Note: Descriptions are shown in the official language in which they were submitted.
1 161925
This invention relates to an improved instrumented remote center
compliance device, and more particularly to an instrumented system including
one or more translational displacement sensors located about the operator
member of the device for sensing displacement in one or more degrees of free-
dom of the operator member.
A remote center compliance device (RCC) is a passive device for aid-
ing insertion and mating manoeuvers in robot machines and assembly equipment.
RCC's typically include a structure which supports an operator member and
establishes a remote compliance center near the functioning end of the oper-
ator member. See United States Patents No. 4,098,001 and ~,155,169. In some
robot and assembly applications there is a need for feedback from the RCC;
however, force measurement is not always ideal for this purpose. For example,
force sensors generally cannot withstand the large forces that occur when the
RCC is driven to the limit against mechanical stops. In addition, force
sensors generally cannot resolve the very small forces on the RCC when it is
operating in its more normal range, not at its limits. Further, the mounting
of the force sensors, usually between the RCC and its support from the host
machine, interfeTes with the compliance of the RCC; the compliance of the re-
mote center is not simply that of the RCC but the combination of the compliance
of the RCC and the compliance of the force sensor apparatus.
Typical angular deflections of an RCC are of the order of 5 and
such angles are very difficult to measure using angular rotation sensors. In
addition, the kinematic rotation center of the RCC is not a fixed point but
rather a varying point. The general angular rotational sensor enforces a
fixed axis of rotation within the sensor. In addition, the operator means of
the RCC is subject to various translation. In consequence, angular rotational
sensors need be connected to the operator means of the RCC by means of the
- 1 - '3~
1 1~1925
kinematic equivalent of splined shaf~s accommodating either axial or lateral
relative motion. This is a significant difficulty which is avoided hy the
use of translational displacement sensors exclusively.
It is therefore an object of this invention to provide an improved
instrumented RCC which uses only translational-displacement measuring sensors
to measure position and angular displacement in one or more degrees of free-
dom.
The invention is featured i-n an improved instrumented remote center
compliance device which has an operator member and a remote compliance center
near the end of the operator member. More specifically, the invention fea-
tures one or more translational displacement sensors located proximate the op-
erator member for sensing displacement in one or more degrees of freedom of
the operator member. By translational displacement sensor is mean* one which
measures motion of the operator member in terms of translations which can
then be resolved into actual translakional and rotational displacements. The
sensors are arranged so-as to produce a change in output from at least one of
the sensors in response to changes in position relative to the radial axes of
the operator member. In a preferred embodiment, there are first and second
translational displacement sensors spaced from the operator member for sensing
displacement thereof, and the first and second sensors are disposed to one
another at a first angle about the axis of the operator member. There are
third and fourth translational displacement sensors spaced from the operator
member for sensing displacement thereof. The third and fourth sensors are
spaced from the first and second sensors along the axis of the operator member
and are disposed to each other at a second angle about the axis of the oper-
ator member. The sensors are disposed so as to produce an output from at
least one sensor for changes of position of the operator member relative to
the radial axes. By displacement herein is meant both angular and transla-
tional movement.
Typically, the first and second sensors are in one plane and the third
and fourth are ln a second, parallel plane, and the first and second angles are
equal. ln a simple case the first and second angles may both be equal to 90
and the sensor in each pair may be aligned with a sensor in the other pair.
If necessary or desirable, fewer or more translational displacement sensors
may be used, for example a fifth sensor may be used to sense a fifth degree of
freedom of motion of the operator member.
The invention also features means for solving the equation X = ~Xl,
where ~ is a transfer matrix relating the translational displacement sensor
output signals to displacement applied to the remote center compliance device
which produces those output signals; Xl is the vector whose elements are the
outputs of the sensors for determining X, which is a vector whose elements are
the components of the displacement supplied to the device. Although the sensors
illustrated in the specification are of the photo-electric type, this is not a
necessary limitation of the invention, for other types of translational trans-
ducers may be used and are sufficient, for example LVDT's, linear-displacement
potentiometers, or any other translational displacement-sensitive transducer.
