IUT JOURNAL OF ENGINEERING AND TECHNOLOGY (JET), Special issue (IUT-ICCET), June 2025
1s In e na ional Con e ence on
Co e Enginee ing & Technology (IUT-ICCET 2024)
Jou nal homepage: h ps://je .iu oic-dhaka.edu/
High-Resolu ion Displacemen Measu emen Using a Le e
Accele ome e Combina ion
1MD SHAH WALI ULLAH*, 1 SHAKIB ARAFAT TAPU, 1 REDOYAN JOYAB HIRA and
1 MUKTA CHAKMA
1Depa men o Mechanical Enginee ing, Bangladesh Uni e si y o Enginee ing and Technology,
Dhaka-1000, Bangladesh.
*E-mail o he co esponding Au ho : [email protected] .ac.bd
ABSTRACT
Measu ing small linea displacemen wi h high esolu ion is a challenge ha has been deal wi h using nume ous complex
me hods. This s udy ocuses on de eloping an expe imen al sys em ha le e ages a mechanical ampli ica ion mechanism
con e ing diminu i e de lec ions in o la ge ones which a e easily de ec able wi h he help o a ailable elec o-mechanical
componen s and o p oduce digi al eadou s. This ampli ica ion is achie ed by a le e -like mechanism. Le e ans o ms
and ampli ies he linea displacemen in o angula displacemen , which is hen picked up by he accele ome e . The change
in g a i a ional accele a ion in one o he axes o he accele ome e can be calib a ed o measu e he linea displacemen .
Such a mechanism p o ides use s he possibili y o adjus esolu ion and ange as needed. The a o emen ioned mechanism
has been es ed in a da a acquisi ion sys em wi h p ope calib a ion by p ecisely de ec ing and measu ing he mo emen o
a sha wi h a high esolu ion main aining g ea accu acy. Mo eo e , he use o o he-shel componen s can educe he
cos signi ican ly o e mo e con en ional app oaches..
KEYWORDS: Le e Mechanism, Linea Displacemen , Da a Acquisi ion.
NOMENCLATURE
l dis ance o he sha om he pi o [mm]
d displacemen o he sha [mm]
θ angula o a ion [°]
1. INTRODUCTION
In he mode n wo ld, accu a e me hods o measu ing displacemen wi h g ea p ecision a e a c i ical
equi emen . E en mino ad ancemen s in p ecision a ec s he as majo i y o enginee ing and scien i ic
applica ions including ields like con ol enginee ing, mic o-manu ac u ing and obo ics. A wide a ie y o
adi ional displacemen measu emen echniques, such as Linea Va iable Di e en ial T ans o me s (LVDTs)
[1] o lase in e e ome y [2] a e al eady in use bu hose o en ace limi a ions in e ms o cos and ope a ional
complexi y. To add ess hese challenges, his expe imen al esea ch pape p esen s a no el app oach ha uses
a mechanical le e sys em and a high-sensi i i y accele ome e along wi h a mic o con olle in o de o achie e
high- esolu ion displacemen measu emen which would be a o dable on a global scale. The esea ch was
conduc ed expe imen ally as a pa o da a acquisi ion p ojec o measu e o que in a To sion me e [3].In his
sys em, wi h he applica ion o o que, he wis ing o he specimen was con e ed in o linea displacemen o a
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needle-like sha a ached o he se up. The o al displacemen o he sha om he beginning o he ailu e o
he es specimen due o he applica ion o o que was only 6mm which was oo small o e ec i e calib a ion.
So, a seesaw-like mechanism o pa icula dimension and heigh was designed o con e he 6mm linea
de lec ion o a la ge s a ic accele a ion o g a i y, making i easie o measu e wi h ADXL 345 [4]. This me hod
enhances he esolu ion o he accele ome e by ampli ying small displacemen s h ough a mechanical le e
sys em. Thus, his ampli ica ion acili a es he p ecision and esponsi eness o ADXL 345 while mi iga ing
noise and d i , making i sui able o applica ions whe e adi ional me hods migh ail o be cos -p ohibi i e.
This pape discusses he ounda ion o he le e -accele ome e measu emen sys em wi h minimal cos , p esen s
he design and expe imen al alida ion, and explo es i s po en ial applica ions in a ious indus ies. This
esea ch was conduc ed expe imen ally and he esul s demons a e he sys em’s capabili y o measu e
displacemen s wi h highe p ecision and accu acy, o e ing a e sa ile and cos -e ec i e al e na i e o all he
con en ional me hods p ac ically.
