Quick error verification of portable coordinate measuring arm

Transcription

1 Quck error verfcaton of portable coordnate measurng arm J.F. Ouang, W.L. Lu, X.H. Qu State Ke Laborator of Precson Measurng Technolog and Instruments, Tanjn Unverst, Tanjn 7, Chna Tel.: + 86 [] Fax: + 86 [] E-mal: luwanl8@6.com Abstract The features of portable coordnate measurng arm (PCMA) offered b the FaroArm s dscussed. A new technque for rapd volumetrc error verfcaton of PCMA has been presented. A modular space frame to verf and calbrate the measurng accurac of PCMA has been nvented, whch conssts of standard balls, lnks and bases. An effectve verfcaton procedure s developed. The volumetrc error data of PCMA measurement on the calbrated frame can be used to verf whether the measurng accurac of PCMA mantans the manufacturer specfcatons. Theoretcal analss and expermental results have demonstrated that usng ths technque to verf PCMA, PCMA can be calbrated ver accuratel and quckl. The proposed method can be appled for calbraton, verfcaton, and perodc reverfcaton acceptance test of PCMA. Kewords: Portable coordnate measurng arm, error verfcaton, modular space frame. Introducton Portable coordnate measurng arm (PCMA) has been successfull ntroduced nto measurng technolog. Among the large-scale-sze measurng technologes, such as CMM, theodoltes, photogrammetr, and laser trackers, PCMA possess man advantages [-], such as lght, portable, hgh speed, hgh accurac and readl settng up anwhere. It s wdel used n the automotve, aerospace, heav engneerng, ralwa and energ ndustres. A robot-lke manual machne allows the user to acheve measurement tasks easl n man cases, such as mantenance, assembl, qualt assurance, nspecton and reversed engneerng. The structure of portable measurng arm make t perfect be used n workshop. Another applcaton of PCMA s the calbraton of ndustral robot. To carr out measurement tasks n the manufacturng ndustr, the accurac of the PCMA s one of ts most mportant requrements. Exstng PCMA are verfed and calbrated ver dfferentl. A testng jg or standard ball s used to calbrate PCMA, but t onl can verf the sngle-pont accurac nstead of volumetrc accurac. A horzontal artculated coordnate measurng devce can acheve the requred accurac together wth calbraton and compensaton procedures, whereas t can not be used for measurng and gudng the PCMA along an reference lne adjustable n varous spatal drectons. Another possblt for measurng PCMA could be a Cartesan CMM. However, the measurng results dd not prove to be useful snce a hgh devaton of results appeared, caused b deflecton of the CMM sstem as a consequence of reacton forces caused b pushng [-]. Therefore, at present, a crtcal need exsts n order to overcome dsadvantages of exstng technques, to assess volumetrc accurac of PCMA. The purpose of ths paper s to present a technque and devce developed b authors to verf and calbrate PCMA ver smpl and effectvel.. Portable coordnate measurng arm The workng prncple of PCMA s lke human arm, but wth more precson and greater flexblt. As shown n Fg., the PCMA manl ncludes probe 7, jonts ( = -6), and -

2 mount 8. The probe 7 s used to touch measured pont. Sx jonts can rotate (,,,, ) respectvel, whch s gven b hghl accurate shaft encoders, to make probe 7 reach and measure an D pont. The mount 8 can be set up at an poston wth the help of varous mountng optons such as magnetc and vacuum mounts. X X 6 P Z 6 6 O O 6 l Z Y 6 Y Z d Z Y 6 X X O O Y Z d Z Y X X O O 8 7 Y Z d Y O Fg.. Workng prncple of portable coordnate measurng arm. X In order to stud the relatonshp amount the axes, the measurng mathematcs model and the lnear measurng errors equaton of probe of PCMA usng Denavt-Hartenberg (D-H) are establshed. The transformaton matrx of D-H can be wrtten as []: nx ox x px n o p T nz oz z pz () Where, P = (p x, p x, p x ) T s the poston of orgn of th coordnate sstem wth respect to the (-)th coordnate sstem; N=(n x, n x, n x ) T s the X drecton cosne of th coordnate sstem wth respect to the (-)th coordnate sstem; O=(o x, o x, o x ) T s the Y drecton cosne of th coordnate sstem wth respect to the (-)th coordnate sstem; A=(a x, a x, a x ) T s the Z drecton cosne of th coordnate sstem wth respect to the (-)th coordnate sstem. Table.. The parameters of translaton matrxes of PCMA. Axs 6 p d d d d l Accordng to equaton (), the parameters of coordnate transformaton of PCMA can be wrtten as Table. The measurng mathematc equaton of PCMA wth respect to the O X Y Z coordnate sstem can be wrtten as [6]: T T T T T T T P () 6 6 -

