An experimental interface design for a single-link elastic manipulator system

Transcription

1 Internatonal Research Journal of Appled and Basc Scences. Vol., 3 (8), , 2012 Avalable onlne at www. rjabs.com ISSN X 2012 An expermental nterface desgn for a sngle-lnk elastc manpulator sstem M. Doosthosen 1, M. H. Koraem 2*, A. M. Shafe 3, B. Kadkhodae 4 1- M.Sc. Student of Mechatronc Engneerng Department, Islamc Aad Unverst, Scence and Research Branch, Tehran, Iran 2- Professor of Mechancal Engneerng Department, Iran Unverst of Scence and Technolog, Narmak, Tehran, Iran. 3- Ph.D. Canddate of Mechancal Engneerng Department, Iran Unverst of Scence and Technolog, Tehran, Iran 4- M.Sc. Student of Mechatronc Engneerng Department, Islamc Aad Unverst, Scence and Research Branch, Tehran, Iran *Correspondng Author Emal: hkoraem@ust.ac.r Abstract The hgh speed vbraton of a flexble robotc arm compared to the low speed of software and hardware nterface between the computer and expermental setup s one of the most mportant obstacles for measurng and control of such a sstems. In ths paper, a combnaton of usng hgh speed dgtal to analog convertor (DAC) components on an electrcal nterface board and usng Natonal Instrument s LABVIEW software package s proposed as a soluton for ths problem. Dnamc modelng of the sstem s developed based on Gbbs-Appell (G-A) formulaton and Assumed Mode Method (AMM). The accurac and completeness of the dnamcal model of the sstem s dependent on the number of modes used to descrbe the sstem. An expermental setup of a sngle-lnk elastc robotc arm s prepared and the electrcal nterface board works between ths expermental setup, user and computer. The nput data b the electrcal nterface board are the number of mode shapes up to 4 and the profle of the nput torque va tme. Then these data transferred to the manpulator sstem. Fnall user can see the vbraton of the elastc lnk n graphcal nterface envronment and model valdaton carred out b comparng both expermental and theoretcal results. Kewords: Elastc manpulator, Interface, Labvew, Vbraton, Gbbs-Appell Introducton Desgnng the nterface for varous sstems s done based on dfferent requrements. But creatng the nterface between the user and machne s the man reason. The desgned nterface should contan all sstem components as much as possble, and completel govern the sstem performance, and allow the user to obtan suffcent knowledge of the sstem n the same smulated envronment and can appl the desred changes to the sstem model. Educatonal aspects are one of the extensve applcatons of smulaton envronments that are used n nterfaces. Software packages provded n educatonal products for tranng varous sstems, devces and expermental set-ups, enable the user to have a laborator and get famlar wth varous sstem components and work wth the model of the sstem, and examne the effects of parameters' varatons. (Marín et al., 2005) used Java programmng and Tele-lab software program for creatng an nterface envronment for a robotc arm. (Khasongkram et al., 2002) desgned a graphcal smulator envronment and the requred nterface for communcatng wth the devce and controllng t usng Matlab-GUI. (Hasanul and Basher, 2007) modeled a flexble manpulator and represented the results of the model. He used Euler-Bernoull beam theor (EBBT) for extractng the equaton of moton. The problem of dnamc modelng of flexble lnks n robotc sstems has been a major problem n recent ears. Accurate modelng of the lnk s an essental step for successful controllng of such sstems. It

