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LOCATING A POINT IN 2-D SPACE, A LOW BUDGET TABLET PEN

By :- Bimalendu Shankar

Final B.E. Electronics Instrumentation & Control Engg

University College of Engineering

Rajasthan Technical University, Kota

[email protected]

A B S T R A C T

Often we use costly TABLET PEN for the purpose

of electronic drawing but, many of us is unable to

purchase the one due to its cost, also drawing is a

typical task to be completed using a simplemouse due to its uncomfortable design for

drawing. Moreover it required a steady hand of

artist. Keeping in mind we decided to try out a

low budget alternative to mimic the purpose of

mouse w hi le resembling the pen.

Our design uses Hall Effect sensors and a magnet

to locate any point. Magnet is used as pen which

is moved over a restricted area consisting of Hall

sensors. Signal from Hall sensor is function of

position of magnetic pen, which is then used todetermine the exact position of pen using

B I L I N E A R I N T E R P O L A T I O N . These data can be

feeded to computer using USB and thus a low

cost alternative of the PE N may be manufactured.

I. INTODUCTION

Tablet pen is definitely a need of time in

present electronics era, where everymoment we use electronic gadgets for

various purpose. One of these purpose

include electronic drawing by artist on

computer, Tablet pen one which comes in

use for this purpose. Professional artist can

easily purchase a Tablet pen, but an

armature student artist may find it costlier,

moreover a low price alternative is always

welcomed. This low price alternate design

canbe used for the purpose of some simple

digital geometrical drawings like squares,

rectangles, triangles, and spheres etc, also

some simple drawings.

However the accuracy and sensitivity of

the Pen may be poor than expected but,

this may drive the research at higher levelfor alternate method of designing Human

Interface Devices.

II. HALL EFFECT

Hall sensors are used as magnetic field

sensors, thus they measures any change in

magnetic field with respect to someconstant filed, which in the most of the

cases is earth s magnetic field. The sensors

can be so calibrated that they may avoid

any such undesirable field at the output.

This drive us to think that hall sensors can

be used to mimic the purpose of locating a

point in two dimensional space, using a

Hallbach Magnet array.

The Hall effect was discovered by Dr.Edwin Hall in 1879 while he was adoctoral candidate at Johns HopkinsUniversity in Baltimore. Hall wasattempting to verify the theory of electronflow proposed by Kelvin some 30 yearsearlier. Dr. Hall found when a magnet wasplaced so that its field was perpendicularto one face of a thin rectangle of goldthrough which current was flowing, adifference in potential appeared at the

opposite edges. He found that this voltagewas proportional to the current flowingthrough the conductor, and the flux density


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The simple formula for the Hall coefficientgiven above becomes more complex insemiconductors where the carriers aregenerally both electrons and holes whichmay be present in different concentrations

and have different motilities. For moderatemagnetic fields the Hall coefficient is

(5)

where is the electron concentration,the hole concentration, the electronmobility , the hole mobility and theelectronic charge.

For large applied fields the simplerexpression analogous to that for a singlecarrier type holds.

(6)

IV. QUANTUM HALL EFFECT

In the presence of large magnetic fieldstrength and low temperature, one canobserve the quantum Hall effect, which isthe quantization of the Hall voltage.

As the output of quantum Hall effect isquantized i.e. there is a step change atoutput for step change in field strength,thus better avoidance to unnecessary

nearby field can be obtained.

V. HALL SENSOR S TRANSFER

FUNCTION

As clear from equation 1 and 2 the Hallvoltage output of the sensor is directlyproportional to the field applied, thus the

polarity of output voltage should alsochange with change in direction of the

field applied. This system would requiredplus and minus power supplies, therebyincreasing the complexity of the systemand also questions the sensitivity andstability.

In order to avoid two power supplies, afixed offset or bias is introduced into thedifferential amplifier. The biased valueappears when no field is applied, and iscalled null voltage. When a positivemagnetic field is sensed the voltage atoutput raises above the null voltage, whilein the case of negative filed the voltagedrops below the null voltage but remainpositive and hence avoid the need of minus

power supply, as shown in figure 3.

Figure 3. Transfer function of Hall sensor, usedwith Null voltage concept

Figure 4. Transfer function

Figure 4. shows the analogueapproximation of transfer function.


