Development of Torque Sensor with High Sensitivity for Joint of Robot Manipulator Using 4-Bar ...

12 Pages·2016·5.46 MB·English

sensors
Article
Development of Torque Sensor with High Sensitivity
for Joint of Robot Manipulator Using 4-Bar
Linkage Shape
Hong-XiaZhang1,Young-JaeRyoo2andKyung-SeokByun1,*
1 DepartmentofMechanicalEngineering,MokpoNationalUniversity,Jeonnam585543,Korea;
[email protected]
2 DepartmentofControlEngineeringandRobotics,MokpoNationalUniversity,Jeonnam58554,Korea;
[email protected]
* Correspondence:[email protected];Tel.:[phone]
AcademicEditor:Suk-SeungHwang
Received:29March2016;Accepted:14June2016;Published:1July2016
Abstract: Thetorquesensorisusedtomeasurethejointtorqueofarobotmanipulator. Previous
researchshowedthatthesensitivityandthestiffnessoftorquesensorshavetrade-offcharacteristics.
Stiffnesshastobesacrificedtoincreasethesensitivityofthesensor. Inthisresearch,anewtorque
sensorwithhighsensitivity(TSHS)isproposedinordertoresolvethisproblem. Thekeyideaof
theTSHScomesfromits4-barlinkageshapeinwhichtheangulardisplacementofashortlinkis
largerthanthatofalonglink. Thesensitivityofthetorquesensorwitha4-barlinkshapeisimproved
withoutdecreasingstiffness. Optimizationtechniquesareappliedtomaximizethesensitivityofthe
sensor.AnactualTSHSisconstructedtoverifythevalidityoftheproposedmechanism.Experimental
resultsshowthatthesensitivityofTSHScanbeincreased3.5timeswithoutsacrificingstiffness.
Keywords: torquesensor;robotmanipulator;jointtorquecontrol;4-barlinkage
1. Introduction
Industrial robot manipulators have been widely used to improve productivity in various
industriessuchasautomotive,electronicsandshipbuilding. Toincreasetheintelligenceoftherobot
manipulator,manykindsofsensorshavebeendeveloped. Amongthese,sensorstomeasureforceand
torquehavebeenincreasinglyusedinrobotmanipulators. Thesesensorscanimprovetheperformance
oftherobotmanipulator[1].
ForcesandtorquesofendeffectorandjointtorquesarerelatedbytheJacobianmatrixasfollows[2]
Γ“ JTF
“ ‰
T
F“ F ,F ,F ,T ,T ,T (1)
x y z x y z
Γ“rT ,T ,T ,T ,T ,T sT
1 2 3 4 5 6
where,T ´T arethetorqueatthejointsofthemanipulator. F ,F ,F ,T ,T ,T areforcesandtorques
1 6 z y z x y z
attheendeffectorofthemanipulator. JistheJacobianmatrixofthemanipulator.
As shown in Figure 1, the sensors to measure force and torque can be classified as 6-axis FT
(force/torque) sensors and joint torque sensors. The 6-axis FT sensors (Figure 1a) are attached to
theend-effector. Itcandirectlyandpreciselymeasurethereactionforcesandtorquesbetweenthe
manipulatorandtheenvironmentwhichthemanipulatorcontactswith. The6-axisFTsensorsare
smallandsensitive. Forexample,asshowninFigure2,theFTsensorJR3[3]isusedattheendeffector
oftherobotmanipulator. However,thissensoronlycanmeasuretheforce/torqueatthedistalendof
themanipulator. Itcannotdetecttheconflictorexternalforcesactingonthemanipulatorbody. Asa
Sensors2016,16,991;doi:10.3390/s16070991 www.mdpi.com/journal/sensors
Sensors 2016, 16, 991 2 of 12
of the robot manipulator. However, this sensor only can measure the force/torque at the distal end of

Sensors 20t1h6,e 1 6m, 99a1n ipulator. It cannot detect the conflict or external forces acting on t2h oef 1 m2 anipulator body. As a
Sensors20r16e,s1u6,l9t9,1 an FT sensor attached at the end effector of a manipulator cannot be2 oufs12ed to improve the safety
of the robot manipulator. However, this sensor only can measure the force/torque at the distal end of
the manoipf uwlaotorrk. iInt gca ennnovti rdoetnemct ethnet sco wnfhliectn o hr euxmterannasl faonrcde sr aocbtiontgs oanr eth we morakniipnugl aitno rt hboed sya. mAse a s pace.
rreessuulltt,, aann FFTT sseennssoorr aattttaacchheedd aatt tthhee eenndd eeffffeeccttoorr ooff aa mmaanniippuullaattoorr ccaannnnoott bbee uusseedd ttoo iimmpprroovvee tthhee ssaaffeettyy
ooff wwoorrkkiinngg eennvviirroonnmmeennttss wwhheenn hhuummaannss aanndd rroobboottss aarree wwoorrkkiinngg iinnt thhees saammees sppaaccee..

(a) (b)
(a) (b)
Figure 1. FFoirgcue raen d1 .t oFroqrucee s eannsdor tso forqr muea nsiepnuslaotrosr .f (oar) 6m-aaxnisi FpTu(floartcoer/t. o(raq)u 6e-)a sxeniss oFrTs;( (fbo)r jcoein/tt otorrqquuee ) sensors; (b) joint torque
Figure 1. Force and torque sensors for manipulator. (a) 6-axis FT(force/torque) sensors; (b) joint
tsoernqsuoerss.e nsseonrss.ors.