2 Intl. Res. J. Appl. Basc. Sc. Vol., 3 (8), , 2012 s well known that flexble mult-bod sstems have man applcatons n man practcal engneerng, such as aeronautcs, aerospace and robotcs. So, a good dnamc model for these knds of robots s mportant n man engneerng applcatons. Fnte Element Method (FEM) and Assume Mode Method (AMM) are two mportant approaches for modelng elastc robotc manpulators. In AMM, the lnk flexblt s usuall represented b a truncated modal seres, n terms of spatal mode Egenfunctons and tme-varng mode ampltudes. If the benefts assocated wth the lghtness of flexble robotc manpulators are not to be sacrfced, accurate dnamcal models have to be developed. To nclude the effects of shear and rotatonal nerta the assumpton of Tmoshenko beam theor (TBT) can be used. TBT and AMM have been used b (Loudn, 2010, Ouang et al., 2007, and Zheng et al., 2002) for dervng the equaton of moton of flexble robotc manpulators. There are man choces for wrtng the governng equaton of moton of elastc robotc manpulators. Moton equaton b G-A formulaton has been used the least for dervng the dnamc equatons of robotcs manpulators. In the feld of robotcs, more recent nvestgatons can be found n the nvestgaton of (Vossough et al., 2008) where G-A formulaton s used for moton equatons of snake-lke robots; n the work of (Mata et al., 2002) where nverse and forward dnamcs equatons of moton of N-rgd lnks are presented n recursve form; and n the research of (Koraem and shafe 2009) where moton equatons of elastc lnk manpulators are presented. Most of the work n the feld of elastc robotc manpulator confned to theoretcal nvestgatons. For valdaton the theoretcal results b expermental test-bed t can be ponted out to the works of (Cannon, 1984, Rovner, 1987, and Shaheed and tokh 2002) where n ther nvestgatons a setup for sngle lnk elastc robotc manpulator s prepared. The man goal of ths paper s desgnng an nterface for a model of elastc sngle-lnk manpulator sstem that ts equatons have been extracted based on G-A method. The nterface s desgned wth LABVIEW software. Therefore, n the followng, knematc and dnamc equatons of manpulator robot wth elastc lnk are descrbed. Also the smulator and nterface model s desgned and the prepared expermental set-up s ntroduced and the results of nterface connecton wth the sstem are also provded. Knematcs of a Sngle-Lnk Elastc Manpulator Sstem The sngle-lnk flexble manpulator sstem consdered n ths work s shown n Fg. 1, where XYZ and x represent the statonar and movng coordnate s frames, respectvel. Fgure 1. Sngle Lnk Elastc Robotc Manpulator The poston vector of arbtrar dfferental element Q wth respect to the local reference sstem x s shown b r. The approach of modal analss s used to ncorporate the deflecton of the lnk. So, r { } T = + u v w (1) where = { 0 0} T s the poston vector of dfferental element Q wth respect to o, when the elastc lnk s undeformed; u, v and w are small dsplacements n ox, o and o drectons, respectvel. To express these small dsplacements, the approach of assumed mode method s used as, T m u v w t r (2) = = { } ( ) ( )

3 Intl. Res. J. Appl. Basc. Sc. Vol., 3 (8), , 2012 r = where { } T x s the Egenfuncton vector whose components longtudnal and transverse mode shapes of the lnk; x, and are -th s the -th tme dependent modal generaled coordnate of the lnk; and m s the number of modes used to defne the deflecton of the lnk. The total transverse dsplacement of the centerlne of dfferental element Q s due to bendng and shear. So the total slopes of the deflected centerlne about o and o drectons due to the bendng and shear deformaton can be represented as w = ϕ + (3) v = ϕ + (4) where ϕ and ϕ are the slope of the deflected centerlne due to shear and, are the slope of the deflected centerlne due to bendng. Shear has no nfluence on rotatng the dfferental element Q ; and ths dfferental element undertakes rotatons onl due to bendng and torson. So the rotaton of ths element n ox, o and o drectons can be consdered as x, and, respectvel. These small angles can be represented b truncated modal expanson as m T = t (5) { x } = ( ) ( ) = 1 where { } T = x s the Egenfuncton vector whose components rotatonal mode shapes of the lnk n ox, o and o drectons, respectvel. x, and are -th Gbbs-Appell Method In ths secton the sstem s acceleraton energ and ts dervatves wth respect to quasacceleratons are developed for constructon the G-A formulaton. Wth the assumpton of TBT, the acceleraton energ of the sstem can be represented as = l 1 T 1 T S ( )( r Q r Q ) d + J( ) d (6) J are But wth the assumpton of EBBT onl the frst term of Eq. (6) should be preserved. Also ( ) and ( ) mass per unt length and mass moment of nerta matrx per unt length, respectvel. Note that r Q and are lnear and angular acceleraton of dfferental element Q. These two terms can be stated as, r Q = r + 2 r + r + ( r ) (7) m = ( t) j( ) j = 1 j (8) In above expressons, and are angular veloct and angular acceleraton of the lnk, respectvel; Also r and r are veloct and acceleraton of dfferental element Q wth respect to the orgn of the local reference sstem, respectvel. Dnamc Equatons of Flexble Lnk Manpulator Sstem Moton equaton of vscoelastc robotc manpulators wll be completed b consderng the generaled forces whch are caused b the remanng external force terms. Let us assume that there s no external load on the lnks of the consdered robotc manpulator. So, the generaled forces n the deflecton equatons wll be ero. The generaled force n the jont equatons s the torque that apples to the jont. Wth ths assumpton, the dnamc equatons of moton n the G-A formulaton wll be completed as follows: The jont equatons of moton S D V + + e = (9) q q q The deflecton equatons of moton 1728