~0 This invention also features a method of measuring an unknown dis-
placement on the operator member of a remote center compliance device having a
remote compliance center near the end of the operator member which includes
disposing one or more translational displacement centers about the device for
producing output signals representative of displacements of the operator mémber
Known displacements are applied to the operator member so that there exists no
sensed displacement which cannot be expressed in terms of one or more applied
displacements. Each of the output signals produced by each of the sensors
~=~ -3-
~ 161925
in response to the applied displacements is measured. A transfer matrix ID
defined by the equation Xl = ~X as determined by the applied displacements
and the corresponding sensor output signals, where X is a vector whose elements
are the components of the applied displacements and Xl is a vector whose
elements are the outputs of the sensors is calculated. An unknown displacement
is applied to the operator member. Each of the output signals from each sensor
in response to the unknown displacement is measured and the unknown displace-
ment is calculated by solving the equation X - ~Xl where Xl is a vector whose
elements are the sensor outputs in response to the unknown displacement and X
is a vector whose elements are the componen~s of the unknown displacement.
Other objects, features and advantages will occur from the following
description of a preferred embodiment and the accompanying drawings, in which:
Figure 1 is an axonometric view of a remote center compliance device,
RCC, of the type shown in United States Patent No. 4,155,169, which may be
instrumented according to this invention;
Figure 2 is a more detailed sectional view of an RCC device such as
shown in Figure 1 with instrumentation according to this invention taken along
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` -3a-
` . 1 l~lg25
line 2-2 of Figure 3;
Figure 3 is a plan view of the improved instrumented RCC device of
Figure 2 taken along line 3-3 of Figure 2;
Figure 4 is a block diagram of a computer circuit for resolving
measured translational displacement signals into resolved translational and
rotational displacements;
Figure 5 is an axonometric schematic diagram illustrating basic
parameters used in resolving measured displacement signals into resolved
translational and rotational displacements;
Figure 6 is a more simplified schematic of the instrumentation of
an RCC where the angle between the sensors in each pair of sensors is at an
angle other than 90;
Figure 7 is a diagram illustrating a basis for conversion from the
axes of the sensors in Figure 6 to the X,Y axes in Figure 6;
Figure 8 is a block diagram of a computer circuit for calculating
the resolved translational and rotational displacements from the measured
displacement outputs of the sensors;
Figure 9 is a simplified schematic diagram of the placement of sen-
sors on an instrumented RCC when each of the sensors is in a different plane
and at a different angle to the X,Y axes and there is no vertical alignment
between any of the sensors;
Figure 10 is a schematic diagram showing one placement of a fifth
sensor, which enables monitoring of all five degrees of freedom of motion of
an RCC;
Figure 11 is a block diagram of a computer circuit for resolving
the measured displacement signals into the resolved translational and rota-
tional displacements;
9 2 ~
Figure 12 is a block diagram of a circuit which may be constructed
using calibration techniques to resolve measured displacement signals into
resolved translational and rotational displacements;
Figure 13 is a schematic diagram of an RCC of the type shown in
United States Patent No. 4,098,001;
Flgure 14 is a simple block diagram of a circuit for resolving the
measured displacement signals into the resolved translational and rotational
displacements for the RCC in Figure 13; and
Figure 15 shows an alternative circuit similar to that in Figure 14
for resolving measured displacement signals into resolved translational and
rotational displacements for the RCC's in Figure 13.
The invention may be accomplished by disposing a number of transla-
tional displacement sensors on an RCC so that the relative angular and trans-
lational displacement between the moveable or operating member and the rest
of the RCC can be detected. RCC's are disclosed in United States Patents No.
4,098,001 and 4,155,169. Any number of sensors may be used, but they should
be disposed so that an output is produced from at least one sensor for changes
of position of the operator member rela~ive to the remainder of *he RCC. The
number of sensors used may be commensurate with the number of degrees of free-
dom that it is desired to monitor, for example, one sensor may be used tomonitor one degree of freedom, four sensors to measure four degrees of free-
dom, five sensors to measure five degrees of freedom. However, more sensors
may of course be used. RCC's typically do not have more than five degrees of
freedom; they are constrained to permit no displacement in the axial direction.