(a) (b)

Figure 2. Manipulator working with FT sensor (JR3).
(a) (b)
Figure2.ManipulatorworkingwithFTsensor[3].
On the other hand, joint torque sensors (Figure 1b) measure torque forces at joints. The joints of
Figure 2. Manipulator working with FT sensor (JR3).
a robot manipulator generally consist of an actuator, a reducer, an encoder, a break, a bearing, etc.
Ontheotherhand,jointtorquesensors(Figure1b)measuretorqueforcesatjoints. Thejoints
Joint torque sensor can be added such as a DLR (Deutsches Zentrum für Luft- und Raumfahrt e.V.;
ofarobotmanOipnu tlahteo rogtehneerr ahllayncdo,n jsoisitnotf taonrqacutuea stoern,saorresd u(Fceirg,uanree n1cbo)d mer,eaabsrueraek ,taorbqeaurein fgo,rectce.s at joints. The joints of
German Aerospace Center), joint of manipulators LWRIII [4]. Feedback from the joint torque sensors
JointtorquesensorcanbeaddedsuchasaDLR(DeutschesZentrumfürLuft-undRaumfahrte.V.;
can be au sreodb otot mcoamnpipenuslaateto fro rg ethnee rnaollnyli nceoanristiiesst oanf da nm aocdteuliantgo ru,n ac erretadinutcieesr ,o af nm eanncipoudlaetro,r a break, a bearing, etc.
German Aerospace Center), joint of manipulators LWRIII [4]. Feedback from the joint torque
dynamiJcos in[5t] .t oFruqruthee rsmeonrseo, rj ociannt tboerq aude dseedns osursc hca ans par eDveLnRt a(Dcceiduetnstcsh oers rZeednuctreu dmam füagre L buyf t- und Raumfahrt e.V.;
sensorscanbeusedtocompensateforthenonlinearitiesandmodelinguncertaintiesofmanipulator
controlling the manipulator force. This can lead to the improved intelligence of robot manipulators.
German Aerospace Center), joint of manipulators LWRIII [4]. Feedback from the joint torque sensors
dynamics[5]. Furthermore,jointtorquesensorscanpreventaccidentsorreducedamagebycontrolling
Nowadays, more and more robots are working together with people. These kinds of robots
themancipaunl atboer fourscee.dT htios cacnomleapdetnostahteei mfporro vtehdei nnteollnigleinnceeaoriftrioebso tamnadn ipmuoladtoerlsi.ng uncertainties of manipulator
should have safety functions to prevent collision accidents in an unstructured real environment [6].
Nodwyandaayms,icmso r[e5]a.n dFumrotrheerrombootrsea,r ejowinortk itnogrqtougee thseernwsoitrhsp ecoapnl e.pTrehveseenkt inadcscoidferonbtos tsor reduce damage by
Safety-based design of the manipulator can involve a FT sensor which measure forces and torques at
shouldhavesafetyfunctionstopreventcollisionaccidentsinanunstructuredrealenvironment[6].
the endc-eofnfetcrtoorll ionf gth teh reo bmoatsn [i7p].u Hlaotwore vfeorr, cwe.h eTnh ais c coallnis iloena dis tcoa utsheed ibmy portohevre pda irntst eolfl itghee narcme ,o f robot manipulators.
Safety-baseddesignofthemanipulatorcaninvolveaFTsensorwhichmeasureforcesandtorques
human safetyN caonwnoatd baey esn,s umreodr [e8 ]a. Tnhde rmefoorree i nr othbiso sttsu dayr,e t hwe ojorinkti ntogr qtuoeg seetnhsoerr uwseidt hfo rp jeooinptsl eo.f These kinds of robots
attheend-effectoroftherobots[7]. However,whenacollisioniscausedbyotherpartsofthearm,
the robot manipulator is discussed.
should have safety functions to prevent collision accidents in an unstructured real environment [6].
humansafetycannotbeensured[8]. Thereforeinthisstudy,thejointtorquesensorusedforjointsof
There are many previous studies on joint torque sensors. Figure 3 shows various types of these
theroboStamfeantyip-ublaastoerdi sddeisscigunss eodf. the manipulator can involve a FT sensor which measure forces and torques at
torque sensors. Solid [9] (Figure 3a) and hollow [10] (Figure 3b) cylinders are simple and rigid
Thethreea reenmda-enfyfepcretvoiro uosf sttuhdei ersoobnojtosi n[t7t]o.r qHuoewseenvsoerrs,. wFighuerne 3as hcoowllsisviaornio uiss tcyapuesseodf thbeys eother parts of the arm,
structures. Designs researched to increase the sensor sensitivity include the hub-sprocket design [11]
torque sensors. Solid [9] (Figure 3a) and hollow [10] (Figure 3b) cylinders are simple and rigid
(Figure h3cu),m thaen h osallofewty c rcuacnifonromt dbees iegnns [u12r]e (dF i[g8u]r.e T 3hde) raenfdo trhee ihno ltlhowis hsetxuadfoyr,m th seen jsooirn [t1 3to] (rFqiguuer es ensor used for joints of
structures. Designsresearchedtoincreasethesensorsensitivityincludethehub-sprocketdesign[11]
3e). Tortqhuee rsoebnosotr ms wanithip suploakteo rt oips odloisgcyu [s1s4e] d(F. igure 3f) provide high sensitivity. However, the
(Figure 3c), the hollow cruciform design [12] (Figure 3d) and the hollow hexaform sensor [13]
resulting compliance introduces a joint angle error that should be minimized. As a modification of
There are many previous studies on joint torque sensors. Figure 3 shows various types of these
(Figure3e). Torquesensorswithspoketopology[14](Figure3f)providehighsensitivity. However,the
the hub-sprocket design, the sensor of HIT (Harbin Institute of Technology) [15] was designed based
resultingtocroqmupeli asnecnesinotrrso.d uScoelsiad jo[i9n]t a(nFgilgeuerrreo r3tah)a tasnhodu lhdoblelomwin im[1i0ze] d(.FAigsuarmeo d3ibfi)c actiyolninofdtehres are simple and rigid
on shear strain theory and the sensor of LWRIII [16] had four beams with a hole to increase sensitivity.
hub-sprsotcrkuecttduersiegsn. ,Dtheessiegnnsso rreofseHaIrTc(hHeadrb tion iInnsctriteuatseeo fthTeec shennolsoogry s)e[1n5s]iwtiavsitdye siingcnleuddbea stehdeo hnub-sprocket design [11]
shearstraintheoryandthesensorofLWRIII[16]hadfourbeamswithaholetoincreasesensitivity.
(Figure 3c), the hollow cruciform design [12] (Figure 3d) and the hollow hexaform sensor [13] (Figure
3e). Torque sensors with spoke topology [14] (Figure 3f) provide high sensitivity. However, the
resulting compliance introduces a joint angle error that should be minimized. As a modification of
the hub-sprocket design, the sensor of HIT (Harbin Institute of Technology) [15] was designed based