4 Intl. Res. J. Appl. Basc. Sc. Vol., 3 (8), , 2012 S D V + + j j e j = 0 Results j = 1,2,..., m (10) In ths paper, a computer program called Vrtual Instruments (VI), s developed usng the LABVIEW software package to obtan the beam response. LABVIEW stands for Laborator Vrtual Instrument Engneerng Workbench. It nteracts wth the user n two separate forms of dspla such as front panel and block dagram. The front panel s the user nterface to the VI and the block dagram of the VI s the functonal dagram of the sstem (Hasanul and Basher, 2007). Dfferent stages of the block dagram of the VI of the sstem under nvestgaton are dsplaed n fgures (2-5). The functonalt of these block dagrams wll be descrbed n the sequence the are executed. Block dagram assocated wth the sstem smulaton s a sub VI whch has been coded nsde the sstem nterface. Fgure (2) shows part of block dagram wndow of ths sub VI. Fgure 2. 1 case structure wth a sequental structure and 2 MAT scrpt loop for solvng arm dnamc equaton based on Gbbs-Apple formulaton. Ths part of the program conssts of four case structures that n each one, the extracted equatons have been wrtten n the two nner loop of MATLAB scrpt based on G-A formulaton. LABVIEW has the ablt to use MATLAB software n parallel as well, especall when the mathematcal calculaton s hgh and bulk and more processng speed s needed. Wth ths feature of LABVIEW software, wthout full mplementng heav MATLAB software, onl ts processor s used and LABVIEW can receve and use ts results. MATLAB Scrpt s a tool that LABVIEW provdes the programmer for ths purpose. Of course, runnng all MATLAB codes s not possble b ths tool. For example, n wrtng the program of the sngle-lnk elastc manpulator, after extractng the robot dnamc equatons n the frst MATLAB scrpt loop based on Gbbs method, t s also requred to wrte a program for solvng these dnamc equatons. Ode solvers do ths process n MATLAB. However t s done n LABVIEW n another wa whch s observed n second loop of MATLAB scrpt n fgure 2. The program wrtten for extractng robot dnamc equatons as MATLAB code has hgh computatonal complext. Therefore, LABVIEW runs ths code b MATLAB. Ths program has the ablt to extract the dnamc equaton of the sstem; consderng the nfnte mode shapes. But what s ntended n the nterface desgn s ncreasng the number of mode shapes from one to four; extractng robot equatons; solvng them; obtanng hub angle profle; hub veloct; mode shapes; creatng the anmaton of moton of elastc arm and dsplang ts vbratons; and fnall connectng the smulator program wth the sstem as an nterface. Fgure (3), shows the desred sub VI front panel wndow. Hub angle poston, hub angle veloct and mode shapes of elastc robotc manpulator are obtaned b ths smulaton program. 1729

