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An absolute linear encoder with
multiple codification system
A. Argeseanu1, I. Torac2,, K. Leban3
Dpt. of Electrical Engineering, “Politehnica” University of Timisoara, Romania
Tel: +40 256 403457, E-mail: [email protected]
Tel: +40491823, Fax: +40491816, E-mail: [email protected]
student Electrical Engineering, “Politehnica” University of Timisoara, Romania
E-mail:[email protected]
The paper contains the theoretical aspects and the experimental results of a
new absolute linear encoder system. The design of the new encoder uses a
múltiple codification and the final contribution is the color codification. This
development alows a fine encoding for a longer distance.
Keywords: absolute linear encoder, graduated scale, multiple coding, optical
fiber sensor
1. Introduction
.For long distances (10m - 100m) and fine accuracy (0.5mm) applications of
linear motors used in intelligent warehouses or factories, it is impossible to use
a classical absolute linear encoder. For a shorter application (9m) it is
necessary to codify 18000 segments. The binary code used on the classical
absolute encoder implements this case using 15 bits (using 15 bits it is possible
to encode 32768 words and that means the maximal length of the
displacement). Practically speaking, the classical binary encoder needs a
precision-graduated-scale with 15 tracks and an optical-head with 15 optical
sensors. Such an encoder is unacceptable because of technical and
economical conditions: low reliability and overcharge price.
The design of the new quasi-absolute linear encoder for long displacement and
fine resolution, starts from few theoretical ideas:
-the graduated scale of the encoder contains a number of equal steps
- each step is double encoded
- for each step is used also a fine resolution codification
- the combination of these two action-encode realizes a new encoder-concept
The absolute codification of the steps is made using the mathematical concept
of the combination computation. The new absolute linear encoder concept uses
few different elements to encode the steps:
- each step is shared in sectors and the length of these sectors is used in the
new codification algorithm
- the scheme of the sectors for each step
- the sign attached to each sector
- the colour codification
Because the encoder uses a multiple codification, it is more clearly to start with
the white/black solution (the case of two colours).
2. The white/black (binary) solution
In the long distance application case, the number of segments is 5: A, B, C, D,
E. Without sign information, using 5 elements, the maximum number of codewords is 120 and all these combinations are:
{A,B,C,D,E}, {A,B,C,E,D}, {A,B,D,C,E}, {A,B,D,E,C}, {A,B,E,C,D},
{A,B,E,D,C},…………….. {E,D,B,C,A}, {E,D,C,A,B}, {E,D,C,B,A}
Using the sign information, for each combination is possible to find 2 5  3840
new combinations. Here below, there is a part of all 3840 combinations, using
the same rule:
A, B, C, D, E - positive sign
a, b, c, d, e - negative sign
, {a,b,C,d,E},{a,b,C,d,e},{a,b,c,D,E},{a,b,c,d,E},{a,b,c,D,e},{a,b,c,d,e}
The real ruler with double codification is presented in Fig.1, where
1- step track, 2- micro-step sign codification track, 3- micro step length
codification track, 4- fine resolution track, OS-optical screen.
Figure 1:. The particular case of 5 sectors.
In accordance with Fig.1, the active tracks are:
- fine resolution track: 0.5mm resolution
- micro-step sign codification track : it is an active track that offers information
needed in the double codification of the micro-steps.
- micro-step length codification track: it is an active track that offers information
about the length of all micro-steps. In this way, it is achieved the double
codification of the micro-step: length codification and sign (positive/negative; 0/1
logic) codification.
The first optimized variant achieves the same coding performances using only 4
active tracks and 4 optical sensors (Fig.2).
Figure 2:. The optimized version.
Using the positive binary logic (white = 1 logic level, black = 0 logic level) is
simple to achieve the length information. In the case of the step "aBcdE", the
signals achieved from the micro-step sign codification track are in Figure 3. The
signals are in respect of the terms of binary code.
Figure 3. The signals of the step “aBcdE”.
There are many possibilities to choose the dimension of the micro-steps. The
only one restriction is:
 L
i 1
 Ls
Ls  micro  step length
Ls  step length`
In the particular case of the application:
 L
i 1
 Ls  40mm
The segments in the case of micro-steps dimension, are:
La  LA  4mm, Lb  LB  6mm, Lc  LC  8mm,
Ld  LD  10mm, Le  LE  12mm
Fig.4 shows the signal diagrams obtained in the case of two successive steps:
the 49th step and the 50th step. The literal (algebraic) expressions for both steps
are: {aBCED} and {aBCEd}.