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VI. MAGNETIC FIELD

As our design uses Hall sensors to locateany desired point in two dimensions, weuse magnet with appropriate field as

primary sensor of the system which sensesthe desired location with respect tostationary Hall sensors.

A magnet produces a vector field, themagnetic field, at all points in the spacearound it. It can be defined by measuringthe force the field exerts on a movingcharged particle, such as an electron. Theforce (F) is equal to the charge (q) timesthe speed of the particle times the

magnitude of the field (B),

Or F = q*v x B (7)

where the direction of F is at right anglesto both v and B as a result of the crossproduct. This defines the magnetic field'sstrength and direction at any point. Thisforce is same which cause theaccumulation of charge carrier across theface of Hall sensor, and hence the Hallvoltage.

The change in field for the permanentmagnet depends on its design. Magneticfield of a few magnets is shown below.

Figure 5. Magnetic field of Spherical Magnet.

Figure 6. Magnetic field of two hemispherical

magnetswith gap between them.

Figure7. Magnetic field of a single Bar magnet.

Figure 8. Magnetic field of Hallbach Magnet.


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f(x, y) f(0,0)(1-x)(1-y) +f(1,0)x(1-y)+f(0,1)(1-x)y + f(1,1)xy (16)

Or equivalently, in matrix operations:

(17)

Contrary to what the name suggests, theinterpolation is notlinear.

The result of bilinear interpolation isindependent of the order of interpolation.If we had first performed the linearinterpolation in the y-direction and then inthe x-direction, the resultingapproximation would be the same.

Trilateration and Triangulation may alsobe used but as both of these uses threereference point to determine the location ofany point on a 2-D plane. Since ourvoltage displacement relationship is notlinear, as clear from figure 5 to figure 9,we could not locate the reference point anddetermine the unknown point using thesemethods. Hence these methods areignored.

VIII. DESIGN OF THE TABLET PEN

Basic structure of the design can be splitinto two components, one is mousecomponent which include the drawing pad,magnet and the programmed mousemicrocontroller, while other is USBcomponent which include USBmicrocontroller and port etc which isprogrammed to transfer the data to

computer.

Also as a mouse not just measures therelative position of the mouse and movethe cursor on the screen accordingly butalso senses the relative velocity with whichthe mouse is moved, in our case the

magnet, this data gives us the distancetraversed by the cursor on the screen. Thuswhile programming the mousemicrocontroller these facts should be keptin mind.

One way of programming may include thelook table method, in which the calibrationtable consisting of relative position ofmouse and the position of cursor onscreen, i.e. the direction of cursor

movement, while a second look up tablewould consists of calibration of relativespeed with which the mouse or magnet ismoved over the pad to the distance towhich the cursor is moved over the screen.

Figure 11. Gives the basic block diagramdesign of the pen. The mouse moves andoperates based on the user s actions. Leftclicks and right clicks can open documentsand change properties on files. When theuser moves the mouse, the mouse willmove as well in the same general direction.The direction and displacement of themouse is based on relative motion notabsolute motion. How much the mousemoves depends on how fast the user movesthe mouse. If the user moves the mousefaster, the mouse will move a greaterdistance. Likewise, if the user moves themouse slowly, the mouse will move a

shorter distance.

From above discussion it is clear that themouse part is more complicated than USBpart of the mouse, there we need to, first ofall prepare the two calibration table one fordirection while other for distance. Thecalibration method is explained latter inthis paper.


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Figure 11. Basic block diagram of the Tablet Pen.

IX. DETECTION OF POINT IN 2-D

As clear from above figure 11 that Hall

sensors are used to detect the location of

primary moving element, which is magnet

in our case.

The sensors can be mounted on a Bakelite

board or any other inert plastic board of

sufficient and adequate length and width,

on their edges and then are covered with

some flexible non-magnetic and non-conducting material. This board is also

called as drawing board.

Also the sensors are connected to power

supply which may be derived from battery.

Voltage output of the sensor is required to

be feeded to ADC card before it can be

sent to mouse microcontroller.

The output variation of A1302EU a LinearHall Sensor of Allegro make is

1.3mV/Gauss, which is very small to

directly connect the sensors output to

ADC. Thus a differential amplifier is

required to be used with sufficient gain.

Also as the circuit requires protection from

high frequency noise, we should use a low

pass filter before connecting the output to

ADC.

Figure 12 shows the general idea of the circuit

required to sense the location of any point using

Hall sensors.

