Cubic Stress Tensor Sensor for Robot Skins

Transcription

1 SICE Annul Conferene 00 August 0-, 00, The Unversty Eletro-Communtons, Jpn Cu Stress Tensor Sensor for Root Skns Shohe Kyot n Hroyuk Shno Deprtment of Informton Physs n Computng, The Unversty of Tokyo, Tokyo, Jpn (T : +---9; E-ml: {kyot, shno}@l.t.u-tokyo..jp ) Astrt: The purpose of ths reserh s to proue sensor hp tht mesures stress tensor n n rtrry pont n n st oy suh s n rtfl skn for root. The sensor onssts of ue-shpe rg oy n su-sensors tht mesure norml stress on eh orner of the ue. We expln the theory to eompose sher stress n non-unform norml stress. Also, we frte prototype sensor. The theory s exmne y the prototype. The expermentl results show tht the sensor n mesure the norml stress n the sher stress t one. Also, the results suggest tht the sensor n mesure the grent of ontt surfe. Keywors: Ttle sensor, Elst oy, Stress tensor, Symmetr.. INTRODUCTION In lte yers, to know ontt stte wth the ojet, mny reserhes re onute for mesurng fore vetor struton n fs of humn nterfe n rtfl skn for roots []. Mny of fore struton sensors re ommerlze s ones tht mesure only norml fore struton on the ontt surfe [,]. A Stress Tensor Sensor (STS) propose n ths pper s smll u sensng hp emee n n st oy for mesurng ll omponents of stress tensor roun t. The usefulness of the tensor sensor s summrze s ) Completeness of the nformton: Even f the STS orentton s rtrry, ny omponent of the stress tensor s lulte from the t of the STS. In orer to mesure ertn omponent of stress presy, we nee to onser the nterferene from other stress omponents. Usul sensors lle norml stress sensor lso respons to other stress omponents f t s set n n st oy. Mesurng ll omponents s resonle n proly the smplest wy to eompose the stress omponent nterferene. ) Dretness of sensng: STSs re suppose to e ple ner the surfe, otng n n st oy. In usul prtl ttle sensng, the sensors re ple t the ottom of thk st oy. But the exstene of the st oy etween the ttle sensor surfe n the sensors lowers the sptl n temporl resoluton of sensng the surfe fore struton. In our STS sensng, the fore on the surfe s retly mesure y the sensor hps otng ner the surfe. The e of the STS s lrey seen n some prevous reserhes []. But t hs not een onsere s prtl metho sne t s ffult to wre the STS n n st oy. However, the reent vnements of wress networkng tehnologes nlung two-mensonl sgnl trnsmsson [] mkes t rst to rze wress STS. Ths s the mn motvton of the reserh. The other prolem of the prevous STS s the Surfe Fore Norml Stress Sensor () () Fg. An exmple of the prevously reporte stress sensors. The sensor mesures () the sher stress s the fferene etween the outputs of the su-sensor n () the norml stress s the summton of the outputs of the su-sensors. When the ontt surfe nlnes, the sensor msnterprets the norml stress fferene s the sher stress. nompleteness of sensng. The prevous sensor ouln t stngush etween the sher stress n the non-unform norml stress. Fg. llustrtes typl prnple to mesure the fore reton seen n prevous reserhes. Multple norml stress su-sensors n rg oy struture re emee n n st oy. Ths rg oy onverts the tngentl fore on the surfe nto the norml fore fferene nse, n fore vetor s lulte from the sum n fferene of the outputs of su-sensor set t the ottom of the st oy []. The norml fore F z n tngentl fore F x on the surfe re lulte s follows y the outputs of eh su-sensor V n V s F z k( V V ) () F x k ( V V ) () The onstnts k n k epen on the Young s moulus, posson s rto n the shpe of the rg oy Ths metho s useful for the reson tht t n get fore vetor y ng smple struture to onventonl norml fore struton sensor. But the prolem s tht the sensor msnterprets the norml stress fferene s the sher stress when the ontt surfe nlnes. In ths pper, we present sensng prnple of STS free from the seon prolem. We frte prototype n exmne the prnple PR000/0/ SICE