on shear strain theory and the sensor of LWRIII [16] had four beams with a hole to increase sensitivity.
Sensors2016,16,991 3of12

Sensors 2016, 16, 991 3 of 12

Sensors 2016, 16, 991 3 of 12

(a) (b) (c)

(a) (b) (c)

(d) (e) (f)

Figure 3. Various structures of torque sensor. (a) solid cylinder; (b) hollow cylinder; (c) hub s procket;
Figure3.Variousstructuresoftorquesensor.(a)solidcylinder;(b)hollowcylinder;(c)hubsprocket;
(d) hollow crucifo(rdm); (e) hollow hexaform; (f)( esp) oke topology. (f)
(d)hollowcruciform;(e)hollowhexaform;(f)spoketopology.
Figure 3. Various structures of torque sensor. (a) solid cylinder; (b) hollow cylinder; (c) hub sprocket;
In previous research studies, the sensitivity and the stiffness of torque sensors have trade-off
(d) hollow cruciform; (e) hollow hexaform; (f) spoke topology.
Icnhaprraecvteiroiustsicsr.e sTeoa ricnhcresatused itehse, sthenesisteivnistyit iovfi ttyhea nsdentshore, stthieff nsteifsfsneosfs tohraqs utoe sbeen ssaocrrsifihcaedv.e Htriagdh e-off
charatcotersriiosIntniac lsp .srteTifvofinoienuscssr reisea sisemeaprtchoher tsastneuntd sbiieetcsiv,a uitthsyee otshfeent hsdieteifsvleeitncyts iooannr,d bt hythe sees ntsitsfioffnfrnse esassds dhosaf s ptootorsqibtuieoen ss aeecrnrrsoiofirrscs e thhdaa.tvH eca itgnrhnadoteto -brosefi fo nal
compensated by the joint servo controller. However, it is desirable to design a sensor structure that
stiffnescshaisraicmteproisrtticasn. tTboe cianucrseeatshee tdhee flseecntsiiotnivbityy soefn tshoer ssaendsdosr,p tohseit isotinffenrersosr shaths attoc abne nsoatcrbieficceodm. pHeingsha ted
generates a large strain for a given payload to increase the Signal-to-Noise (S/N) ratio and sensitivity
bythetjoorisniotnsaelr vstoiffcnoenstsr iosl liemr.pHorotawnte vbeecr,aiutsies tdhee sdireaflbelcetitoon dbeys sigennsaorsse andsdosr pstorsuitciotunr eertrhorast tgheant ecraantneost abela rge
of the sensor. Therefore there are two conflicting requirements: high stiffness and high sensitivity for
straincfoomrpaegnisvaetend pbayy tlhoea jdointot sienrcvroe acosenttrholeleSr.i gHnoawl-etvoe-rN, iot iisse d(eSs/irNab)ler atoti odeasnigdn sae snesnistoivr isttyruocftutrhee thseatn sor.
torsion. In this paper, a new torque sensor with high sensitivity (TSHS) is proposed to resolve this
generates a large strain for a given payload to increase the Signal-to-Noise (S/N) ratio and sensitivity
Thereforetherearetwoconflictingrequirements: highstiffnessandhighsensitivityfortorsion. Inthis
problem.
of the sensor. Therefore there are two conflicting requirements: high stiffness and high sensitivity for
paper,anewtorquesensorwithhighsensitivity(TSHS)isproposedtoresolvethisproblem.
This paper is organized as follows. In Section 2, the proposed torque sensor with high sensitivity
torsion. In this paper, a new torque sensor with high sensitivity (TSHS) is proposed to resolve this
Tish iesxpplaapineerdi.s Soercgtiaonni z3e ddeascsrfiboellso swims.uIlnatiSoenc tmioond2el,inthge inpcrloupdoinsged fitnoitreq ueleemseennsto arnwaliytshish (iFgEhAs)e annsdit ivity
