Yaser Maddah, Al Maddah Relablty and Qualty Improvement of Robotc Manpulaton Systems Yaser Maddah Department of Mechancal and Manufacturng Engneerng Unversty of Mantoba Wnnpeg, MB R3T 5V6 CANADA Al Maddah Department of Mechancal Engneerng department, K. N. Toos Unversty of Technology, Vanak Sq., Tehran, IRAN y_maddah@umantoba.ca, http://home.cc.umantoba.ca/~ummaddah/ Abstract: - Ths paper reports the procedure of expermental evaluaton and objectve/quanttatve comparson, among dfferent performance parameters, of the Cartesan (3P) robots. Here, frst by mplementng the equatons of moton, the mechancal model of ths type of robot s smulated usng Workng Model software. Next, the ntal model of robot s desgned based on the results concluded from the smulated model and the robot structure ncludng control unt, mechancal elements and operatng procedure s descrbed. Also, some tests are appled on the prototype robot n order to verfy the analytcal sde of desgn procedure. The experments consst of calbratng the robot moton along all three axes (prsmatc jonts) and valdaton of three performance ndces, whch are easy to measure va smple expermentatons namely accuracy, repeatablty and maxmum allowable load carryng capacty. The acceptable values of the ndces are predefned as nput of desgn process. The data derved from the expermental tests showed that the robot satsfes the acceptable values. The man contrbuton of ths paper s to mprove the robot desgn by exertng the changes obtaned from assessment of some defned statstcal and mechancal ndces. Key-Words: - Desgn, Cartesan robot, Performance ndex, Expermental test, Desgn mprovement. 1 Introducton Industral robots come n several forms. They are used to automate a wde range of tasks n manufacturng and assembly lnes n vrtually every ndustry. Based upon the requred applcaton, a full assortment of robot formats can be mplemented such as SCARA, artculated arms and Cartesan confguratons and nstalled depends upon the workng area, accuracy and so on. Specfcally, a growng trend s to smplfy the automaton process by utlzng Cartesan robots allowng for fewer controllers, enhancng nstablty and offerng more ntegrated and unfed software. The Cartesan confguraton provdes three lnear axes of movement at rght angle to each other for robot. The modes of movement are smlar to those of a mllng machne, provdng movement n X, Y and Z axes. It may also be termed a rectangular confguraton snce ts workng range sweeps out a three dmensonal rectangular volume. Partcular advantages of ths confguraton nclude easy programmng movement, hgh accuracy, large pay load capacty, control system smplcty, large area coverage, structural smplcty and easy to expand. Consderng the wde applcaton of Cartesan robots and the need of good accuracy n varous felds, proposng the relable and easy to do methods to calbrate Cartesan robots s one of the most mportant stages n desgn and manufacturng processes. The calbraton s the process of determnng the actual values of knematc and dynamc parameters of the ndustral robots. Knematc parameters descrbe the relatve poston and orentaton of lnks and jonts n the robot whle the dynamc parameters are related to arm masses, moment of nerta and nternal jont frcton. Thus, n ths paper, we present the procedure of calbraton and workng mprovement of Cartesan robots n terms of some performance ndces. These ndces values are measured n order to evaluate how much they are close to the agreed values for a fabrcated prototype robot as a case study. Recently, nterests n desgn, manufacturng, control and calbraton of robots wth prsmatc jonts have been ncreased wth a varous theoretcal and practcal contrbutons beng made [1, 2]. ISSN: 1991-8763 339 Issue 9, Volume 6, September 2011