A circuit similar to above figure 12 is

required to be made for all the four

sensors. Using this circuit we can read the

data output of ADC to desired register of

the mouse microcontroller.

X. CALIBRATION OF DRAWING

BOARD

The calibration is required in order to

determine the exact location of magnetic

pointer. This mapping of coordinate is one

of the most difficult tasks to do.

Drawing pad

Mouse

Microcontroller

USB

MicrocontrollerUSB

Hall Se nsors Magnet

Computer

ush

uttons

+ve Gnd

Battery for Power

supply

Potential

divider circuit

Diff

Am li

Mouse

MC U

Gn d

Hall sensor


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For the mapping we will use a simple

arrangement where, we will make a virtual

grid pattern, as shown in figure 13 below.

Figure 13. Drawing board, showing the grid pattern

forcalibration.

Now for calibration purpose we will place

our magnetic pen to each of the point of

intersection in the above grid pattern. Now

the output of all the four Hall sensors aftersufficient amplification and A/D

conversion are inputted to the mouse

microcontroller. In the microcontroller the

inputted data undergoes a conversion

according to equation (16), using this

equation we can estimate the value of an

identical Hall sensor placed at that

coordinate. Now this estimated value is

tabulated in a lookup table, against the

known coordinate. We will use the

exponential interpolation method to

estimate the coordinate of any point

between two calibrated points.

To increase the accuracy of determination

of the point we can increase the numbers

of grids.

Also the exponential interpolation brings

out satisfactorily accurate result, as clear

from figure 14 and figure 15.

Figure 14. Exponentially decaying curve, showing

relationship between Vout and Drelative or Total

effective Air Gap.

Figure 15. Showing the relationship between Voutand distance Drelative , when the effective air gap is

constant.

Figure 14. Shows that the output voltage

decays exponentially with increase in

effective air gap. It compels us to think of

the effect of magnetic pen, when it is in the

vicinity of drawing board unintentionally.

To avoid the affect we should determine

the limit of effective output voltage,

named as threshold voltage. Any output

voltage below threshold should be

avoided, and counted as unintentionalencounter of magnet with the sensor.

4

2

3

1

(0, 1)

(0,0)

(1, 1)

(1,0)


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For this we should cover the sensors witha

non magnetic sheet over which the pen

would move. This would maintain a

constant air gap.

Also as clear form figure 15, where the

output voltage also changes with change in

distance D, while remaining the effective

air gap constant. Using this we can

determine a similar threshold for

movement of the pen over the sheet.

XI. DETERMINATION OF

RELATIVE DISPLACEMENT,

DIRECTION OF MOVMENT

Let us suppose that our pen is placed at the

centre of the board, at this moment the

output of all the four sensors would be

same. Now the pen is moved in upward

direction then the output of sensors 3 and 4

would increase, while that of 1 and 2would decrease simultaneously.

Comparison between the change in

outputs of the sensor 1 with 4 and that of 2

with 3 would let to determine the

movement on Y-axis. An increment in

output of sensor 3 and 4 and simultaneous

decrement in output of sensors 1 and 2,

shows the upward movement of pen, while

vice versa show the downward movement.

In similar fashion any movement along X-

axis can be determined by comparing the

change in output of sensors 1 with 2 and

that of 4 with 3.

Let us consider an example as shown in

figure 16, the pen is moved from centre

toward the sensor 4.

Figure 16. An example to illustrate the

determination of direction of movement.

In figure consider that initial position of

the pen be the origin, now the pen moved

towards sensor 4, then

1. Output of sensor 4 will increase.

2. Outputs of all other will decrease.

Now let s compare the change in outputs,

we will reach to following results

1. Comparison in change in output of

4 and 1 shows an upward

movement, so would be result of

comparison between 2 and 3.

2. Comparison in change in output of

4 and 3 shows an movement in left

direction, so would be result of

comparison between 1 and 2.

Now using above comparison resultswe can easily reach to a conclusion

that the pen is moved in IInd quadrant

toward sensor 4, relative to initial

position.

The above gained knowledge

(information) mixed with the

knowledge of calibration and linear

approximation would let us to

determine the final position. Byrepeating this algorithm at high

4

2

3

1

(0, 1)

(0,0)

(1, 1)

(1,0)


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frequency, we would get a smooth

curve, replicating the original move of

the pen.