problem.
isexpolpatiinmeidz.atSioenc.t iEoxnpe3ridmeesnctrailb veaslisdiamtiuonla otfi othnem seondsoerl iins gprienscelnuteddin ing Sfienctiitoene 4l.e Cmoenncltuasnioanlsy asrise d(FraEwAn) and
This paper is organized as follows. In Section 2, the proposed torque sensor with high sensitivity
optiminiizs Saeetxicoptinloa.ninE 5ex.d p. eSreicmtieonn t3a ldveasclirdibaetsio snimoufltahtieonse mnsoodreliisnpg rienscelundteindgi nfinSietec teiolenm4e.nCt oannacllyussisio (nFsEAar)e adnrda wn
inSectoiopntim5.ization. Experimental validation of the sensor is presented in Section 4. Conclusions are drawn
2. Torque Sensor with High Sensitivity
in Section 5.
2. TorqueTSo einncsroeraswe istehnsHitiigvihtyS wenitshiotuivt istaycrificing stiffness, a new torque sensor with high sensitivity
(T2.S THoSr)q ius ep Sroepnossoerd w aisth s hHoiwghn Sine nFsigituivreit y4. The TSHS is a 3-beam torque sensor with a 4-bar linkage.
To increase sensitivity without sacrificing stiffness, a new torque sensor with high sensitivity
The support portion of the TSHS is separated from the sensing portion. The stiffness is related to the
(TSHS)ispTroo pinocsreeadsea ssesnhsoitwivnityi nwFitihgouurte s4a.crTifhiceinTgS sHtifSfnisesas, 3a- bneeawm totroqruqeu seesnesnors owritwh ihthigah 4s-ebnasirtilvinityk age.
3-beam support portion while the sensitivity is related to the 4-bar linkage sensing portion. External
(TSHS) is proposed as shown in Figure 4. The TSHS is a 3-beam torque sensor with a 4-bar linkage.
ThesupportportionoftheTSHSisseparatedfromthesensingportion. Thestiffnessisrelatedtothe
torque causes the strain detected by the sensing portion of the sensor. The strain is measured by a
The support portion of the TSHS is separated from the sensing portion. The stiffness is related to the
3-beamsupportportionwhilethesensitivityisrelatedtothe4-barlinkagesensingportion. External
strain gauge. The sensitivity can be increased, irrespective of the stiffness.
3-beam support portion while the sensitivity is related to the 4-bar linkage sensing portion. External
torquecausesthestraindetectedbythesensingportionofthesensor. Thestrainismeasuredbya
torque causes the strain detected by the sensing portion of the sensor. The strain is measured by a
straingauge. Thesensitivitycanbeincreased,irrespectiveofthestiffness.
strain gauge. The sensitivity can be increased, irrespective of the stiffness.

Figure 4. Torque sensor with high sensitivity (TSHS).

FiguFriegu4r.eT 4o. rTqourequsee nsesnosrowr witihthh higighhs seennssiittiivviittyy ((TTSSHHSS).) .
Sensors2016,16,991 4of12
Thekeyideaforincreasingthesensitivitycomesfromthe4-barlinkagemechanismasshown
inFigure5. IntheFigure5a,assumethatthelonglinkL rotates∆θ bytheexternalforceFatpoint
4 4
P ofthe4-barlinkage. ThemotionistransferredtotheshortlinkL byconnectinglinkL . If∆θ is
34 2 3 4
small,theratiooftheangulardisplacementofL (∆θ )and∆θ isthesameastheangularvelocity
2 2 4
ratioasfollows
∆θ ω
2 “ 2 (2)
∆θ ω
4 4
wSehnesorres, 2ω0126,a 1n6d, 99ω14 aretheangularvelocitiesofeachlinkL2andL4,respectively. 4 of 12