Yaser Maddah, Al Maddah Azhdar et al. [3] presented a modelng and smulaton of a flexble 2 DOF robotc arm ncludng prsmatc and revolute jonts. They fabrcated the robot wth flexble elements from ether alumnum and lamnated composte materals. Reynoso [4] nvestgated the desgn, knematc and dynamc modelng and expermental tests of a Cartesan robot. In ths study, the effect of dsturbances such as frcton were consdered. Henz et al. [5] used a Cartesan robot for capturng flyng objects n laboratory envronment. For ths purpose, a camera system measured the object's poston durng a throw n subsequent perods of tme and based on these measurements the processor of robot can predct the capturng pont wth an ncreasng accuracy. Ghorab et a1. [6] appled some expermental tests on a prototyped model of a robotc manpulator n order to mprove the desgn of robot. Also, they employed the nternatonal certfed standard requrements ncludng ISO 9283 and IEC 31010 to reduce the robot errors and mproved the end-effector movement. Callegar et al. [7] presented a hgh-speed Cartesan robot produced by Campetella Robotc Center. Ths robot was characterzed by goo dynamc performance but was chosen by the producer for re-engneerng. Cheng et al. [8] presented knematc analyss of a robot desgned for studyng the feasblty of loadng packages nsde a flatbed traler. Ths ten DOF robot provded a large workspace, whch s acheved by operatng three redundant prsmatc jonts n arm. There exsts a varety of research work on determnaton of load capacty, Wang et al. [9] developed a technque to maxmze the dynamc load capacty for an entre trajectory rather than n the neghbourhood of the robot confguraton. Tmar et al. [10] consdered the problem of specfyng the feed rate varaton along a curved path, that yelded the mnmum traversal tme for a mult-axs CNC machne subject to gven bounds on the feasble velocty and acceleraton along each axs. Maddah et al. [11] proposed an algorthm for determnaton of maxmum allowable load carryng capacty of the robotc arms. In ths approach, the maxmum load s calculated by portonng the end-effector man trajectory to some sub-trajectores and calculatng the requred actuaton torque of each motor. In ths paper, desgn, modelng and expermental study of Cartesan robots are presented. Here, after descrpton of the related ssues of Cartesan robots, the calbraton method and performance ndces are descrbed and the proposed procedure s valdated by mplementng some experments on a prototyped robot. Secton 2 addresses the desgn procedure whch starts by the dervaton of robot equatons. Secton 3 presents the defntons mplemented n ths paper and s followed by explanaton of the control algorthm and the program wrtten to record the poston of robot end-effector whch s descrbed n Secton 4. In Secton 5, the expermental analyss for the prototype robot s presented and the test results are analyzed (Secton 6). The experments are done on the prototype robot to ncrease the accuracy of robot as well as to mprove the workablty of prototyped model. Moreover, an algorthm for determnaton of load capacty of ths type of robot s explaned and fnally, n order to verfy the proposed algorthm, consequences of analytcal, software smulaton and expermental studes are performed for the manufactured robot as a case study. 2 Smulaton and Modelng The desgn process of robot ncludes some theoretcal and practcal stages. In ths study, to desgn the ntal model of 3P robot, the followng algorthm s mplemented. Frst, the knematcs and dynamcs formulatons of robot are derved consderng the antcpated dutes for robot. Next, based on the theoretcal data, the robot elements are desgned and then smulated usng Workng Model software n order to obtan the torque requred for each actuator n some gven trajectores. Then, the ntal model s prototyped, after that some crtera to analyze the prelmnary robot are presented. 2.1. Theoretcal Modelng The knematcs and dynamcs modelng of robotcs systems s the frst stage n desgn of robots. Ths modelng concludes the formulatons determne the posture (poston and orentaton) and torques of the robots, theoretcally. In knematc analyss, the study of the poston, velocty and acceleraton and all hgher order dervatves of the poston varables are nvestgated. The knematc of robotc systems nvolves the study of the geometrc and tme-based propertes of the moton and n partcular how the varous lnks move wth respect to each other as tme evolves. For the Cartesan robot wth rgd lnk, the drect knematc soluton gves the coordnate of the tool attached to last lnk wth respect to the reference coordnate (Fg. 1). In ths fgure, d 1, d 2 and d 3 are prsmatc jont dsplacements n x, y and z drectons, respectvely [12]. Furthermore, n order to obtan the amount of requred torque for each actuator, the calculaton of ISSN: 1991-8763 340 Issue 9, Volume 6, September 2011