Figure 4. Step 49th and step 50th
The first new codification must make the links between the algebric codifications
of the steps (using letters) to the numerical codifications. For that goal the next
observations are very important:
- the step contain five mini-steps: A,B,C,D,E
- the sign codification determines five more variables: a,b,c,d,e
- the number of algebraic variables is ten: a,b,c,d,e,A,B,C,D,E
Using these observations, the firs new codification becomes a natural one: for
ten algebric variables is natural to use all digits: 0,1,2,3,4,5,6,7,8,9 like that:
a=0; A=5; b=1; B=6; c=2; C=7; d=3; D=8; e=4; E=9
To obtain that new codification the algorithm must use all information about
mini-steps (length and sign information) using the next logical structure:
IF the number of fine resolution impulses is 8 and the sign is 0, THEN a becomes a=0
IF the number of fine resolution impulses is 12 and the sign is 0, THEN b becomes b=1
IF the number of fine resolution impulses is 16 and the sign is 0, THEN c becomes c=2
IF the number of fine resolution impulses is 20 and the sign is 0, THEN d becomes d=3
IF the number of fine resolution impulses is 24 and the sign is 0, THEN a becomes d=4
IF the number of fine resolution impulses is 8 and the sign is 1, THEN A becomes A=5
IF the number of fine resolution impulses is 12 and the sign is 1, THEN B becomes B=6
IF the number of fine resolution impulses is 16 and the sign is 1, THEN C becomes C=7
IF the number of fine resolution impulses is 20 and the sign is 1, THEN D becomes D=8
IF the number of fine resolution impulses is 24 and the sign is 1, THEN D becomes D=9
For all steps, the new numerical codification are:
{98765}{98760} {98715} {98710} {98265} {98260}{98215} {98210} {93765} {93760}
{93715}{93710} {93265} {93260} {93215} {93210}{48765} {48760} {48715} {48710}
{48265}{48260} {48215} {48210} {43765} {43760}{43715} {43710} {43265} {43215}
{43260} {43210}
{56789}{56784} {56739} {56734} {56289} {56284}{56239} {56234} {51789} {51784}
{51739}{51734} {51289} {51284} {51239} {51234}{06789} {06784} {06739} {06734}
{06289} {06284}06239} {06234} {01789} {01784} {01739}{01734} {01289} {01284}
{01239} {01234}
The second new codification realizes the correspondence, the agreement of the
“name”, the code of the steps and the position of the linear motor. With the view
of that purpose, it is necessary to choose an arbitrary origin of the displacement.
The logical origin is the origin of the first step. Supplementary, the algorithm
accepts to set the origin on the left limit of the displacement (that is the usual
convention but it is possible to accept another agreement).
Using that usual convention and accepting the principal direction of the
displacement from left to right (the secondary direction becomes the opposite
direction: from right to left), the relation between steps and distance is the
D=distance[mm], Nstep=number of step, Lstep=step length=40[mm]
If the linear motor works in opposite direction, the relation becomes:
D=Di─ Nstep*Lstep[mm]
Di=initial distance[mm]
According all these observations with the basic of the new absolute encoder
algorithm, the new codifications asked by the software design make the
followings operations:
- the length of the mini-steps is coded like numbers - Nms - (the number of fine
resolutions impulses counted on the mini-step interval)
- the numbers Nms, are:
- A or a=8 B or b=12 C or c=16 D or d=20 E or e=24
According to the sign of the mini-steps and the first new codification, the ministeps became:
a=0 A=5 b=1 B=6 c=2 C=7 d=3 D=8 e=4 E=9
The second codification produces the relation between the step and the position
(distance from the origin), in accord with the example from the Table 1:.
Table 1: The relation step/distance
3. Experimental set-up
The experimental set-up is shown in Fig.5. The experimental set-up, able to
obtain these objectives is composed by: 1- dc electrical machine; 2- clutch
(plate clutch); 3- bear; 4- roll; 5- coded ruler (scale); 6- axle; 7- speed indicating
generator; 8- power unit (chopper) & control; 9- distance adjustment (OX
direction); 10- angle adjustment; 11- distance adjustment (OY direction); 12optical fiber sensor; 13- optical amplifier; 14- oscilloscope. The experimental
set-up uses two types of optical fibre sensors, made by SUNX: sensor fibre type
FD-FM2 -for the normal resolution and sensor fibre type FD-G4 and the lentil
type FX-MR3 -for the fine resolution.
Figure 5: The experimental set-up
The principle of the experimental set-up is to obtain the relative linear speed
between the optical reader head and the coded ruler. The linear displacement is
replaced by the rotary movement of the roll and in this way is obtained the
relative speed of the optical reader head in rapport with the coded ruler.