(a) (b)
Figure 5. 4-bar linkage mechanism. (a) small rotation of 4-bar linkage, (b) instant center of 4-bar
Figure5.4-barlinkagemechanism.(a)smallrotationof4-barlinkage,(b)instantcenterof4-barlinkage.
linkage
Theangularvelocityratiotheoremcanbeusedtoobtaintheangularvelocityratio[17]. Inthe
The key idea for increasing the sensitivity comes from the 4-bar linkage mechanism as shown in
Figure5b,pointP istheinstantcentercommontolinks2and4. ItsvelocityV isthesamewhether
Figure 5. In the F2ig4ure 5a, assume that the long link L4 rotates  by the extePr2n4al force F at point P34
P isconsideredasapointoflink2oroflink4. Wecanwrite 4
24
of the 4-bar linkage. The motion is transferred to the short link L2 by connecting link L3. If  is
4
V “ω ¨l “ω ¨l (3)
small, the ratio of the angular displapc24ement2 ofP L242P 1(2 ) a4ndP 24P14 is the same as the angular velocity
2 4
wrahteiore a,sl followiss distancefromP toP andl isdistancefromP toP . FromEquation(3),the
p24p12 12 24 p24p14 14 24
angularvelocityratioisasfollows ω2“42lP24P4214 ((24))
ω l
4 P24P12
wheIrne,t he2 Faignudr e54b ,atrrei athnge laenPguPlar Avealoncdittireisa nofg leeacPh lPinkB La2r aensdim Li4l,a rretsrpiaencgtilveesl.yT. heangularvelocity
12 24 14 24
ratiocTahneb aenogbutlaairn vedeloasciftoyl lroawtios theorem can be used to obtain the angular velocity ratio [17]. In the
Figure 5b, point P24 is the instant center common to links 2 and 4. Its velocity VP24 is the same whether
P24 is considered as a point of link 2∆ oθr2 o“f liωnk2 4“. WlP2e4 Pc1a4n“ wlr4itsein µ (5)
∆θ ω l l sinν
4 Vp 42lPP2P4P124lP2P (3)
24 2412 2414
wherel andl arethelengthofeachlinkL andL respectively,andµandνaretransmissionangle
2 4 2 4
bwethwereee,n lpe2a4pc1h2 ilsin dki.sItfanlcsei nfµroimsl aPr1g2 etro tPh2a4n alndsi nlpν24,p∆14θ is idsilsatragnecret hfraonm∆ Pθ14. to P24. From Equation (3), the
4 2 2 4
angular velocity ratio is as follows
The4-barlinkageshapeofTSHSisdifferentfromtheideal4-barlinkagemechanism. Thereareno
realjoints. Ifthelinksaretoostrong,amplificatio2nblPy24P1t4h e4-barlinkageshapedoesnotwork. Hence,
L2isthinlydesigned. Linksreceiveabendingmo4melntaswellascompression/tensionforces. Bendi(n4g)
by∆θ and∆θ produceastrainforceoneachlinkofP2t4hP12esensor. When∆θ islargerthan∆θ ,strainof
2 4 2 4
L2islIanr gthere tFhiagnurthe a5tbo, ftrLia4.ngle P12P24A and triangle P14P24B are similar triangles. The angular velocity
ratio can be obtained as follows
2 2  lP24P14 l4sin
(5)
4 4 l l2sin
P P
2412
where l2 and l4 are the length of each link L2 and L4 respectively, and  and  are transmission
angle between each link. If l sinis larger than l sin,  is larger than  .
4 2 2 4
The 4-bar linkage shape of TSHS is different from the ideal 4-bar linkage mechanism. There are
no real joints. If the links are too strong, amplification by the 4-bar linkage shape does not work.
Hence, L2 is thinly designed. Links receive a bending moment as well as compression/tension forces.
Sensors 2016, 16, 991 5 of 12
Bending by  and  produce a strain force on each link of the sensor. When  is larger than
2 4 2
Sensors2016,16,991 5of12
 , strain of L2 is larger than that of L4.
4
When the external moment force is loaded on the torque sensor, the sensitivity of the torque
sensWorh iesn ptrhoepoexrttieornnaall tmo othme esntrtafionr coen itshleo astdreadin ognauthgee taotrtaqcuheedse tnos oshr,otrht elisnekn Lsi2t iovfi ttyheo f4-tbhaer tloinrqkuagee
sesnhsaopre iwsphirloep tohret isotinffanletsost ohfe thster atoinrqoune tsheenssotrra iisn pgraoupgoertaiottnaaclh teod thtoe ashngorutlalirn dkeLfo2romfatthieon4 -obfa trhlei nseknasgoer.
shTahpee swenhsiilteivtihtey satnifdfn setsifsfnoefstsh eoft othrqeu teorsqeuneso sreinssporro aproe rdtieofninaeldto atsh feoallnogwusl ardeformationofthesensor.
Thesensitivityandstiffnessofthetorquesensoraredefinedasfollows

Ksensitivity  nε (6)
K “ z (6)
sensitivity
n
z
n
K Kstiffness“nzz ((77))
stiffness
δ
wwhhereereε εis itsh tehset rsatrinaino fotfh tehest srtarianing aguaguegea tattatcahcehdedt otos hshoortrtl ilninkkL L2o offt hthee4 4--bbaarrl liinnkkaaggee sshhaappee,, δδi sist hthee
2
anangguulalrard edfeofromrmataiotinoonf othf ethseen sseonrsaonrd anndi sntzh ies etxhteer nexatlemrnoaml emnot.mTehnetp. eTrhfoer mpearnfocerminadnecxe λinisdedxe fine dis
z
defined as the product of the sensitivity and the stiffness as follows
astheproductofthesensitivityandthestiffnessasfollows