Yaser Maddah, Al Maddah equatons of moton s necessary. The proposed model of robot must be accurate enough to gve smple to use results whch satsfactorly descrbe the operaton of the actual system. The model smulates all the man exstng forces/torques n the Cartesan robots such as the centrfugal term. The knematcs and dynamcs formulaton are presented n [12]. Z d 3 d 2 d 1 Y X Typcal path Fg.1. Generalzed coordnates of Cartesan robot. 2.2. Smulaton Study Based on the robot equatons of moton, the ntal and approxmate model of the Cartesan robot s desgned (Fg. 2). usng ths model, the values for poston trackng and requred torques are obtaned usng Workng Model software. Then usng the data exported from software, the model s ntalzed for fabrcaton. As a result, the creaton of ntal model seems to be essental n order to valdate the derved mathematcal formulatons of prototype robot. Ths model s generated n Workng Model software. Ths software helps the users to model and smulaton the dynamcal mechansms and provdes some analyses such as moton analyss, forward and nverse dynamc and fnte element analyss (FEA). As concluded from smulaton output, there are some consderable errors between the analytcal and smulaton results. The maxmum torques n analytcal approach are about 100, 120 and 200 N.mm for motors 1, 2 and 3 whle for smulaton results, the obtaned torques possess more fluctuatons and ther mean values are ncreased about 25%, 28% and 21% n x, y and z drectons, respectvely. The added amounts of torques are caused by some effects gnored n theoretcal formulaton and appeared n software modelng such as unsymmetrcal geometry, frcton force, jont msalgnments and loss n motors. Fgure 3 llustrates the result of smulaton study whle robot travels a straght path from pont (40,40,40) to (235,235,235). As shown, there exst some errors n poston of end-effector due to the exstence of noted sources. X axs (d=12 mm) Z axs (d=10 mm) Lnear bush 20 mm Y axs (d=20 mm) Cube profle 40 40 mm 2 Lnear bush 20 mm Fg.2. Model smulated n Workng Model software. ISSN: 1991-8763 341 Issue 9, Volume 6, September 2011
Yaser Maddah, Al Maddah Poston [mm] 250 200 150 100 50 0 Actual Path - Along X axs Actual Path - Along Y axs Actual Path - Along Z axs Desred Path 0 1 2 3 4 5 Tme [sec] Fg.3. Results of smulaton study n straght trajectory. 2.3. Desgn Improvement The desgn algorthm usually accompanes some changes n the robot whch are determned accordng to the performance characterstcs such as the rsk analyss n safety sde of desgn, accordance wth the predefned accuracy and repeatablty as well as the amount of load carred by end-effector. Ths approach can be also wdely used n manufacturng ndustres. Ths algorthm starts wth the analyss of changes n desgn, error estmaton stages and effect of changes on values of agreed ndces and t s followed by evaluaton of the errors and the related sources. The man part of ths assessment process s the evaluaton of needed changes n the values of ndces as well as the resdual error n the system after applyng the requred changes. As explaned n [12], some components of robot had hgh effect n error ncrementng whch must be mproved n order to reduce the naccuracy for the system. Thus, some correctve actons were needed for these crtcal tems to mprove the performance ndces. The consdered varables to evaluate the desgn qualty were a) potental rsks (R) whch are many recognzable errors or defects n the desgn process n order to be reduced, especally those that affect the work qualty and user safety and can