-the rotary movement of the roll produces the relative speed of the CR, easy
and cheaper
-the basic idea of the experiments is to determine the maximum speed that the
optical reader head can work correctly- 100% accuracy, without lost signals (the
maximum frequency that the optical reader head can be capable to recognize)
-this maximum speed must be described in some specifically conditions: the
distance between the optical fiber and CR, the angle between the optical fiber
and the CR and the optical characteristics of the colours on the CR
-the specifically conditions are imposed by the DAX and DAY: distance
adjustment and angle adjustment. The distance accuracy is  (0.1mm) and the
angle accuracy is  (15’)
The conclusions of the experimental measurements are:
-the maximum work frequency for both optical fiber sensors is 4000 [Hz] , when
the fiber is perpendicular on the coded ruler
-the maximum liner speed (imposed by the finest coded ruler) is 2 [m/s]
-the variance of the angle between the optical fiber sensor and the coded ruler
reduces the maximum work frequency for both optical fiber sensors (3000Hz)
and the maximum liner speed
-a bigger variance of the angle between the optical fiber sensor and the coded
ruler determines an insolubly data acquisition
-there are not differences between the two cases: with glassy, smooth roll
(coded ruler) or rugged roll (  0.5mm). The equipment immunizes again this
kind of mechanical “noise” and this observation is very important in practical
4. The colors codification
The paper offers a new codification for the ministeps: a colors codification. If
each ministep is able to be painted in many colors, the power of the algorithm
increases. For each step combination, using 5 colors, it is possible to obtain:
55  3125 new combinations.
If the step is {A,B,C,D,E}, we use Ai , Bi , Ci , Di , Ei  where:i=1,2,3,4,5
Ai =five colours for the A ministep, Bi =five colours for the B ministep
C i =five colours for the C ministep, Di =five colours for the D ministep
E i =five colours for the E ministep
With both codifications, the number of individually steps is 120  3125  375000 .If
each step is 40mm length, the all 375000 steps measure 1500000mm. That is
the maximum length of the linear motor displacement using this type of absolute
linear encoder, with 5 ministeps and 5 colours. The power of the method is
presented in the Table 2. A simple analyze of the possible situations (5
ministeps with 2,3,...8 colours, 6 ministeps with 2,3,..8 colours and 7 ministeps
with 2,3..8 colors) shows the maximal distances in each situation.
5 ministeps
6 ministeps
7 ministeps
Table 2 The maximal coded displacements in several ministeps and colours situations
In the case of 5 colors, it is possible to use the same topology of the coded
ruler. For all 120 combinations of initial A,B,C,D,E segments ({A,B,C,D,E},
{A,B,C,E,D}, {A,B,D,C,E}, {A,B,D,E,C}, {A,B,E,C,D},…………….. {E,D,B,C,A},
{E,D,C,A,B}, {E,D,C,B,A}) must expand the specific combinations in accord with
colours codification:
The 116th combination is E D A C B. Considering the initial notation in the
colours codification Ai , Bi , Ci , Di , Ei  where:i=1,2,3,4,5, the maximum variants
are 55=3125: 0 0 0 0 0 ; 0 0 0 0 1 ; 0 0 0 0 2 ; 0 0 0 0 3 ; 0 0 0 0 4 ; 0 0 0 1 0 ;
0 0 0 1 1; 0 0 0 1 2 ; 0 0 0 1 3 ; 0 0 0 1 4 ; 0 0 0 2 0 ; 0 0 0 2 1……………….
44344;44400; 44401; 44402;44403; 44404;44410;4
4 4 1 1 ; 4 4 4 1 2 ; 4 4 4 1 3 ; 4 4 4 1 4.
The dedicated software uses he exposed version. The linear encoder uses the
same topology with five segments. In this way, the initial white/black software
could be the core of the final software. The only one software development
obtain the relation between the step (in the actual case of the 3125 variants)
and the distance in accord with the origin of the displacement.
5. Conclusion
The present paper contains the theoretical aspects of a new absolute linear
encoder system. The system uses a set of codifications and the last innovation
is the colours codification. In this way, it’s possible to obtain major advantages
in contrast with classical linear encoders: long distances applications (the
maximum distance using the proposed system is 15000m!) and the better
resolution is 0.25mm with additional lens.
Randy Frank, Understanding Smart Sensors 2nd ed, 2000 Artech House Publisher
R. Pallas-Areny, J. G. Webster, Sensors and Signal Conditioning 2nd ed, 2001 John Wiley&Sons
Keyence, General Catalog Fiber OpticSensor 2005
Keyence, General Catalog Laser Sensor 2005
A.Argeseanu, D. Teodorescu, Noise Resection Circuit for the Balancing Machine Patent RO102697