Once the translational displacement signals are obtained from the sensor or
sensors, they must be converted or resolved into an acceptable coordinate form
to provide useful information. Typically in an X and Y coordinate system the
-
192S
X and Y translations, XJ Y~ and the X and Y rotations ~X~ ~y~ of the operator
member are desired to describe the movement of the operator member with respect
to the remote compliance center. Computing circuits are necessary to resolve
the measured displacement signals into the actual displacements o:E the oper-
ator member. The soundness of the block diagrams of the computing circuits
disclosed herein may be verified and defined analytically through the use of
geometry and algebra, or empirically by a calibration technique also taught
herein.
A simple arrangement which uses a relatively simple computing circuit
results from using four translational displacement sensors, two in the plane
perpendicular, i.e. radial, to the axis, of the operating member and two in a
second plane parallel to the first plane. The sensors in each plane are at
90 to each other, and each is aligned with the sensor in the plane above.
However, this is not a necessary limitation on the invention. For example,
the angle between the sensors in each pair need not be 90, and in fact the
angle between one pair of sensors need not be equal to the angle between the
other pair of sensors. The sensors need not be aligned each with another one,
and in fact each of the sensors may be in a different plane. Of course, the
number of sensors need not be fixed at four, but may be any number equal to
or greater than the number of degrees of freedom that it is desired to moni-
tor. For proper results, however, the sensors should be disposed so that
there is an output produced from at least one of the sensors for changes of
position of the operator member. In contrast the use of rotationally sensi-
tive sensors for any one or more of the sensors results in the difficulty of
connecting such sensors, with their fixed axes of rotation, to the operator
member, with its five degrees of freedom, two of translation and three of ro-
tation, by means of the kinematic equivalent of a splined shaft with universal
l ~6192~
joints at the ends, with all attendant disadvantages such as backlash, fric-
tion and inertia.
There is shown in Figure 1 a remote center compliance device 10
which includes a deformable structure 22, from the central portion 24 of which
is suspended operator member 16 having longitudinal or axial axis 17. De-
formable structure 22 may also include three or more radially extending beams
26, 28, and 30, which are equally spaced and terminate in an intermediate
rigid annular member 32. Beams 26, 28, and 30 lie along radial axes, i.e.
axes perpendicular to the axial axis. Member 32 is carried~by a second de-
formable structure 34 which includes three longitudinal beams 36, 38, and 40,
which extend to a fixed portion such as housing 12, as illustrated in Pigure
2.
Attached to member 16, Figures 2 and 3, is a stop member 42 whichlimits the extent of motion of operator member 16 to prevent damage to the
RCC. Also mounted to operator member 16 is a shade 44 which has two shade
elements 46 and 48, whose outer edges 50, 52 sharply delineate the shadow area
from that illuminated by light sources 54, 56 on translational displacement
sensors 58, 60 carried by supports 62, 64 on housing 12. Light sources 54,
56 are carried by support 66, also mounted on housing 12. Light source 54
and 56 may be Monsanto Electronic Special Products MVlOB light-emitting diodes,
for example, and translational displacement sensors 58 and 60 may be Reticon
RL 256G solid-state line scanners with associated timing and counting cir-
cuitry, for example. Sensors 58 and 60 may be considered the X axis sensors.
A second set of translational displacement sensors 76 and 78 ~partly obscured)
is typically provided, Figure 3, with a second pair of light sources 72 and
74 ~partly obscured). Shade 44 includes a second pair of shade elements 80
and 82 ~not shown). The signals from sensors 58 and 60 are referred to as
- 7 -
9~5
X2 and Xl, respectively, and those from sensors 76 and 78 as Y2 and Yl, res-
pectively.
The measured translational displacement signals Xl, X2, Yl, Y2 may
be resolved into the actual translational X, Y, and angular or rotational ~X'
displacements of operator member 16 by the computing circuit shown in
Figure 4. There, Xl is multiplied by the factor ~) in multiplier circuit
100, and by the factor (S) in multiplier circuit 102, where L is the distance
from remote center 70 to the X2, Y2 signal sensing position and S is the dis-
tance between the Xl, Yl and X2, Y2 signal sensing positions, shown in Figure
5. X2 measured displacement signal is multiplied by the factor (l ~ S) in
multiplier 104, and by the factor ~(S) in multiplier 106. Measured signal
Yl is multiplied by the fac~or (L) in multiplier 108 and ~(S) in multiplier
llO. Measured displacement signal Y2 is multiplied by the ~actor (1 - L) in
multiplier circuit 112, and by the factor ~S) in multiplier circuit 114.