5 Intl. Res. J. Appl. Basc. Sc. Vol., 3 (8), , 2012 Fgure 3. Front panel wndow of dnamc equaton b solvng sub VI. Fgure 4, shows part of nterface block dagram wndow related to the smulaton n the nterface program. Robot dnamc equatons n F(x) block wll be generated, and the obtanng results such as hub angle poston and mode shapes wll be used n the contnuaton of the program. Fgure 4. Usage of sub VI named (f(x)) n nterface program. In Fgure 5, part of the program n whch hub angle profle and also hub veloct are plotted va tme has been presented. Ths s done usng a FOR loop. Angle profle arra after generatng n the prevous stage enters ths loop, and one row of ths arra s read and plotted n each teraton. Another part whch s specfed n ths fgure s another sub VI block dagram that ts nner program has been shown n fgure 6. Ths part s related to elastc lnk large moton and calculaton due to torque actons. Fgure 5. Program of plottng the hub angle, hub veloct and small deflecton of elastc arm In fgure 6, the block dagram s the program that generates the hub angle poston from the external observer vew. In ths program, the generated hub angle profle n the prevous stage enters WHILE loop as a one-dmensonal arra (that theta s the hub angle of the lnk along the horontal axs). The lnk s dscreted to a set of fnte ponts wth polar coordnates ( X, X tan(). Here, the lnk s dvded b 50 ponts and Whle r,. Thus, x and loop repetton has been used. For ever that enters WHILE loop, lnk has a specfc ( ) that are obtaned for lnk length formaton n each new entr should be placed n Pthagoras functon 1730

6 Intl. Res. J. Appl. Basc. Sc. Vol., 3 (8), , 2012 each tme and compared wth the desred lnk length that s presented b the user at the begnnng of the program. If lnk length has not been completed et, whle loop repetton s contnued along the lnk for generatng more ponts, otherwse, t wll stop, and the next enters the loop. Fgure 6. The block dagram of the program for lnk large moton from the external observer vew. Ths has been presented n fgure 7, clearl. Fgure 7. Provdng arm large moton, wth varable The result of these operatons, n the front panel wndow of the program wll be seen n fgure 9. In fgure 8, another part of the nterface program block dagram has been presented, n whch lnk vbratons are dsplaed from the observer vew attached to the jont. 1731

7 Intl. Res. J. Appl. Basc. Sc. Vol., 3 (8), , 2012 Fgure 8. Block dagram of the program of lnk vbraton dspla from the observer vew attached to the jont. Ths program as s clear from ts con at the top rght corner of fgure 8 s a sub VI n the program whch s shown n fgure 5. In ths part of the program, transverse vbratons of each pont of the lnk are calculated usng the mode shapes extracted from the prevous part. The bendng of the lnk at an moment s obtaned b puttng these ponts together n WHILE loop whch s presented n fgure 8. Fgure 9 shows the result of runnng the above programs n the front panel page of the nterface. Fgure 9. Hub angle, hub veloct, large moton and small deflecton of elastc arm. What the user observes b runnng elastc manpulator nterface program s an mage of expermental set-up for whch the nterface has been desgned, and some explanatons about the sstem and program have been presented. After ntroducton to the set-up and the exstng stages n the nterface program, the user s asked to move to the next page b pressng the Next button. Then, the user enters a page presented n fgure 10. Fgure 10. User can change the length of lnk, the tme of smulaton and the number of mode shapes. 1732