2. LITERATURE REVIEW
Accele ome e s a e used o measu ing he spa ial posi ion o a de ice using he double in eg a ion o
he accele a ion like Pa k e al. (2013) [5]. Bu ypically, his me hod is e y e oneous. To educe he e o
Fe e o R e al. (2019) [6], (2016) [7] used Kalman il e wi h g ea e ec . Fu he wo k has been done o
in oduce a be e me hod o i ing polynomial ex emum wi h a be e co ec ion e ec o elimina e he end
e m e o caused by he DC componen by Niu e al. (2019) [8]. O he wo ks based on his double in eg a ion
me hod include aul de ec ion using ib a ion ansduce s by Ka alin e al. (2014) [9]. The main limi a ions in
double in eg a ion me hod a e noise ampli ica ion, e ec s o ib a ion and ex e nal dis u bances, high
compu a ional cos , ini ial condi ions and cumula i e e o s. Cumula i e e o s mainly a ise because he
in eg a ion p ocess compounds inaccu acies in accele ome e da a o e ime, namely in he o m o senso noise,
bias d i and sampling a e e o s. Ve y small luc ua ions in ini ial accele ome e da a also ge s ampli ied when
i ’s in eg a ed wice. Va ia ion in sampling a e can also dis o he inal ou pu . Fo small displacemen his
cumula i e e o is mo e signi ican . Niu e al. [8] measu ed displacemen using he double in eg al me hod wi h
hei de eloped polynomial i ing algo i hm in he ange be ween 12.47 m o 12.76 m wi h an e o anging
om 1.79% o 0.53%. Hoang e al. [10] measu ed displacemen om 0 cm o 200 cm ange wi h a maximum
e o o app oxima ely 0.4%. Fe e o e al. [6] showed ha e o in double in eg al me hod ange om 79.5%
o 67.5% when displacemen is measu ed in he ange o 10 cm o 30 cm. In oduc ion o Kalman Fil e
signi ican ly educed he e o o 16.7% o 10.7% in he same ange. Pang e al. [11] showed ha use o Kalman
il e esul s in a posi ion e o o 17.66 m pe mg pe squa e min. Howe e , he le e accele ome e combina ion
elimina es he need o double in eg a ion. Ra he a simple linea i is enough o p o ide displacemen da a
wi h e y high accu acy. This newe me hod bypasses he need o in eg a ion al oge he , hus e o
mul iplica ion is conside ably less.
3. METHODOLOGY:
This s udy u ilizes a le e -accele ome e mechanism o measu e he e ical displacemen o a machine
sha . The dimensions o he le e we e hus made speci ic o he sha in ques ion. All s uc u al pa s we e
3D p in ed and as o he accele ome e , ADXL 345 was selec ed o i s compac shape and epea abili y. To
calib a e he se up, eadings we e aken om accele ome e o e e y 0.05mm displacemen o he sha . The
men ioned displacemen was measu ed by a Mi u oyo Heigh Gauge [12].The linea mo emen was ansla ed
in o an angula displacemen o equi ed magni ica ion and hen a linea i was applied o he acqui ed da a o
aking measu emen . A duino Mega 2560 [13] was used as he mic o con olle o his ope a ion. A ST3375
LCD [14] was used o show ou pu alues. Gene al lowcha o he ope a ion is isualized in igu e 1.
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Figu e 1: Flowcha o he ope a ion
3.1. Design
In his speci ic case, he design pa ame e s o he le e we e adjus ed acco ding o he ee space below
he sha whose mo emen needed o be measu ed. The accele ome e was moun ed on one end while he sha
head was placed a he o he end. The downwa d displacemen o he sha esul ed in angula o a ion abou he
pi o . Al hough he displacemen migh be e y small, he angula ampli ica ion esul ed in a la ge o a ion
abou he X-axis o he accele ome e . Al hough he e is a ansla o y mo ion, only he o a ional mo ion is
de ec ed by he accele ome e .
3.2. Sensi i i y con ol
The deg ee o angula o a ion can be easily con olled jus by placing he posi ion o he needle-like sha
u he away om o close o he pi o ing poin . In his s udy, he sha was placed a 6mm, 8mm, and 10mm
u he om he pi o as shown in Figu e 2. The esul ing angula o a ions a e shown below-
anθ = d
l
Fo l = 6 mm and d = 4.8 mm,
anθ = 4.8
6
⇒ θ = 38.65°
Fo l = 8 mm and d = 4.8 mm,
anθ = 4.8
8
⇒ θ = 30.96°
Fo l = 10 mm and d = 4.8 mm,
anθ = 4.8
10
⇒ θ = 25.64°
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(a) l = 6 mm (b) l = 8mm
(c) l = 10 mm
Figu e 2: Schema ic diag am o he sha posi ion om he pi o and co esponding angula o a ion.
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Figu e 3: Pic u e o expe imen al se up
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Figu e 4: Va ia ion o ADXL eading wi h he change o e ical displacemen o he sha .