 n 
λ“KKsensesnitsiivtiivtiytyKsKtifstfinffnesesss“ nnεz nδzz“δε ((88))
z
3.3. SSiimmuullaattiioonn
3.31..1.F FininitieteE ElelmemenenttA AnnalaylsyissisM Modoedlel
TThheejo joininttt otorqrquuees esnensosorsrsa raereu ususualallylya sassesmembbleldedw witihthr erdeduucecresr.sT. Thhees tsitfiffnfnesessso offt htheejo joinintti sisr erlealtaetded
wwitihthn nootto nonlylyt htheet otroqruquees esnesnosrorb ubutta laslosot hteher erdeudcutciotinong egaerara nadndth teheli nlikn.k.T Thheec hcharaarcatcetreirsitsitciscso offt hthee
enentitrierej ojoinintti sisa nanooththererr erseesaearcrhcht otoppici.c. IInn tthhisis ppaappeerr,,t hthees stitfiffnfneesssso offt htheet otorrqquuees seennssoorri sisd disisccuusssseedd..
ToTroqruqeues esnesnosrosrsa raerem matacthcehdedw witihtht htheer erdeduuctcitoinong geaerarw witihthr artaetdedt otorqrquueeo off4 040N Nmm( h(haramrmoonnicicd drirviverer
SSHHGG-3-23-28-08-02-U2UHH))[ 1[81]8.].
TThheeb boouunnddarayryc ocnondditiitoinono foft htheeT TSHSHSSis isd defiefninededa sass hshowownnin inF iFgiugurere6 .6T. Thheei ninnnererp paratrti sisfi fxixededa nandd
ththeee xetxetrenrnalalt otorqruquee4 040N Nmmis islo laodadededo nono uotuetrers usrufrafcaeceB .B.

Figure 6. Boundary condition of the TSHS.
Figure6.BoundaryconditionoftheTSHS.
The material comprising the sensor is hard aluminum alloy AL6061-T6. The material parameters
ThematerialcomprisingthesensorishardaluminumalloyAL6061-T6. Thematerialparameters
are as follows: the elastic modulus E68,900 Pa, Poisson’s ratio 0.33 and the density 2.71
are as follows: the elastic modulus E “ 68,900 Pa, Poisson’s ratio µ “ 0.33 and the density
g/cm3. In this paper, FEA software ANSYS [19] is used to analyze the torque sensor. Figure 7 shows
ρ“2.71g/cm3.Inthispaper,FEAsoftwareANSYS[19]isusedtoanalyzethetorquesensor. Figure7
mapped mesh of TSHS using the element solid 45. There are 2712 elements and 4480 nodes.
showsmappedmeshofTSHSusingtheelementsolid45. Thereare2712elementsand4480nodes.
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Sensors 2016, 16, 991 6 of 12
Sensors 2016, 16, 991 6 of 12

Figure 7. Mapped Mesh Model of the TSHS.
FFiigguurree 77.. MMaappppeedd MMeesshh MMooddeell ooff tthhee TTSSHHSS..
3.2. The Optimization
3.2. The Optimization
3.2. TheOptimization
The TSHS has many design variables and the sensitivity of the TSHS is related to these variables.
The TSHS has many design variables and the sensitivity of the TSHS is related to these variables.
TheTSHShasmanydesignvariablesandthesensitivityoftheTSHSisrelatedtothesevariables.
The optimization by the ANSYS software is used to maximize the sensitivity of the TSHS. The ANSYS
The optimization by the ANSYS software is used to maximize the sensitivity of the TSHS. The ANSYS
TheoptimizationbytheANSYSsoftwareisusedtomaximizethesensitivityoftheTSHS.TheANSYS
optimization routines use three types of variables that characterize the design process: design
optimization routines use three types of variables that characterize the design process: design
optimizationroutinesusethreetypesofvariablesthatcharacterizethedesignprocess:designvariables
variables (DV), state variables (SV) and objective variables (OV). These variables are represented by
variables (DV), state variables (SV) and objective variables (OV). These variables are represented by
(DV), state variables (SV) and objective variables (OV). These variables are represented by scalar
scalar parameters in the ANSYS Parametric Design Language (APDL) [19]. Figure 8 shows the
scalar parameters in the ANSYS Parametric Design Language (APDL) [19]. Figure 8 shows the
parametersintheANSYSParametricDesignLanguage(APDL)[19]. Figure8showstheoptimization
optimization data flow.
optimization data flow.
dataflow.

FFFiiiggguuurrreee 888... OOOppptttiiimmmiiizzzaaatttiiiooonnn dddaaatttaaa fflfllooowww...
In this paper, a 3-beam torque sensor and the TSHS are compared. Fixed parameters and design
In this paper, a 3-beam torque sensor and the TSHS are compared. Fixed parameters and design
Inthispaper,a3-beamtorquesensorandtheTSHSarecompared. Fixedparametersanddesign
variables (DV) of the two models are shown in Figure 9 and Table 1. Fixed parameters (wrw, wrn, nr,
variables (DV) of the two models are shown in Figure 9 and Table 1. Fixed parameters (wrw, wrn, nr,
variables(DV)ofthetwomodelsareshowninFigure9andTable1. Fixedparameters(wrw,wrn,
B) are the same for the two sensors. The link length (e) where the strain gauge is attached has to be
B) are the same for the two sensors. The link length (e) where the strain gauge is attached has to be
nr,B)arethesameforthetwosensors. Thelinklength(e)wherethestraingaugeisattachedhastobe
longer than the strain gauge length. In this research, it is determined to be 4.5 mm. Design variables
longer than the strain gauge length. In this research, it is determined to be 4.5 mm. Design variables
(L, B1, L1, B2, CN) have initial values and upper and lower limits, described in Table 1.
(L, B1, L1, B2, CN) have initial values and upper and lower limits, described in Table 1.
TToo iimmpprroovvee tthhee sseennssiittiivviittyy wwiitthhoouutt rreedduuccttiioonn ooff tthhee ssttiiffffnneessss ooff tthhee ttoorrqquuee sseennssoorr,, tthhee ssttrraaiinn εε
aanndd tthhee ddeeffoorrmmaattiioonn δδ ooff tthhee ttoorrqquuee sseennssoorr aarree uusseedd aass SSVV wwhhiillee tthhee ssttrraaiinn εε iiss sseelleecctteedd aass OOVV..
Sensors2016,16,991 7of12
longerthanthestraingaugelength. Inthisresearch,itisdeterminedtobe4.5mm. Designvariables
(L,B1,L1,B2,CN)haveinitialvaluesandupperandlowerlimits,describedinTable1.
Sensors 2016, 16, 991 7 of 12