These multiplier factors are relatively simple since the translational dis-
placement sensors are arranged in pairs in parallel planes aligned with each
other and with each pair at 90 to each other. The Xl, X2 derived outputs
from circuits lO0 and 104 are combined in summer 116 to provide the actual dis-
placement X. The Xl, X2 derived outputs from circuits 102 and 106 are com-
bined in summer circuit 118 to provide the displacement Oy~ The Yl, Y2 derivedouputs from circuits 108 and 112 are combined in summer circuit 120 ~o pro-
vide the actual Y displacement, and the Yl, Y2 derived outputs from circuits
110 and 114 are combined in summer 122 provide the ~X output. That this
approach is sound may be seen from Figure 5, where ~1 and ~2 are both equal
to 90. The relationship of the measured displacement signals Xl, X2, Yl, Y2
to the actual displacements X, Y, ~X~ ~y in terms of L and S is:
~ 16192~
Xl = X - ~)y (L-S) (1)
X2 = X - (3y (L) (2)
Yl = Y ~ ~X ~L-S) (3)
2 (~)X (L) (~)
These equations may be expressed in matrix form for easier solution:
~X~ 1 0 0 (S-L) ~X
J X21 1 (-L) I Y l
1~ 0 1 (L-S) 0 ~i t
lY2~ 1 (L) 0 l J
which may be simply expressed as:
Xl = ~A lX (6)
Thus, Xl is a vector whose elements are the outputs of the sensors.
These equations of course are not exact, they are standard approxi-
mations known and used in geometry. In order to solve for the actual dis-
placements X, the matrix may be inverted,
X = ~Xl (7)
to the state:
~X~(LS) ~ S~ 0 ~X~
Y ~ (--S~ S) ¦ X2l
~X ~ o (-S) (S-) l yll (8)
~` J (S) (-S) o o ~Y2J
In the general case wherein Xl may be of higher dlmension than X,
equations (6) and (7) can be written Xl = ~X and X = ~Xl, respectively, where
~* ~ equals II and II is the identity matrix. In ~he useful special case
previously described-in-detail wherein X and Xl are of the same dimension,
and ~ are square matrices and simply ~ equals ~ 1.
Alternatively, when the sensors are not at 90 to each other, that
l ~61925
is when ~1 and ~2 are not equal to 90 as shown in Figure 6, the measured
signals are represented by Ul, U2, Vl and V2, which can be resolved in terms
of the Xl, X2, Yl, and Y2 coordinates shown in Figure 6, where Ul and Xl are
separated by the angle al; U2 and X2 by the angle a2; Vl and Yl by the angle
~1; and V2 and Y2 by the angle ~2. This conversion may be accomplished as
shown in Figure 7 using equations:
x = a cosà
a = u - b
b = e sina
y = e + c > ,~,
c = a sina ~9)
f cos~ = V
j cos~ = x
j sin~ = g
~g + f = Y ~
which result in the matrix expression:
-sina cosa
l~l = sina __ ~ l (10)
cos~
For the specific case of Xl, Yl the matrix expression appears as:
sinalcos(x
1 ~ n~; 1 l (Il)
and for X2, Y2 the matrix expression appears as:
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- "- J1$1925
I' 1 sincl2cosc~2 ~ .
~ X2 ~ U5~2 ~ D2
These two expressions (11) and (12) are combined to produce:
¦ Yl ¦ sinc~ O 1 ~I I
~ = sinQl2cosa
X2~ I C5~2 ~U2~
2, 0 sin~2 cosB 2
which when rearranged to present Xl, X2, Yl, Y2 in the desired order, appears
as:
` Sin~lCs~l _ /
Xl 1 cosBI U
Sin~2CoS~21
X2 ~ = cos2~ C05~2-cos~2 ' IVl ~ ~14)
Yl 1 cosBI cos2c~2 ~ ~
2 2C5~2 J~2)
- 11 -
1 16~925
Expression (14) may now be simply state~:
Xl = ~Ul ~15)
Since we know from expression (7) that X = ~Xl, we can substitute in expres-
sion (15) to arrive at expression (16)j which fully expanded appears as
e~pression ~17).
