Note: Descriptions are shown in the official language in which they were submitted.
ENCODER DISC
BACK~ROUND OF THE INVENTION
This invention relates to an improved encoder
disc for an encoder of the type having a scanning unit
for scanning the disc to measure an angular position
characteristic of the disc.
Encoders such as shaft angle encoders have
been used for some time to provide an electronic signal
indicative of the angular position of the shaft to
which the encoder is mounted. Such encoders include
discs having either absolute or incremental tracks, or
a comhination of the two. Absolute tracks provide~a
parameter that varies in accordance with the absolute
position of the disc, while incremental tracks provide
repetitive signals that can be counted to determine
movement away from a reference position.
European Patent Application EP O 276 402 dis-
closes an encoder disc which, as shown in Fi~ure 2,
includes both incremental and absolute tracks. Note in
particular ~he outermost track which varies in width in
a linear manner between a minimum width at O degreas
and a maximum width at 180 degrees. This width vari-
ation is indicated in Figure 4, where the signal Ul is
shown as triangular in shape.
Though the triangular waveform produced by
the encoder disc of the above-identified EP O 276 402
-- 1 --
3~3~5~
-- 2 ~
is suitable for some applica-tions, it is often prefera-
ble to provide a measuring track which varies in width
sinusoidally rather than linearly. Such sinusoidal
waveforms eliminate the cusps of triangular waveforms
and associated scanning difficulties. Additionally,
processing systems for sinusoidal signals are commonly
avai~able.
It is an object of the present invention to
provide an improved encoder disc for an encoder of the
type described above which provides such a sinusoidally
varying measuring track in a particularly simple and
cost effective manner.
SUMMARY OF THE INVENTION
. . . _
According to this invention, an encoder disc
for an encoder of the type described initially above
comprises a disc body having first and second reyions
on the disc body. The first region is defined between
two circles of differing radii and offset centers posi-
tioned such that the smaller circle is contained within
the larger circle. The second region is situated adja~
cent the first region, and the first and second regions
have differing characteristics of a scanned parameter
such as light transmission. The first region forms a
measuring track which varies in width substantially
sinusoidally around the disc body.
In the preferred embodiment described below,
the measuring track is transparent and the surrounding
region of the disc is opaque. Preferably, the disc
body defines a central axis of rotation, and the cen-
ters of the two circles are each offset by a substan-
tially e~ual amount from the central a~is such that the
two centers and the central axis are colinear with the
central axis positioned between the two centers. This
arrangement has been found to provide a measuring track
~3~
-- 3
which approximates a sinusoidal variation in track
width with surprising accuracy.
The invention itself, tog~ther with further
objects and attendant advantages, will best be under-
stood by reference to the followiny detailed descrip-
tion, taken in conjunction with the accompanying draw-
ings.
BRIEF DESCRIPTION OF T~E_DRAWINGS
Figure la is a plan vi~w of an encoder di c
which incorporates a presently preferred embodiment of
this invention.
Figure lb is a schematic representation of an
encoder which incorporates the encoder disc of Fig-
ure 1.
Figure 2 is a schematic representation of the
disc of Figure 1, in which proportions have been exag-
gerated for clarity of illustration.
Figure 3 is a geometrical construct used be-
low to analyze the schematic representation of Figure
2.
Figure 4 is a graph showing errors associated
with the encoder disc of Eig. l.
DETAILED DESCRIPTION OE THE PRESENTLY
PREFERRED EMBODIMENTS _ _ _
Turning now to the drawings, Figure la shows
a plan view of an encoder disc which incorporates a
presently preferred embodiment of this invention. This
disc includes a disc body 10 which defines a central
axis of rotation 12 and a periphery 14. Typically, the
periphery 14 is at a fixed radius from the central axis
12. The disc body 10 defines four first regions
16a-16d, and a second region 18 which differs in char-
acteristics of a scanned parameter such as light
~3~7~i~
transmission. Typlcally, one of the first and second
regions 16a-16d, 18 is opaque, and the other is trans-
parent. In this embodiment it is the firs-t regions
16a-16d that are transparent. The second region 18 is
immediately adjacent to the first regions 16a-16d and
in this embodiment surrounds them. The following dis-
cussion applies equally to all of the first regions
16a-16d, and the reference number 16 wi]1 be used ge-
nerically to refer to any of the first regions 16a-16d.