(a) (b)
Figure 9. Design variables of torque sensors. (a) 3-beam torque sensor; (b) TSHS.
Figure9.Designvariablesoftorquesensors.(a)3-beamtorquesensor;(b)TSHS.
Table 1. Parameters of the TSHS.
Table1.ParametersoftheTSHS.
TSHS
3 Beams
TSHS
3Beams Initial Value Lower Limit Upper Limit
wrw (mm) InitialValue 75L owerLimit UpperLimit
wwrnrw (mm) 60
Fixed 75
n(mr m(m)m) 20
PaFriaxmedeter wrn(mm) 60
B (mm) 10
Parameter nr(mm) 20
e (mm) - 4.5
B(mm) 10
eL(m (mmm) ) - - 64 643.5 70
B1 (mm) - 5.0 3.8 6.0
L(mm) - 64 63 70
DV BL11(m (mmm) ) - - 457.0.5 435.8 560. 0
DV LB12(m (mmm) ) - - 407..55 04.45 0.560
B2(mm) - 0.5 0.4 0.6
CN (deg) - 15 14 15.5
CN(deg) - 15 14 15.5
3.3. FEA Results
Toimprovethesensitivitywithoutreductionofthestiffnessofthetorquesensor,thestrainεand
After optimization to improve the sensitivity of the torque sensor, the optimal design of both the
thedeformationδofthetorquesensorareusedasSVwhilethestrainεisselectedasOV.
TSHS and FEA results are shown in Table 2. Figure 10 shows deflection and strain FEA results of the
t3o.3rq.uFeE AseRnseosurslt.s Deformation results are similar while strain of the TSHS is larger than that of 3-beam
sensor.
Afteroptimizationtoimprovethesensitivityofthetorquesensor, theoptimaldesignofboth
theTSHSandFEAresultsareshowninTable2. Figure10showsdeflectionandstrainFEAresults
Table 2. The optimal design and FEA results of TSHS.
ofthetorquesensors. DeformationresultsaresimilarwhilestrainoftheTSHSislargerthanthatof
3-beamsensor. TSHS
3 Beams
Initial Value Optimal Result
L (mm) - 64 65
B1 (mm) - 5.0 5.0
DV L1 (mm) - 47.5 47.5
B2 (mm) - 0.5 0.55
CN (deg) - 15 15
ε 3.51 × 10−4 6.70 × 10−4 12.2 × 10−4
SV
δ (rad) 21.6 × 10−4 21.6 × 10−4 19.8 × 10−4
OV ε 3.51 × 10−4 6.70 × 10−4 12.2 × 10−4
 0.163 0.310 0.615
Sensors2016,16,991 8of12

Sensors 2016, 16, 991 8 of 12

(a) (b)

(c) (d)
Figure 10. Deflection and strain FEA results of torque sensors. (a) Deflection of 3-beam sensor; (b)
Figure 10. Deflection and strain FEA results of torque sensors. (a) Deflection of 3-beam sensor;
Deflection of TSHS; (c) strain of 3-beam sensor; (d) strain of TSHS.
(b)DeflectionofTSHS;(c)strainof3-beamsensor;(d)strainofTSHS.
4. Experimental Results
Table2.TheoptimaldesignandFEAresultsofTSHS.
4.1. Experimental Equipment
TSHS
3Beams
The actual 3-beam torque sensor and TSHS aIrnei tibaoltVha lcuoenstructeOdp ttiom avleRreifsyu lvtalidity of the
proposed mechanism as shown in Figure 11. Both actual torque sensors include holes for bolting. A
L(mm) - 64 65
pair of 4-bar linkage shBa1p(me mse)nsing port-ions is attached 5t.o0 each supporting 5b.0eam of the TSHS for
symmetry. StrDaVin gaugLe1s( mamre) attached -to sensing porti4o7n.5s of the torque 4se7.n5sor. Table 3 shows
B2(mm) - 0.5 0.55
specifications of the strain gauge. The Strain gauge was measured by NI 9237 of National
CN(deg) - 15 15
Instruments.
ε 3.51ˆ10´4 6.70ˆ10´4 12.2ˆ10´4
SV
δ(rad) 21.6ˆ10´4 21.6ˆ10´4 19.8ˆ10´4
OV ε 3.51ˆ10´4 6.70ˆ10´4 12.2ˆ10´4
λ 0.163 0.310 0.615
4. ExperimentalResults
4.1. ExperimentalEquipment
Theactual3-beamtorquesensorandTSHSarebothconstructedtoverifyvalidityoftheproposed
mechanismasshowninFigure11. Bothactualtorquesensorsincludeholesforbolting. Apairof4-bar
linkageshapesensingportionsisattachedtoeachsupportingbeamoftheTSHSforsymmetry. Strain

gaugesareattachedtosensingportionsofthetorquesensor. Table3showsspecificationsofthestrain
(a) (b)
gauge. TheStraingaugewasmeasuredbyNI9237ofNationalInstruments.
Figure 11. Torque sensors. (a) 3-beam torque sensor; (b) TSHS.
Sensors 2016, 16, 991 8 of 12