Table 1. Accele ome e o A duino Mapping
ADXL 345 pin
Co esponding A duino pin
SDA
SDA
SCL
SCL
Vcc
5V
GND
GND
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Table 2. ST3375 o A duino Mapping
ST3375 display pin
Co esponding A duino pin
LED
3.3
SCK
52
SDA
51
A0
9
Rese
8
CS
53
GND
GND
VCC
5
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Figu e 5: Bes i cu es o he displacemen -ADXL ou pu .
3.3. In e acing wi h A duino
ADXL 345 was in e aced wi h A duino ia I2C p o ocol [15] . A se ial clock pin (SCL) o he A duino
Con olle boa d pulses a a egula in e al, and a se ial da a pin (SDA) o e which da a is ansmi ed be ween
A duino and accele ome e . The accele ome e is supplied wi h 5V om he A duino boa d di ec ly. A ST3375
LCD was also in e aced wi h A duino so ha he ou pu alues can be displayed. Table 1 indica es he pinou
e e ences be ween ADXL 345 and A duino and Table 2 ells he same be ween ST3375 LCD and A duino.
Figu e 3 shows he inal se up.
3.4. Taking da a o calib a ion and inding cha ac e is ics equa ion
X-axis eadings o ADXL 345 we e aken om he A duino se ial moni o o 0.05mm o displacemen . These
eadings indica e he change in g a i a ional accele a ion due o o a ion. Fi s ly, wi h l = 6mm, i e ADXL
alues we e aken o e e y displacemen alue. Su icien ime was allowed o s abilize he eadou om he
ADXL. A plo o he a e aged ADXL alue agains he displacemen o he sha was done and is shown in
Figu e 4. The ini ial ADXL eading (a 0mm) was sub ac ed om all he ou pu s o elimina e dependency on
ini ial s a ing angle. A bes - i line was de e mined h ough eg ession analysis, shown in Figu e 5, which was
hen used as he cha ac e is ic equa ion o he se up. Finally, he A duino was p og ammed o show ou pu in
millime e s co esponding o he angula displacemen which was sensed by he accele ome e . The ADXL 345
ou pu is ai ly linea , so when he cha ac e is ic equa ion is known, he p og am is w i en such ha he ini ial
angle o he le e wi h he ho izon al axis doesn’ need o be pe ec ly ze o. Basically, any s a ing angle is
conside ed as he s a ing poin (0mm) om which he measu emen is ini ia ed. The same p ocess was epea ed
o l = 8mm and l = 10mm o obse e he change in sensi i i y and how he e o in measu emen a ies. All he
da a we e aken wi hin he p esc ibed ope a ing condi ion o he ADXL 345 and ex e nal ac o s like high
ai low we e elimina ed by conduc ing he expe imen in a closed oom.
4. RESULTS AND DISCUSSION
A e calib a ion, he se up was es ed by measu ing he e ical displacemen o he same sha . The
esul shows accep able accu acy o he sha placemen a 6mm om he pi o . Howe e , he accu acy
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dec eases, and unce ain y inc eases signi ican ly as he sha was placed a 8mm and 10mm om he pi o . To
isualize he esul , a sca e plo consis ing o heigh gauge measu emen in X-axis and mode o he ou pu s
aken om he se up in Y-axis was plo ed. Absolu e de ia ion o ou pu s om he mode a each poin was
mul iplied by 10 and shown using he e o ba in Figu e 6. The mul iplica ion was conduc ed o enhance
isualiza ion because he ue de ia ion is oo small o be dis inguished easily.
4.1. E o analysis
One inhe en sou ce o e o in his se up is he heigh gauge used du ing calib a ion p ocess. The heigh gauge
in ques ion is Mi u oyo digi al heigh gauge 192-611 wi h he accu acy o ±0.05mm wi h quan izing e o o
±1. As he heigh gauge is e y widely used, he analysis is limi ed o compa ing measu ed ou pu s o he heigh
gauge ou pu only. The accele ome e has a sensi i i y o ±2G o ±16G. As his sensi i i y will au oma ically
in oduce e o s while ge ing ou pu da a, calcula ing he inal ou pu accu acy o he se up will include all he
in e media e e o s. To analyze he epea abili y o he se up, he displacemen ou pu placing he sha a 6mm
om he pi o (l = 6mm) was aken 5 imes o a ange o linea displacemen o he sha (0.05mm-4.8mm)
wi h 0.05mm inc emen o each s ep. Then o each s ep, he s anda d de ia ion was calcula ed. The a e age
s anda d de ia ion and maximum s anda d de ia ion o he whole ange o ou pu we e hen calcula ed o
ep esen he epea abili y. To measu e accu acy, he maximum di e ence be ween he ou pu esul and he
ac ual displacemen ( om he heigh gauge) o each s ep was calcula ed and a e aged ou . These s eps we e
hen epea ed o l = 8mm and l = 10mm. The bes esul s we e ob ained when he sha was placed 6mm om
he pi o . All he indings a e p esen ed in Table 3.