be potentally or actually and b) performance ndces ncludng accuracy and repeatablty of robot for gven trajectory. Thus, the performance ndex (PI) was calculated. The allocated values of these varables are between 0.1 and 1, whch the number represents the mportance of the related varable n requred changes. For nstance, one denotes the most mportance effect of the related varable n desgn change. The value of PI was used to rank the change effects n the robot desgn whch PI=0.01 shows the condton that the acton appled on desgn has no effect on the workng mprovement. The amount of each effect was numberzed based on the crtera pre-defned and s smlar to the crtera defned n falure modes and effects analyss (FMEA) method [13]. 3 Defnton of Indces To nvestgate the performance of the robot, based on the defned ndces, some expermental tests are performed for Cartesan prototype robot. These agreed values are consdered equal to 5mm, 10mm and 15mm for accuracy and 5 tme and 10 tme repeatablty. Also, the maxmum amount of dynamc load capacty for gven path (Secton 5.3) s predefned equal to 5 kg. These ndces are measured for straght trajectory wth the length of 250 mm n dagonal drecton of cube XYZ (Fg. 1). All ndces must satsfy the above agreed values, otherwse, the robot desgn must be changed to acheve desred values. 3.1. Accuracy The accuracy of ths robot s defned as the degree of closeness of end-effector poston to ts actual value. Accuracy ndcates proxmty of measurement results to the true value (Fg. 4). The accuracy of actual robot s under the effect of the followng factors such as accuracy of manufacturng mechancal parts of the robot, accuracy of assemblng the consttutng parts of robot, accuracy durng the robot operaton that s nfluenced by external forces, electroncs system accuracy, motors operatons, exstng clearance n the system, wear behavors (change n accuracy of the robot n long duraton), change n accuracy of system after assemblng and change n the system accuracy durng the preventve mantenance perodc program. 3.2. Repeatablty The repeatablty or test-retest relablty of robot poston s the varaton n measurements of endeffector poston taken by a sngle user or nstrument on the same tem and under the same condtons (Fg. 4). A measurement s sad to be repeatable when ths varaton s smaller than the agreed values defned before. The repeatablty condtons nclude same measurement procedure, same observer, and same measurng nstrument used under the same condtons as well as same locaton and repetton over a certan perod of tme. ISSN: 1991-8763 342 Issue 9, Volume 6, September 2011
Yaser Maddah, Al Maddah Start Pont (0, 0) m Start Pont (0, 0) m Fnal (Actual) End Pont Radus =Repeatablty Desred End Pont xd=2 m and yd=0 m Frst Stop Pont Radus=Accuracy Desred End Pont xd=2 m and yd=0 m Fnal End Pont (n th Stop Pont) Second Stop Pont. Fg.4. Defned path and related varables for accuracy and repeatablty tests. 3.3. Load Capacty Determnaton of load capacty of robot leads to select and attach the proper tool n end-effector. In order to determne load capacty of the robot, proper modelng of robot s a pre-requste. Here, the computatonal procedure to determne the maxmum allowable load capacty s outlned. To calculate the dynamc load carryng capacty of robot, after dscretzng the gven trajectory nto m ponts, jont moton constrants, Jacoban sngularty condtons and jont velocty constrants are checked [11]. In cases n whch each of the constrants s volated, the gven trajectory s unrealzable and a new trajectory should be selected. At next step, acceleraton of each jont s found and then the dynamc equatons are employed to compute the load and end-effector dynamc effects. Once the below condtons are satsfed, the value of mass carred by end-effector and related coordnate are recorded. - The jont knematcs varables ncludng the jont orentatons and veloctes should be bounded by two upper and lower lmts: d mn, d d max, d & d& mn, d& (1) max, Note that =1,2,3 s the jont number of Cartesan robot. - Non-sngularty condton of robot: Non-zero condton of Jacoban matrx for gven trajectory: J ( d, d&, xe, ye, ze ) 0 (2) where (x e, y e,z e ) s the coordnate of end-effector along the specfc trajectory whch can be a functon of tme. - Calculated torques should be bounded too usng the followng equaton. q& q& T0 ( 1+ ) T T0 (1 ) (3) ω ω In (3), T 0 s the stall torque of each motor and depends on the characterstc of actuator, q& denotes the full-loaded angular velocty of th motor for gven path and ω represents the angular velocty of motor whle carryng no load. Also, T s the torque of the th actuator. 