.0 (59A) 
The expression (60) corresponds to the following. 
EQU iFiX[mT-1.866].ltoreq.mo.ltoreq.iFiX[mT+1.866] (60A) 
The expression (61) corresponds to the following. 
EQU iFiX[&lt;lT-1.809&gt;].ltoreq.lo.ltoreq.1999 (61A) 
The expression (62) corresponds to the following. 
EQU iFiX[&lt;lT+1.809&gt;].gtoreq.lo.gtoreq.0 (62A) 
The expression (63) corresponds to the following. 
EQU iFiX[lT-1.809].ltoreq.lo.ltoreq.iFiX[lT+1.809] (63A) 
The capability for miscalculation of an accurate absolute position is 
illustrated below, which is based on the existence of errors as indicated 
above. 
As shown in FIG. 15, the ratio of teeth numbers of each gear is 
EQU 31:32:33 
Further, each resolver 103, 104 and 105 includes ten (10) poles, 
respectively. 
Thus, where the gear G(32) rotates at 1/5 revolution after the gear G(31) 
continues to rotate in the same direction more than 1/5 revolution from 
the position at absolute origin, the number of pulses dm produced by 
rotation of the gear G(31) is calculated by the expression below. 
##EQU29## 
Similarly, the number of pulses dl of the gear G(33) to the gear G(31) is 
calculated by the following expression. 
##EQU30## 
Thus, 
EQU [.DELTA.m]&lt;&lt;dm, [.DELTA.l]&lt;&lt;dl (64) 
This means that .rho.o will become accurate where the expression (64) is 
satisfied even if there are errors .DELTA.m(=1.866) and .DELTA.l(=1.809) 
in the measured data lo and mo, and the data lo and mo including the 
errors are utilized when .rho.o is determined in the flow chart of FIG. 
13. That is, .rho.o is not subject to the influence of errors. Further, 
the absolute position is determined by the following expression when 
.rho.o is decided. 
EQU Po=2000.rho.o+no 
i.e. .rho.o is not affected by errors in the gear train since the values mo 
and lo are not used. In other words, in the expression of STP 3 in FIG. 
13, the value of the right portion thereof will be changed by 62.5 as 
.rho. is increased by one (1) so that errors will not be made when .rho. 
satisfying the value mo is clocked since the errors of mo are not 
comparable to the value 62.5. The same applies to (J) and lo of STP 9. 
Thus, from another point of view, there are no problems even if the values 
mo and lo include errors therein when .rho. of STP 3 and .rho.(J) of STP 9 
are determined correctly i.e. gears which are roughly worked will be able 
to be used and furthermore, the lives of gears will be increased even if 
they become gradually deteriorated in accuracy. 
Resolvers of the rotary type are illustrated in FIGS. 4 and 9 as detectors. 
However, in the present invention, any type of detectors can be utilized 
provided that the detectors have a regular period and the absolute 
quantities thereof such as lo, mo and no are able to be measured within 
one period. That is, detectors of the linear type like inductsyn 
(trademark) and magnetic scale can be utilized. Resolvers are not even 
limited to the rotary type. 
Furthermore, systems for processing the measured data are illustrated in 
FIGS. 8 and 13. However, the systems are not limited to the described 
embodiments. For instance, the expressions (1), (2) and (3) can be solved 
as simultaneous equations. 
In the present invention, three (3) resolvers for measuring are activated 
by one motor which is used to move a member to be measured as illustrated 
in FIGS. 4 and 9. However, one of the resolvers can be removed by using 
signals from a detector for position feed back already provided in feeding 
controllers, such as a resolver, rotary encoder or the like fixed in a 
machining tool. As illustrated in FIG. 16, resolvers 207, 208 and 209 for 
the detector are connected to the axles of pulse motors PM1, PM2 and PM3 
in order to be rotated. In this case, the gear train is not necessarily 
provided. Instead, the number of pulses P(.DELTA.X) corresponding to 
movement .DELTA.X provided by a NC unit for the machining tool will be 
supplied to the pulse motor 203. Further, the number of pulses 
P(31/32.multidot..DELTA.X) will be supplied to the pulse motor 204 and 
still furthermore, the number of pulses P(31/32.multidot..DELTA.X) will be 
supplied to pulse motor 205. Accordingly, the movement .DELTA.X will be 
supplied to a pulse proportioner. 
In FIG. 16, a gear train 212 can be used instead of part 206 of pulse 
motors 204 and 205. In the embodiment of FIG. 16, movement of the driven 
member is electrically transmitted to resolvers etc. instead of being 
mechanically transmitted so that the limited space in a machine tool will 
be more effectively used for fixing of resolvers therein. Further, in FIG. 
16, the pulse motors 203, 204 and 205 are used. However, a synchro is 
provided on the axle of motor 101. 
The process of the present invention, which can determine the absolute 
position from a combination of measured data from detectors having a 
plurality of periods, is almost free from measuring errors since there is 
no weighting factor among measured data from the detectors. Thus, the 
moment of inertia in the gear train can be decreased and it is not 
necessary to correct errors due to attrition of gears. Further, as 
apparent from the embodiments in FIGS. 9 and 13, the absolute position is 
determined by two steps, one of which sets .rho.o and the other of which 
determines Po by using .rho.o such as Po=2000.rho.o+no. That is, the 
absolute position is obtained at high accuracy since mechanical errors of 
the gear train are not included in no. Furthermore, the detecting device 
itself can be smaller in size with longer life. The numbers of teeth of 
gears have no common divisors as illustrated in FIGS. 4 and 9, so that the 
effective detecting range of the device is increased remarkably. 
While the invention has been particularly shown and described with respect 
to a preferred embodiment thereof, it will be understood by those in the 
art that various changes in form and detail may be made therein without 
departing from the spirit and scope of the invention.