(a) (b)

(c) (d)
Figure 10. Deflection and strain FEA results of torque sensors. (a) Deflection of 3-beam sensor; (b)
Deflection of TSHS; (c) strain of 3-beam sensor; (d) strain of TSHS.
4. Experimental Results
4.1. Experimental Equipment
The actual 3-beam torque sensor and TSHS are both constructed to verify validity of the
proposed mechanism as shown in Figure 11. Both actual torque sensors include holes for bolting. A
pair of 4-bar linkage shape sensing portions is attached to each supporting beam of the TSHS for
symmetry. Strain gauges are attached to sensing portions of the torque sensor. Table 3 shows
Sspenesocrisfi2c0a1t6i,o1n6,s9 9o1f the strain gauge. The Strain gauge was measured by NI 9237 of Nat9ioonfa12l
Instruments.

(a) (b)
Figure 11. Torque sensors. (a) 3-beam torque sensor; (b) TSHS.
Figure11.Torquesensors.(a)3-beamtorquesensor;(b)TSHS.
Sensors 2016, 16, 991 9 of 12

Table3.Specificationofthestraingauge.
Table 3. Specification of the strain gauge.
PPaarraammeetetresrs ConCtoennttesn ts
Strain gauge type KFG-02-120-C123L1M2R
Straingaugetype KFG-02-120-C123L1M2R
GGaauuggeeF Faactcotror 2.252 .±25 1˘.0%1.0 %
GGaauuggeeR Reesissitsatnacnece 1191.61 9±.6 0˘.4 0Ω.4 Ω
Gaugesize 3.3ˆ2.4mm
Gauge size 3.3 × 2.4 mm
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stoernqsuoer, hseonriszoorn, thaolrbiazro,nmtaals sb,adr,i amlgaasus,g ediaanl dgsaturgaien agnadu gsetrmaiena sguaruegme emntesayssutreemm.eDnat tsayisstecamp.t uDraetda biys
tchaeptpurroegdr abmy tLhaeb pVrIoEgWram[2 0L]aabsVsIhEoWw n[2F0i]g ausr esh1o3w. n Figure 13.

Figure 12. Experimental equipment.
Figure12.Experimentalequipment.

Figure 13. Program in LabVIEW.
Sensors 2016, 16, 991 9 of 12
Table 3. Specification of the strain gauge.
Parameters Contents
Strain gauge type KFG-02-120-C123L1M2R
Gauge Factor 2.25 ± 1.0%
Gauge Resistance 119.6 ± 0.4 Ω
Gauge size 3.3 × 2.4 mm
Figure 12 shows the experimental equipment. The experimental equipment consists of the
torque sensor, horizontal bar, mass, dial gauge and strain gauge measurement system. Data is
captured by the program LabVIEW [20] as shown Figure 13.

Sensors2016,16,991 10of12
Figure 12. Experimental equipment.

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4 .2. ExperimentalResults
ToverifytheFEAresultofSection3,thetwosensormodelsweretestedforstrainanddeflection.
Table4showstheFEAresultsofSection3andexperimentalresultsofthetwomodels,the3-beam
sensorandtheTSHS.AsshownintheTable4,theexperimentresultsaresimilarwiththeFEAresults.
Thesensitivity(strain)oftheTSHSis3.5timeshigherthanthesensitivityofthe3-beamtorquesensor.
ThedeflectionoftheTSHSisreducedby7%. ThatmeansthatthestiffnessoftheTSHSalsoincreases.
TheperformanceindexλofTSHShasbeenimprovedbyafactorof3.8.
Table4.ComparisonexperimentresultwithFEA.
Name Method Strain Deflection(rad) λ
FEM 3.51ˆ10´4 21.6ˆ10´4 0.163
3beams Experiment 3.48ˆ10´4 22.0ˆ10´4 0.158
Error ´0.85% 1.85% ´2.66%
FEM 12.2ˆ10´4 19.8ˆ10´4 0.615
TSHS Experiment 12.3ˆ10´4 20.5ˆ10´4 0.601
Error 1.40% 3.80% ´2.31%
FEM 3.48 0.916 3.77
TSHS
3beams Experiment 3.53 0.932 3.80
ByanalyzingthedataoftheFEAandtheexperimentalresults,theidealstrain,theFEAstrain
andtheexperimentalstrainwithrespecttothetorqueinputcanbeobtainedasshowninFigure14.
Figure14ashowsthattheFEAresultsandtheexperimentalresultsaresimilarwiththeidealresults.
InFigure14b,thelinearityerrorisbelow1.5%. Inthisrange,itillustratesthattheTSHSexactlyreflects
thepayload.