4 Prototype Robot Based on the process descrbed before, a prototype model of the Cartesan robot s fabrcated as shown n Fg. 5. Ths model s fnalzed after applyng the changes concluded from desgn mprovement. Also, ths robot s desgned on bass of the assumpton n whch each jont has an ndependent actuator wth gear reducton and measurng angular jont poston sensor. Mechancal elements of the robot are modelled usng Sold Works software. In addton, the desgn of 3P robot s carred out usng the desgn prelmnary condtons (.e. agreed values) and the proposed mprovement algorthm to recognze and reduce the exstng errors durng the desgn and manufacturng stages [12]. 4.1. Control Unt The controller ncludes three drvers for three servo motors and used to drve the motors. Each motor has ts own bult-n reducton gears and ncremental encoder. As compared to robot descrbed n [12], the resoluton of the encoders s ncreased from 270 p/rev to 900 p/rev. The commands are sent to the robot va the desgned smulaton software. Ths software s mplemented because the manufactured robot should accomplsh the gven commands accurately and smoothly. Ths s possble n the case that the moton of the robot end-effector s accurate enough relatve to the target-object that s the pont that the end-effector of the manpulator has reached to. The robot works ISSN: 1991-8763 343 Issue 9, Volume 6, September 2011
Yaser Maddah, Al Maddah wth a Pentum IV, 1600 MHz whch s used for path detecton algorthm processng. Fg.5. Manufactured 3P robot. 4.2. Interfacng Program To transform the robot coordnates to global reference coordnate (Fg. 1), the scale secton of wrtten program s mplemented. Wth mages from these two fxed cameras, the postons of objects are shown n mage plane coordnate. As shown n Fgs. 5 and 6, two cameras wth a certan dstance from each other are lookng at the end-effector. One of these two statonary cameras s fxed and zooms along Z axs (camera 1) and second one s located n Y axs drecton (camera 2). Poston of end-effector s determned n mage plane and then s transferred to global coordnate usng derved transformaton matrces. Evaluaton of the mentoned procedure s one of the most convenent approaches to assess the entre actvty of ndustral robots. Also, the measurement of descrbed performance ndces brngs the opportunty of comparson the avalable robot wth other exstng robots. To make tests more applcable, the statstc analyzes are performed based on the defntons descrbed before. As shown n Fg. 6, the cameras take the sequences of photo from object located at end-effector and the encoders read the amount of pulses of motors and the program scales the pctures and recognzes the endeffector and target stuatons among other objects. Then, based on the nput desred path, the amount of error n X, Y and Z drectons s calculated and the controller sends the compensated pulse to the motors n order to modfy the moton of robot. 4.3. Mechancal Elements The mechancal mechansm n manufactured base conssts of three gearboxes and ther own shafts to transmt the angular veloctes of gearboxes to the axs shafts. On the bottom of the robot, coverng platform s a wood plate that the work peces are mounted on. Fg.6. Poston-based control structure of robot and statonary cameras (Modfed from [12]). ISSN: 1991-8763 344 Issue 9, Volume 6, September 2011