X = Aæul ~16)
L L sinal 5~1 L L n~2 2
X ~ (S) CS~ S) ~ s-)coscc2~ ~l-S~ Ul ~
(S) 1 ~S) cos~ (1 L)sina (1 L) 2 Vl ¦
QX¦ (1) sin~ (1) cos ~1 (S) sin~2 (S) cos~ 1 U2
l (1)(1 C~l_ C~ (1 nc~2cosc~2
J cos~l cos~2 - ~v2
A computer circuit which implements this statement includes a
plurality of multiplier circuits 130 through 160, Figure 8, which multiply
the measured displacement signals Ul, Vl, U2, and V2, by the various factors
shown in terms of the dimensions L, S, and the angles ~ and ~, and are then
combined in the combinations shown in summer circuits 162, 164, 166, and 168,
to provide the actual displacements X, Y, ~X~ and 3y~
In a similar manner, in the case where there are four translational
displacement sensors providing four measured signals Ul, U2, Vl, and V2, but
none of the sensors are in the same plane nor aligned with each other, as
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1 ~19~
shown in Figure 9, the measured signals Ul, U2, Vl, V2 may be resolved into
the desired X, YJ ~X~ ~Y components, as shown by ~he following expressions:
l ( ~l)X + ~sin~l)Y - ~Slsin~ x ~ (slcos~ y (18)
2 ~ ~l)X ~Sin~l)Y - ~Llsln~l)ox + ~Llcos~ Y ~19)
Vl ~ ~cos~2)X + (sin~2)Y - ~S2sin~2)~x ~ ~S2cs 2) Y ~20)
V2 ~ (cos~2)X + (sin~2)Y - (L2Sin~2)~x ( 2 2 Y (21)
These expressions may be placed in matrix form,
lrul~ COSC~l sinal -Slsin~l Slcosc~l ' f x
) U2l cos~l sin~l -Llsin~l Llcos~l J ~ ~22)
cosa2 sinc~2 -S2sinc~2 S2coso~2 ; X
2J cos~2 sin~2 -L2sin~2 L2cos~2 l J
and then inverted in the usual way,
~ X l Mll ~12 M13 14 l Ul
: Jl ~ M21 M22 M23 24 ~ U2 ~ ~23)
~X ~ M31 M32 M33 ~34 Vl
M4l M42 M43 M44 2 ¦
to obtain the terms which define the multiplier factors that are implemented
in multiplier circuits 180 - 210 in the computer circui~, Figure 11.
The outputs of circuits 180-210 are combined in the groups shown in
summer circuits 212, 214, 216, and 218, to provide directly the X, Y, and ~X'
displacements.
Although thus far the illustrations have used four translational
displacement sensors to sense four degrees of freedom, this is not a neces-
sary limitation of the invention, as fewer or more sensors may be used to
monitor fewer or more degrees of freedom. For example, a fifth sensor 220,
Figure 10, may be added to produce a ~ displacement signal which senses rota-
tion about the Z axis, axis 17, of the operator member. Sensor 220 is placed
- 13 -
1 161~5
parallel to sensor 78 in order to sense the rotation about Z axis 17. To
effect this, a non-circular member with some sort of camming surface 222 is
used in conjunction with sensor 220 to detect the rotation. Alternatively,
sensor 220 might be placed elsewhere.
With five degrees of freedom being sensed by five sensors, the four
expressions (18) - (21) would be expanded to include a fifth equation, and
there would be a fifth column and fifth row added to the matrices in expres-
sions (22) and (23), while the implementation shown in Figure 11 would be
expanded by the addition of one more multiplier circuit associated wi-th each
of the measured ;nput signals Ul, U2, Vl, V2, and also the addition of a fifth
input, for example ~z.
Alternatively, a calibration technique may be used to veri`~y the
multiplier factors in the computer circuit which resolves the measured dis-
placement signals obtained from an instrumented RCC into the actual displace-
ments of the operator member and body of the RCC relative to each other.
First the instrumented RCC is fixed so that each degree of freedom, for ex-
ample, X, Y, 3X~ ~y~ and ~z, can be varied independently while all the others
remain fixed or at zero displacement. This may be stated in matrix form as:
~ ul~ 11 N12 N13 N14 N15 ~X l
20l U2l N21 N22 N23 N24 N25 ~ I
3 ~ 31 N32 N33 N34 N35 ~ ~X ~(24)
U4 I N41 N42 N43 N44 N45
~ u5J N51 N52 N53 N5~ N55 ~Zl
The U terms are the sensor outputs. If X is displaced a known amount Xl, not
equal to zero, and all remaining possible displacements, Y~X~ ~y~ ~z, are
held at zero, the result may be expressed:
.