XII. ESTIMATION OF

MOVEMENT OF CURSOR ON

SCREEN

The distance traversed by the mouse

pointer on screen doesn t depend on

how much the pen is moved over the

board but, depends on how fast the pen

is moved. Thus for an estimation of

how much a mouse moves we need tomeasure or sense the velocity with

which the pen is moved.

The rate of change of output of sensors

would give us an estimation of, how

fast the pen is moving? Now we can

prepare a lookup table from where the

mouse pointer would decide that how

much it should move for given time

differential of change in output. Linear

interpolation can be used to estimate

any value between two tabulated

velocities.

XIII. COST ESTIMATION

Our model uses following components as

detailed in table 1 below

ComponentName

Number Total Price

Magnet 1 4$

Atmel Mega32(Mouse MC)

1 16$

CrystalOscillator

1 1$

Battery (9V) 1 1$

PCB 2 5$

USBcomponent

1 10$

Linear HallSensor

4 16$

Push Buttons 3 1$

Diff Ampl(Maxs4462)

4 4$

OtherExpenses

5$

TOTAL 63$

Table 1. Showing the estimated price of the model

propounded, price of each component is taken from

e-resources and onlinebusiness site.

The cost of digital pen of various makers

varies from 70$ to 160$. Our pen cost is

estimated to be 65$ based on street price of

every component on unit purchasing, so

definitely price estimated would decrease

considerably if purchased in bulk and

special purpose IC s would also serve the

purchase.

So depending upon need of accuracy and

sensitivity of purpose of application, our

Digital Tablet Pen is ready to revolutionize

the market due to its low cost. However it

suffers several drawbacks also which are

discussed next.

XIV. ADVANTAGES OF OUR

MODEL

The main advantages of our model are as

followed:-

1. Low cost of manufacturing.

2. Easy design.3. New field of application of Linear

Hall sensor.

XV. MAJOR DRAWBACKS OF OUR

MODEL

Following are the major drawbacks I

absorbed with the model


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1. Magnet may affect the user with

pacemakers.

2. Magnet may adversely affect the

electronic components working,

such as hard disk data could bepermanently erased if a strong

magnet is put over it.

3. Stray magnetic fields may affect

the working of our model.

4. High sensitivity and resolution is

susceptible.

XVI. CONCLUSION

The model may be proved as a good low

cost alternative against conventional

digital pens. It has a simple design which

is also an added great advantage. It also

suggest us a new dimension to look on

how to exploit the Hall sensors to

advantages. However its resolution and

sensitivity for practical application is yet to

be tested. Also practical implementation ofthe model described may bring several

more difficulties which are not discussed

in this paper.

XVII. REFERENCES

1. Application notes, by

Microcontroller Division

Application Team :USING THE

ST7263 FOR DESIGNING A USB

MOUSE; http://www.st.com

2. Honeywell MICRO SWITCH

Sensing and Control; Hall Effect

Sensors, Chapter 2.

3. Wikipedia, Hall Effect.

4. Wikipedia, Bilinear Interpolation,

Trilateration and Triangulation.

5. A gallery of magnetic fields.htm6. Wikipedia, Magnetic field.

7. Joystick controller employing hall-

effect sensors - US Patent

5160918.htm

8. Magnetic ball joystick- US Patent

5969520.htm9. Datasheet of ATMEL Mega32

microcontroller,

http://www.atmel.com

10.White Paper:Nokia Digital Pen,October 2003,http://www.nokia.com/forbusiness

11.Continuous-Time RatiometricLinear Hall Effect Sensors; AllegroMicroSystems, Inc.www.allegromicro.com

12.Handwriting Tablet, GraphicsTablets, Digital Pens atTigerDirect_com.htm;www.tigerdirect.com

13.Highly sensitive inertial mouseinvention.htm;www.freshpatents.com

14.Hobby Engineering SensorsCategory.htm

15.Wikipedia, Mouse (Computing),

Pointing Stick.16.www.oldmouse.com; The EarliestComputer Mouses ~ o l d m o u s e_c o m ~.htm; Trackballs - ORBITOrbit X-Y Ball Tracker ~ o l d m ou s e _c o m ~.htm

17.Datasheet of Maxs4462.
http://www.freshpatents.com/http://www.tigerdirect.com/http://www.allegromicro.com/http://www.nokia.com/forbusinesshttp://www.atmel.com/http://www.st.com/


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