2 the grents re equl to zero), from the geometr symmetry, the rtonshp of the norml stress sensor s output V, V, V, V, V, V, V, n V to 0 re expresse s followng equtons. The onstnts n n the equtons epen on the Young s moulus, posson s rto n the shpe of the rg oy. V V V V () V 0 V V V () 0 Fg. The shemt rwng of the sensor mo. The whte squre ntes rg oy. () Fg. Norml stress struton on the rg oy. () Even norml stress 0 s pple. From geometrl symmetry, V, V, V n V re eqully ompresse, n lso V, V, V n V re eqully expne. () The sher stress s pple. (). PRINCIPLE AND SCALING LAW For smplfton of the followng susson, we frst ssume D prolem n fouse on ross seton nlung the x- n z-xs s shown n Fg.. The stress tensor sensor unt onssts of ue-shpe rg oy tht hs norml stress sensors V ple on eh orner of the rg u oy n the enter of squre st oy. It s emee n lner st oy. Suppose unform eformton s gven to the st oy, n tht the rg oy lolly sturs the stress f roun t. Let the stress tensor omponents roun the orgne 0,, 0, n, n onser the grent of the norml stress x, z, z n x. ( ) When the even norml stress 0 (Fg.) s pple to the surfe of sensor unt (other stress omponents n If we pply the smlr nlyss to the other omponents 0, (Fg.), n the grent of norml stress, from lner stty, the rtonshp etween sensor outputs n the stress roun the sensor hp (the rg oy) re expresse s followng equtons. The onstnts,,, g n h re ee y the Young s moulus, posson s rto n the shpe of sensor. The onstnt l s the length of eh se of the ue. V V V V V V V V hl hl hl hl 0 hl hl 0 hl hl x z z x () Bse on Eq. (), we n reonstrut the stress pple to the st oy s followng equtons usng. zx xz x z z x 0 0 V eg fh eg fh eg fh eg fh l V V V V g V V V V l hv V V V g l e V V V V f l f V V V V V V V h V V V V V V V V V V V V e V V V V () () (9) (0) () () () The equtons show tht we n sense the stress tensor roun the sensng hp n the grent of the norml stress re otne from the sensor outputs. In ths sensng prnple the seon prolem ponte out n Introuton hs een solve. An mportnt feture of the sensng s tht the rtos mong,,, n re nepenent of the sensor sze l

3 Therefore the rto of the SN rtos etween the norml stress sensng n the sher stress sensng s nepenent of the sle l. On the other hn, the oeffents etween the sensor outputs n the stress grents nlue the sle prmeter l. It mens tht the sensor outputs eome nsenstve to the stress grents when the sensor sze eomes smll. Therefore the seon prolem n Introuton s mnor one for mro STS.. PROTOTYPE For funmentl experments to onfrm the prnple of the stress tensor mesurement, we frte the sensor whh mesure V, V, V, n V esre n the foregong hpter (Fg.). At frst, the enter ue of the sensor unt ompose of n ryl ue ( mm9 mm) n four ptve stress sensors ple on the orner of the ue. Eh ptve stress sensor onsste of ouple of phosphor ronze etroes. The thkness of the etroes ws 0. mm. The outer etroe s sze s 9 mm9 mm. The nner s re mm9 mm. A polyme m ( mm wth) ws Snwhe etween two pees of etroes s prop n the stne etween the etroes ws m. Proportonl to strength of the norml stress pple to the outer etroes, the stne n the ptne etween the etroes hnge. Beuse ths esgn s for the rtfl skn of the root, we regre the lo of 00gf efore n fter s the upper lmt of the mesurement rnge. We oul hnge the mesurement rnge epenng on the thkness of the GND etroe. We hve the freeom out the Young's moulus of slone ruer nuenng the softness of the whole sensor ement. One of the etroes ws onnete to GND n the other ws onnete to the nput of Shmtt nverter so tht Shmtt nverter oslltor ws forme. The osllton frequeny of the RC oslltor ws etermne y the ptne of the norml stress sensors. The frequeny f of the oslltor n the stne etween the etroes hve the followng rtonshp k k f RC RS C, () where s the etr onstnt of the r, S s the re of the etroe, R s the feek resstne, C s the prst ptne n k s onstnt. When norml stress s pple to the stress sensor, the osllton frequeny vrton f, the stne vrton n the pple norml stress hve the followng rtonshp E Ek R C S f, () S where E s the vrtul Young s moulus of the phosphor ronze ntlever. When s enough smll, s proportonl to f. Therefore sensor outputs V n Fg. orrespone to eh frequeny vrton f. At lst, the enter ue ws emee n 0 mm 0 mm squre-shpe slone ruer (KE-0 Shn-Etsu Cheml Co. Lt), n these re here (Fg.). 0.mm m mm mm mm opper GND sgnl ryl polyme Fg. The photogrph n shemt rwng of the enter ue. Fg. The struture of the prototype. EXPERIMENTS. Setup Fg. shows expermentl setup. Ste pltes were ple t the top n ottom of the slone. By movng the top n ottom ste pltes n the z- n x-reton respetvy, we pple the stress to the sensor. In ths experment, s the ounry onton of the se ws free, = 0. Therefore euse of Eq. (), V V. () An susttutng ths equton to Eq. (), 0 V V. () In the sme wy out the sher stress n the grent of the norml stress, V V V V, () - 9 -