- 14 -
l ~61925
lll = NllXl ~25)
U2 = N21Xl (26)
U3 = N31Xl (27)
U4 = N41Xl (28)
U5 N51Xl (29)
and since the measured values Ul 5 are known and the displacemen~ Xl is known,
this set of equations may be transformed into:
Ul (30)
N
Xl
U2 (31)
N
Xl
u3 (32)
N3
Xl
U4 (33)
N4
Xl
U5 (34)
N - X
In a similar fashion, with Y set equal to Yl, not equal to zero,
and the remaining terms X, ~X~ ~y~ ~z all set at zero, the same action may be
taken to obtain the numerical values for the second column of the matrix of
expression 24. When this is done, with all the numerical values in place in
the matrix of expression (24), a simple matrix inversion results in:
- 15 -
.
1 1619~5
I'x ¦ 11 M12 M13 M14 M15~ Ul 1
¦ Y ¦ 21 M22 M23 M24 M25¦ ~J2 ¦
X ~= 31 M32 M33 M34M35 ~ U3 1 ~ (35)
¦~Y 41 M42 M43 M44 M45l U4
51 M52 M53 M54 M55l U5_
where each of the M values in each row and column of the matrix is a numerical
value and may be directly inserted in the multiplier circuits 250-298, Figure
12, which are combined as shown in summing circuits 300, 302, 304, 306, and
308 to provide the actual displacements X, Y, ~X~ Y~ ~Z
An even simplier implementation occurs with the RCC of Uni~ed States
Patent No. 4,098,001, as shown in Figure 13. In such a device, operating
member 16' typically is supported by a member 310, which in turn is supported
by an intermediate device 312 by means of a number, typically three, flexures
314, 316, only two of which are shown, which converge toward each other and
meet at a point 70' which generally establishes the remote compliance center
along the axis 17' of operator member 16'. Flexures 314, 316 are in turn
fastened to intermediate member 312, which is attached ~o a support 318 by
means of typically three additional flexures 320, 322, only two of which are
shown. Typically flexures 320, 322 control only translational motion, while
flexures 314, 316 independently provide the rotational flexibility for the
instrument. In this case a single translational displacement sensor 330,
located as shown between support 318 and intermediate member 312, provides
the signal X'2, which is indicative of motion along the X axis. Motion about
the Y axis is indicated by the measured signal X'l obtainable from transla-
tional displacement sensors 332, or from X"l, obtainable from sensor 334.
Similar signals Y'l, Y"l, and Y'2 are obtained in the same way with respect
- 16 -
`-` l 1~192~
- to the Y axis translational and X axis rotational displacements. Because of
this independent action in the translational and rotational motion modes in
RCC 10', the actual displacement along the X axis, X, is equal to the measured
value X'2,
X = X'2 (36)
and similarly the displacement along the Y axis is equal to the measured dis-
placement Y'2:
Y 2 (37)
Rotational motion about the X axis, ~X' is either:
1 (38)
~3x =
or:
1 ~39)
~X
Similarly, ~y is either:
X'l (40)
~)y = -- .
or:
X"l ~41)
Y S
Thus the computing circuit implementation to resolve the X'l, Y'l, X'2, and
Y'2 measured displacements into the actual displacements ~yJ ~X~ X1 and Y,
may be simple: direct connections 350, 352, to resolve the X'2 and Y'2 signals
into X and Y displacements. Multiplier circuit 354 multiplies X'l signal by
a factor of (l/L) to obtain ~y~ and multiplier circuit 356 multiplies Y'l dis-
placement signal by a factor of (-l/L) to obtain ~X
Similarly, using the combination X'2, Y'2, and X"l,, and Y"l, only
- 17 -
11 ~6~92~
multiplier circuits 355, providing a factor of (l/S), and multiplier cir-
cuit 360, providing a factor of (-l/S), are necessary to complete the compu-
ting circuit 10. As in Figure 14, X'2 and Y'2 directly provide the X and Y
displacements.