As best shown in Figure 2, the first region
16 is defined as the region between an inner circle 20
having a radius R1 and a center 22, and an outer circle
24 having a radius R2 and a center 26. The central
axis 12 and the centers 22, 26 are colinear along an
offset axis 32, with the central axis 12 posi-tioned
between the two centers 22, 26.
Figure lb schematically shows the manner in
which the encoder disc body 10 can be used in an encod
er. As shown in Figure lb the encoder includes a scan-
ning unit which is fixedly mounted with respect to the
axis of rotation 12 of the di SG body 10. The scanning
unit includes a set of lamps L which generate light
that passes through the disc body 10 to respective
light sensors S. The amplitude of a signal generated
by one of the sensors S is proportional to the amount
of light passing through the respective first region
16. This parameter varies as a function of the width
of the first region 16, which width is measured with
respect to the central axis 12 and is indicated by the
reference symbol W in Figure 2. As the disc body 10
makes one complete revolution the signals generated by
the sensors S vary from a minimum value at a selected
angular position to a maximum value at the selected
angular position plus 180 degrees and back to the mini-
mum value. Surprisingly, it has baan discovered that
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~L3g~5~
-- 5 --
the width W of the first region 16 varies in a
sinusoidal manner to an excellent approximation. Thus,
the signal generated by the sensor S varies sinusoid-
ally (to a close approximation) between the minimum and
maximum values as the disc body 10 makes one complete
revolution. As used herein, a sinusoida:L variation
includes a sine wave with a DC offset.
The encoder disc of Figure 1 can be manufac-
tured by a variety of methods, including the conven-
tional photolithographic methods currently used to man-
ufacture encoder discs. For example, one surface of
the encoder disc body 10 can be plated with an opaque
metal layer, and then photoresist techniques can be
used to remove the opaque metal layer in the first re-
gion 16 bounded by the inner and outer circles 20, 24.
One approach to abrication i5 to coat the opague metal
layer with a photoresist, then to expose the
photore~ist outside the outer circle 24 and inside the
inner circle, and then to use conventional techniques
to remove the metal layer between the two circles 20,
24. Another possible approach is to expose such a lay-
er o~ photoresist between the circles 20, 24 in a
raster scan so as to e~pose the antire first region 16.
The sketch of Figure 2 will be used to clari-
fy the manner in which the width W of the first region
16 varies in an approximately sinusoidal manner. As
shown in Figure 2, the distance between the two centers
22, 26 is indicated by the reference symbol a, while
the distance between the central axis 12 and the center
22 is indicated by the symbol b. As shown, the width W
is mQasured along a radius procaeding from the central
axis 12.
Using the notation defined in the enlarged
geometrical construct of Figure 3, -the following geo-
metrical identities are apparent:
- 5
~3~
-- 6 --
h' = (a-b)sin~; (EQ 1)
C' = (a-b)cos~; (EQ 2)
C~2 - R Z~h~2 (EQ 3)
C" can ~hen be expressed as follows:
C" = (R22-h'2~2 = (R22-[(a-b)sin~]2)~. (EQ 4)
C, which equals C' plus C", can be expressed
as follows:
C = C'+ C" = (a-b)cos~ + (R22-[(a-b)sin~]2)~. (EQ 5)
Similarly, the following three geometrical
identities obtain:
h" = bsin~; (EQ 6)
s" = bcos~; (EQ 7)
(s' ~ s")2 = Rl2 - hn2 (EQ 8)
These identities can be used to calculate s'
as follows:
s' = (Rl2-h"2)~ - s"; (EQ- 9)
= (Rl2-~bsin~)2)~ - bcos~. (EQ- 10)
The width W as shown in the geometrical con-
struct of Figure 3 is equal to C s'. Using the identi-
ties set out above, W can be expressed as follows:
W = c - s; '
= (a-~cos~+(R22-[(a-b)sin~]2)~ - (EQ. 11)
(Rl2-(bsin~)2)~+bcos~;
= acosl~l+(R22-1(a-b)sinl~]2) 2 _ (EQ. 12)
(Rl2-(bsin~)2)~.