4 x V V V V. (9) Therefore, we n resonly efne the stress tensor sensor outputs P norml s the verge of norml stress s follows. Pnorml f f f f (0) Lkewse the sher stress P sher n the grent of the norml stress P gr re gven s, P P sher gr f f f f f f f f Fg. The sensor outputs for the sher stress. Fg.The expermentl setup.. Experments Even norml stress Frst, only the top plte ws move n the z-reton. Fg. shows the results. The horzontl xs represents the splement of the top ste plte. The vertl xs represents P norml, P sher n P gr. Whle P norml nreses propotonl to the plte splement n the z-reton nresng, P sher n P gr re nerly zero. When P norml ws pproxmte y lner, the squre of the orrton ftor ws Fg.The sensor outputs for the even norml stress. Fg.9 The verge of norml stress. Sher stress After the slone ws ntlly strne y movng the top plte n the z-reton up to mm, only the ottom plte ws move n the x-reton. In ths se, t s ssume tht sher stress ws unformly pple on the top n ottom surfe of the slone ruer. Fg. shows the results. The horzontl xs represents the splement of the ottom ste plte. P sher nreses proportonl to the plte splement nresng n the x-reton, whle P norml n P gr oes not seem to hnge. When P norml n P sher were pproxmte respeyvy y lner, the squre of the orrton ftor ws 0.99 n Tlt norml stress At lst, n orer to pply norml stress vre lnerly, we me slope on the top plte. The ottom plte ws fxe n only the top plte ws move n the z-reton tll the whole slone top surfe here wth the slope. In Fg.9, the horzontl xs represents the verge of z-splement of the slone top surfe, n the vertl xs represents the output P norml (P n )

5 The lne P n ' shows the theoretl vlues. In Fg.0, the horzontl xs represents the egree of slop ne, n we plotte the outputs of P sher n P gr. As the theory prete, P gr hnge orng to the ne hnge, whle P sher ws rtvy onstnt. Trnsmsson Lyer, Pro. th Interntonl Conferene on Networke Sensng Systems (INSS 00), June -, Brunshweg, Germny, pp. 0-0, 00. Fg.0 The sensor outputs for the vryng grent.. SUMMARY We propose stress tensor sensor tht s emee n n st oy n mesure the stress tensor roun t. The theory to eompose the sher stress n the norml stress grent ws gven. The theory ws exmne y prototype sensor. The expermentl results showe tht the sensor n mesure norml n sher stress t one tme. Also, the sensor n stngush sher stress n lnerly vre norml stress. In our future esgn, the etrl power n the t sgnls wll e trnsmtte wthout wres. REFERENCES [] M. H. Lee n H. R. Nholls, Ttle sensng for mehtrons -- stte of the rt survey, Mehtrons 9, pp.-, 999. [] e_system_sensor.html [] M. Shmojo, A. Nmk, M. Ishkw, R. Mkno, n K. Muh A Ttle Sensor Sheet Usng Pressure Conutve Ruer Wth Eletrl-Wres Stthe Metho, IEEE SENSORS JOURNAL, VOL., NO., OCTOBER 00] [] M. Hkozk n H. Shno, Dgtl Ttle Sensng Elements Chommuntng through Conutve Skn Lyers, Pro of te 00 IEEE Trnstons on Roots n Automton, 00, [] H. Shno, K. Mtsumoto n S. Ano, Ttle Sensng Bse on Aoust Resonne Tensor Cl, Pro of TRANSDUCERS 9, Vol., pp. 9-, 99. [] H. Shno, Y. Mkno, N. Ymhr, n H. It: Surfe Sensor Network Usng Inutve Sgnl - 9 -