Yaser Maddah, Al Maddah 5 Test Results In expermental tests, frst the prototype robot s tested and the performance ndces are measured and compared wth the agreed values. As the calculated ndces n prelmnary model cannot satsfy the desgn crtera frstly, thus, the mprovement algorthm results (the requred changes) are appled on robot n order to mprove the desgn of the prelmnary model. Also, the tests are repeated whle some correctve actons are consdered durng the desgn and manufacturng process and the performance ndces are calculated. Fnally, the mprovement factors are obtaned and compared to the ntal data. The performance tests are done usng the two-camera measurement technque. As mentoned, the test parameters nclude accuracy, repeatablty of end-effector poston and load capacty of robot. 5.1. Accuracy and Repeatablty: Results Based on the descrbed technque to posture measurement, the amount of accuracy and repeatablty of robot are obtaned n before and after desgn changes. In all experments whch are descrbed n ths secton, the robot s programmed to move n a typcal trajectory wth l=250 mm n dagonal drecton of XYZ cube whch s shown n Fg. 1. In ths experment, the end-effector lnear velocty s 0.12 m/s. Fgure 7 shows the mean values of expermental results obtaned for accuracy and repeatablty tests for gven trajectory. The repeatablty test s done when n=5 and n=10. The bars show the end-effector errors after and before applyng the correctve actons. For each tral, ths test s performed for 10 tmes and the end-effector error s defned as the mean value of the dfference between the desred and actual postons by followng equaton: 10 1 2 2 2 RE = ( X a, X d ) + ( Ya, Yd ) + ( Za, Zd ) 10 = 1 (5) where ( X a,, Ya,, Z ) and ( a, X d, Yd, Z ) are the actual d and desred coordnates, respectvely. The actual coordnates are calculated usng the mentoned mappng algorthm. As llustrated n Fg. 7, the accuracy 5 tme and 10 tme repeatablty error were reduced by 63.5%, 29.3% and 29.8%, respectvely. 5.2. Trajectory Test In next experment, desred poston of endeffector s gven to robot to reach. By computng RE [mm] 1.2 1 0.8 0.6 0.4 0.2 0 Fnal Desgn (After exertng the correctve actons) Prelmnary Desgn (Before exertng the correctve actons) Accuracy Repeatablty (n=5) Repeatablty (n=10) Fg.7. Error mean values of tool movement n accuracy and repeatablty tests. jont angles from nverse knematcs equatons and rotaton of jonts, the end-effector wll reach to the desred poston. By takng photos wth two fxed cameras, the robot equatons and the counted pulses concludes the coordnaton of end-effector n global reference frame are determned. Also, by comparng the desred and actual amounts of end=effector poston, the postonng errors are determned. 5.2.1. Quarter Crcular Path In ths test, the accuracy of robot on the quarter crcular contnuous path s determned and the amount of error durng the robot moton s calculated. The crcle s n horzontal plane.e. the heght of robot end-effector s constant from earth level. The orentaton of the end-effector doesn t vary, thus, the end-effector s always n horzontal plane and also, normal wth respect to crcular path and end-effector sldes along permeter of crcle. Durng moton of end-effector on the path, 10 mages have been taken from end-effector. Usng mappng system, the mage coordnates of ponts are transformed to the reference frame. The desred and actual paths are llustrated n Fg. 8. In ths experment, the mean value of end-effector lnear velocty s 0.08 m/s. 5.2.2. Straght Lne To move end-effector along a drect lne, ts start and end ponts must be determned. Approach vector drecton s normal wth respect to drecton of lne path.e. end-effector s always normal to ts path. Wth pose of end-effector and nverse knematcs equatons of robot, the jont angles are computed. Jonts rotate and end-effector s postoned along ts path. Coordnates of end- ISSN: 1991-8763 345 Issue 9, Volume 6, September 2011