8 Intl. Res. J. Appl. Basc. Sc. Vol., 3 (8), , 2012 In the explanatons of ths page, the user wll be asked to press Run button b determnng the arbtrar values for the lnk length, tme duraton and number of mode shapes (one to four has been consdered as the default n ths program) and wat for generatng robot dnamc equatons and then the results of smulaton. Fnall, tme profle of mode shapes, lnk's hub angle, hub veloct, lnk's large moton from the external observer vew and the lnk's small vbratons from the nternal observer vew wll be dsplaed. The effect of ncrease n the lnk length and other parameters can be observed comparatvel n the next pages of the program. Eventuall, there s the page of connectng to the sstem, n whch the user set tpe of nput torque from several default torques, then sends moton order through the seral port to the desgned nterface board. Expermental Set up Interface Secton After the ntroducton to the sngle-lnk elastc manpulator robot n a varet of tabs desgned n nterface program, set up connectng tab has been desgned n whch the user wll be asked to connect the electronc board of the desgned nterface. Ths nterface communcates wth the computer through the seral port (ths s done b the USB nterface). After that, select the number of each port properl, then choose tpe of the desred torque that the want to enter the lnk b motor, and fnall press Run button. Fgure 11 shows electronc boards desgned to launch motor and collect and send read data from the stran gauges and also expermental set-up. Fgure 11. Sngle-Lnk flexble manpulator and ts nterface electrcal boards and program. In fgure 11, t can be seen that b sendng the desred moton data to the robot and after the small deflecton of elastc lnk, data of the three stran gauges observed on the lnk s collected along the moton and the nterface program wrtten b LABVIEW shows the data n the three graphs arranged n columns; n ths tab a graph has been consdered for dsplang lnk angle varatons and also for the fnal lnk deflecton n fgure 11, the fnal nterface tab s also observed after lnk moton and recevng nformaton. The block dagram part of ths secton of the program has been presented n fgure 12, n ths part at frst codes for openng seral ports and then the code related to readng and wrtng n ths port are gven, and also FOR loop has been used for 400 tmes readng from stran gauges. Fnall, results stran gauges are used, so that the fnal deflecton s extracted and plotted. Fgure 12. Fnal tab of nterface, that desgned for connectng to the robotc elastc arm and sendng moton order and recordng then showng vbraton results of 3 stran gages. 1733

9 Intl. Res. J. Appl. Basc. Sc. Vol., 3 (8), , 2012 Fgure 13. Block dagram of fnal tab of nterface program, for connectng to the robot Conclusons In ths paper, desgnng a research-educatonal software package for elastc robot was ntroduced b LABVIEW software n whch at frst the lnk large moton and vbraton moton are modeled, then the effect of lnk parameters varaton such as length, thckness and the ar dampng, etc. are examned on the sstem response, at the end, nterface creates a drect connecton wth set up, and the user can move elastc arm of the robot through sendng torque order, and show results of stran gauges placed on the lnk for recordng vbratons. References Cannon RH, Schmt E, Intal experments on end-pont control of a flexble one-lnk robot. The Internatonal Journal of Robotcs Research.3 (3): Hasanul A, Basher Modelng and Smulaton of Flexble Robot Manpulator wth a Prsmatc Jont. IEEE SOUTHEASTCON. art. no : Khasongkram W, BanjerdpongchaD, MATLAB Based GUIs for Lnear Controller Desgn va Convex Optmaton. Computer Applcatons n Engneerng Educaton.11 (1): Koraem MH, Shafe AM, Moton Equatons Proper for Forward Dnamc of Robotc manpulators wth flexble lnks b usng Recursve Gbbs-Appell Formulaton. Scenta Iranca Transacton B-mechancal engneerng.16 (6): Loudn M, Elastc lnk robot dnamcs modelng based on beam theores. Internatonal Revew on Modellng and Smulatons, 3 (6): Marín R, San PJ, Nebot P, Wr R, A Multmodal Interface to Control a Robot Arm va the Web: A Case Stud on Remote Programmng. IEEE Transactons on Industral Electroncs, 52 (6): Mata V, Provenano S, Cuadrado J.I, Valero F, Seral-robot dnamcs algorthms for moderatel large number of jonts. Mechansm and machne Theor, No. 37: Ouang H, Wang M, A dnamc model for a rotatng beam subjected to axall movng forces. Journal of Sound and Vbraton. 308 (3-5): Rovner DM, Cannon RH, Experments toward on-lne dentfcaton and control of a ver flexble onelnk manpulator. The Internatonal Journal of Robotcs Research.6 (4): Shaheed M.H, Tokh M.O, Dnamc modellng of a sngle-lnk flexble manpulator: parametrc and nonparametrc approaches.robotca. No. 20: Vossough G, Pendar H, Hedar Z, Mohammad S,2008. Asssted Passve Snake-Lke Robots: Concepton and Dnamc Modelng usng Gbbs-Appell Method.Robotca, 26 (3): Zheng-You Z, Gen-Guo L, Chang-Jun C, Quas-statc and dnamcal analss for vscoelastc Tmoshenko beam wth fractonal dervatve consttutve relaton. Appled Mathematcs and Mechancs (Englsh Edton).23 (1):