-- 6 --
~3bs~
-- 7 --
For the specific case where b--0 (i.e. where
the inner circle 20 is centered on the central axis 12)
EQ 12 simplifies as follows:
W = acos~(R22-(asin~)2)~ - R~ (for b=0). (EQ. 13)
Gi.ven that the desired formula for W is
W=a+acos~, EQ 13 indicates an error equal to the fol-
lowing:
Error = (R22-(asin~)2)~ - R1-a. (EQ 14)
Similarly, when the two circles 20, 24 are
symmetrically positioned with respect to the central
axis 12, i.e. where a=2b and R2=Rl~2b, EQ 12 simpliies
as follows:
W = acos~(R22-(b3in~)2)~ - ~Rl2-(bsin~)2)~. (EQ 15)
In this case, W again is desired to equal
a+acos0, and the error between the desired and actual
values of W is indicated as follows:
Error = (R22-(bsin~)2)~ - (Rl2-(bsin~)2)~-a. (EQ 16)
Analysis has shown that the error is mini-
mized when b is selected to approximately equal ~a.
The minimum 2rror is found at a point where b is
slightly less than ~a, where the offsets of the two
circles (b and a-b) differ from one another by about
0.25%.
Figure 4 is a graph showing the magnitude of
the worst case error for the situation where the two
circles are -tangent at one point and 2b=a. In Figure 4
the X axis indicates the accuracy of the approximation
(worst case percentage error~ and the Y axis indicates
the r~tio of the maximum track width (a~ divided by the
average of the radii of the two circles that define the
track (~(Rl~R2)). Note that for a 4 bit encoder ~which
requires an error less than one part in 16) a/~(RI+R2)
must be less than 0.65. Similarly, for 8, 12 and 14
bit encoders (which require an error of less than one
part in 256,4096 and 16,389, respectively) a/~(Rl+R23
must be less than 0.25, 0.06 and 0.03, respectively.
The values of Rl, R2 ~ a and b can be chosen
to fit the application. Simply by way of example, the
following table defines the dimensions of the embodi-
ment of Eigure la in millimeters.
First 2R~ Center
Region 2RI X Y
. . . _ . _ .
16a 42.05 0 -0.120
41.5~ 0 ~0.120
16b 40.05 0 +0.120
39-55 0 -0.120
16c 36.16 -0.120 0
35.50 ~0.120 o
16d 33.53 ~0.120 0
32.88 -0.120 0
From ths foregoing, it should be apparent
that an encoder disc has been described which provides
the desired sinusoidally varying measuring track in a
particularly simple manner. Of course, the measuring
tracks described above will often be combined with oth-
er tracks, either absolute or incremental, on -the en~
coder disc. For example, four sets of the measuring
tracks described above can be provided on an encoder
disc at 0 degrees, 90 degrees, 180 degrees and 270 de-
grees in order to produce a highly accurate substitute
for a magnetic resolver or inductosyn. In many
-- 8 --
~- 9 -
applications it will be desirable to make the two cir-
cles 20, 24 almost tangent at one point to minimize the
unchanging portion of the width W. However, tangency
is not required in all applications.
Of course, a wide range of materials and fab-
rication techniques can be used to implement this in-
vention. If desired, the first region :L6 can be opaque
and the second region 18 transparent. Furthermore,
this invention is not limited to use with optical en-
coders, but can also be used with capacitive and induc-
tive encoders. It is therefore intended that the fore-
going detailed description be regarded as illustrative
rather than limiting, and that it be understood that it
is the following claims, including all equivalents,
which are intended to define the scope of this inven-
tion.