Yaser Maddah, Al Maddah effector n global reference frame are determned by takng pctures wth two fxed cameras. The postonng error s determned by comparng the desred pose and actual one. Error of tool n traversng drect lne path, when they move along X axs are shown n Fg. 9. The start pont s coordnated by (0, 0, 0) and the fnal pont s located on (150, 150, 150). The lnear velocty of endeffector s consdered to be 0.3 m/s. Y Axs [mm] 6 5 4 3 2 1 0 Desred Path Actual Path 0 1 2 3 4 5 6 X Axs [mm] Fg.8. Desred and actual paths n quarter crcular test. 5.3. Load Capacty Ths secton presents the calculaton of the robot dynamc computatons usng three approaches ncludng analytcal approach, smulaton study and expermental test. In all approaches, the end-effector travels from pont (0,0,0) toward pont (120,120,120). All experments and smulaton studes n ths secton are performed for fnal model of robot after applyng the correctve actons. 5.3.1. Computatonal Method In ths secton, the prevous dagonal trajectory for the load s assumed usng the algorthm presented n Secton 3.3. Consderng the modelng equatons, the task space trajectory s descrtzed nto equally spaced m=40 ponts. The allowable load carryng capacty for the moble manpulator at every pont of the trajectory s determned and maxmum allowable load s found m load =8.16kg at pont X(t)=62.5mm, Y(t)=62.5mm, Z(t)=120mm as shown n Fg. 10. As shown n ths secton, there are some dfferences n the results of analytcal and smulaton approaches n calculaton of maxmum allowable load carryng capacty. The effects of frcton force, load and nerta dstrbuton types are the major reasons of ths dfference. 5.3.2. Smulaton Approach In ths approach, the load capacty value s calculated usng smulaton study. Also, to determne the maxmum load capacty, the model s moved n gven trajectory n Workng Model software and the torques of motors are derved from 1.5 1 0.5 Error [mm] 0-0.5-1 -1.5 1 2 3 4 5 6 7 8 9 10 ex -0.4 0.9-0.1 0.7 1-1.2-0.8-0.2 0.4 0.5 ey 0.8 0.9 0.3 0.5 0.6 0.1 0.2 0.3 0.9 1.2 ez 0.4 0.65 1 0.1 0.25 0.3 0.8 0.75 0.9 1.1 Test No. Fg. 9. Error dagram n x, y, z drectons n straght lne trajectory appled on fnal desgn of robot whch are shown by e x, e y, e z, respectvely. ISSN: 1991-8763 346 Issue 9, Volume 6, September 2011
Yaser Maddah, Al Maddah Fg. 10. Varaton of allowable load along load trajectory and load capacty. software output. In ths estmaton, the amount of plus load mass s ncreased n each tral and the torques are checked. When one of motors reaches to ts crtcal torque, t means that robot s carryng ts maxmum load n gven trajectory. For calculaton of maxmum allowable load, Cartesan robot s moved n gven trajectory and the ntal load s taken to zero, then the load s ncreased by steps of 0.1 kg. Fgure 11 shows the maxmum torques of motor 2 for gven manpulator load n each trals. Fg.11. Torque-load varatons for 2 nd actuator. As a results, accordng to ths fgure, for m load =7.5kg, motor 2 (Y axs motor) reaches ts maxmum value τ=1058 Nmm. As shown n Fg. 11, the torque of motor 2 restrcts the load capacty n end-effector and the maxmum allowable load for gven trajectory s determned as m allowable =7.5kg. In ths estmaton, some dsturbances neglected n theoretcal modelng take nto account such as the effect of frcton forces, unsymmetrcal dstrbuton of robot mass and probable msalgnments n jonts. Ths consderaton makes the results more accurate as opposed to analytcal approach. 5.3.3. Expermental Approach In ths approach, the amount of torque for each motor s derved usng laboratory tests appled on ths robot. The obtaned data are perfectly expermental and all exstng errors sources such as frcton effects have been consdered. The amount of maxmum load capacty for ths path s obtaned about 5.64kg usng three torque-meters nstalled on the actuators (Fg. 11). The mplemented dgtal torque meters are made by Shenzhen Tony Electroncs Company and named SHITO. They are the ntellectualzed nstruments for measurng and settng torque whch are mostly used for nspectng the torque of electrc torque drvers and used to measure the torque produced durng the actuators motons. These sensors are desgned as easy-tooperate, accurate, functonal and portable tools. 6 Statstcal Analyss In order to compare the obtaned results wth the agreed values n desgn stage, the calculated ndces based on the data resulted from experments are consdered accordng to Table 1. As shown n ths ISSN: 1991-8763 347 Issue 9, Volume 6, September 2011
Yaser Maddah, Al Maddah Table 1- Expermented Indces Values. Mean Mean DLCC Accuracy Repeatablty (kg) (mm) 5 tmes (mm) Mean Repeatablty 10 tmes (mm) Agreed Values 5.00 5 10 15 Prelmnary Desgn 3.21 10.70 12.75 19.80 Fnal Desgn 5. 64 3.91 9.01 13.90 table, all derved data are acceptable and also, confrm the fnal desgn based on the agreed values. Thus, the changes appled durng the desgn process are reasonable n the sense of defned and agreed ndces. 7 Conclusons Ths paper addressed the procedure of expermental evaluaton and mprovement of the desgn and applcaton of Cartesan robots by mplementng the expermental tests. Ths desgn was completed based on some predefned ndces whch can be obtaned usng expermental tests. These ndces were specfed durng the desgn process as desgn nputs accordng to the antcpated workablty of Cartesan robots. These performance ndces consst of the accuracy, repeatablty and load carryng capacty. In addton, n order to valdate the descrbed procedure, a prototype model of Cartesan robot was manufactured and tested. Then, after exertng changes durng desgn process (mentoned n [12]), the experments showed great mprovement over the prelmnary desgn of robot. For example, the accuracy, 5 tme and 10 tme repeatablty errors were reduced by 63.5%, 29.3% and 29.8%, respectvely. References [1] S.D. Tmar, R.T. Farouk, T.S. Smth, & C.L. Boyadjeff, Algorthms for tme-optmal control of CNC machnes along curved tool paths, Robotcs and Computer Integrated Manufacturng, 21, 2005, 37 53. [2] P.S. Snches, & F.R. Cortes, A New Cartesan Controller for Robot Manpulators, IEEE/RSJ Internatonal Conference on Intellgent Robots and Systems, 2005, 3536-3542. [3] A. Azhdar, N. G. Chalhoub, & F. Gordannejad, Nonlnear Dynamc Modellng of a Revolute- Prsmatc Flexble Composte-Materal Robot Arm, Journal of Vbraton and Acoustcs, 113 (4), 1991, 461-468. [4] A. G. Reynoso, Structural dynamc model of a Cartesan robot, MIT Artfcal Intellgence Laboratory, PhD Thess, 1967. [5] F. Henz, B. Denns, M. Marcus, M. Anton, N. Gregor, & M. Stefan, Optmzed control methods for capturng flyng objects wth a Cartesan Robot, IEEE Int. Conf. on Robotcs, Automaton and Mechatroncs, 2008, 160-165. [6] H. Ghorab, Y. Maddah, S. M. Hossen Monsef, & A. Maddah, Desgn and Expermental Tests of a Pck and Place Robot: Theoretcal and Expermental Approaches, Internatonal Conference on Applcatons of Electrcal Engneerng, Malaysa, 2010. [7] Massmo Callegar, Ferdnando Cannella, Sergo Mont, Claudo Santoln, & Paolo Pagnanell, Dynamc Model for a Re-Engneerng of a Hgh-Speed Cartesan Robot, IEEE/ASME Internatonal Conference on Advanced Engneerng Mechatronc, Italy, 2001, 560-565. [8] Cheng, H.H., Lee, J.J., & Penkar, R., Knematc analyss of a hybrd seral-and-parallel-drven redundant ndustral manpulator, Internatonal Journal of Robotcs and Automaton, 10(4), 1995, 159-166 [9] L. T. Wang, & B. Ravan, Dynamc load carryng capacty of mechancal manpulators- Part 1: Problem formulaton, Journal of Dyn. Sys. Meas. and Control, 110, 1988, 46-52. [10] Tmar, S.D., Farouk, R.T., & Boyadjeff, C.L., Tme-optmal feed rates along curved paths for cartesan CNC machnes wth prescrbed bounds on axs veloctes and acceleratons, Internatonal Journal of Robotcs and Automaton, 22(2), 2007, 112-125. [11] Y. Maddah, Calculaton of Load Carryng Capacty on a Redundant Manpulator, Internatonal Conference on Crcuts, Systems, Sgnal and Telecommuncatons, Mexco, 2008. [12] Y. Maddah, N. Sepehr, H. Ghorab and A. Maddah, Testng Robotc Manpulator: Improvement and Experence, Internatonal Journal of Systems Applcatons, Engneerng and Development, pp. 35-45, 2010. [13] R. Qang, Research on Sales Qualty System Improvement Based on FMEA. Internatonal Conference on Servce Systems and Servce Management, Chna, pp. 905 909, 2009. ISSN: 1991-8763 348 Issue 9, Volume 6, September 2011