3 Substtutng Equaton () nto () elds: xp cos ksn 6 p sn kcos z () p d l Where, k = when =,,, and k = - when =,,6. The lnear measurng errors equaton of PCMA probe can be wrtten as: p p p p p P d l l d l l () Equaton () Substtuton can be wrtten as: cos k sn k sn cos k sn cos d sn sn k cos k cos sn k cos sn d cos k k k d d l l l 6 P () Where,. Modular space frame In order to verf the performance of PCMA, a novel space frame s desgned. As shown n the Fg., t has the form of a tetrahedron, whch contans a standard ball at each apex. The proposed verfcaton sstem ncludes standard ball, fxaton, carbon fber lnks, and bases. Ths space frame wll be referred to as a modular space frame and can be obtaned easl and rapdl. Fg.. Modular space frame. In the proposed technque, for each dfferent confguraton of the modular space frame two tetrahedrons must be consdered. One conssts of the calbrated dmensons obtaned b a hgh accurac CMM and another s related to the measured dmensons obtaned b PCMA. Snce the relatve poston and orentaton of the two tetrahedrons are unknown, t s necessar to establsh a crteron to defne the relatonshp between the calbrated and measured -

4 tetrahedron. That s, for one apex of each tetrahedron to be supermposed, one edge of each tetrahedron to be co-lnear and two faces to be made co-planar. ' ' and ' ' Fg. Calbrated and measured frame Fg.. Modular space frame. As shown n the Fg., the real lne s the calbrated modular space frame, and the dashed lne s the measured modular space frame. For each confguraton of the modular space frame, the measurng error s defned as the dfference between the calbrated and measured coordnates of the apex that s connected to three lnks. For nstance, n Fg. the dfference between the calbrated co-ordnates ( X, Y, Z ) of the apex and the measured co-ordnates ( X m, Ym, Zm ) of the apex defnes the measurng errors ( E x, E, Ez ). The calbraton process onl nvolves n calbratng the elements that defne the modular space frame, lnks and base. Then the relatonshp between the calbrated and measured co-ordnates of the apces of the tetrahedron can be obtaned. B comparng the calbrated and measured data of the modular space frame, t s possble to determne the errors ( E, E, E ) of the PCMA. The measurng error at each pont defned b the modular space frame s gven as followng: Where, Ex X m X E Ym Y, (6) Ez Zm Z X, Y, Z are the calbrated coordnates of the ponts generated b the calbrated modular space frame, and X m, Ym, Zm are the measured coordnates of the ponts generated b the measured modular space frame.. Experments A prototpal of modular space frame has been bult, and used to verf whether a PCMA mantans the manufacturer specfcatons. The experment laouts are show n Fg.. A calbraton procedure s developed as followng: Calbrate the modular space frame usng CMM; Buld the calbrated data of modular space frame; Measure calbrated space frame usng PCMA; Buld the measured data of PCMA; Compare the calbrated and measured data of space frame; Buld correspondng error database of PCMA; Use the database to verf and calbrate PCMA. x z -6

5 Errors (um) Fg.. Experment laouts. - Measurng numbers Fg.. Measured results of sngle-pont errors. Fgure shows the measured results of volumetrc errors of PCMA. Three dfferent standard balls of modular space frame are measured respectvel. Each standard ball s measured thrt tmes. From the Fg., we can see that the all measured errors of PCMA are wthn the manufacturer s specfcaton (±.mm). The verfcaton tme s onl mnutes.. Concluson. The new technque developed n ths research provdes an effcent approach for measurement and verfcaton volumetrc accurac of PCMA.. The modular space frame provdes a practcal and cost effectve devce to verf the volumetrc accurac of PCMA.. It takes ffteen mnutes to calbrate PCMA b usng the proposed technque, whch s less than the exstng technques. 6. Acknowledgements Ths stud s supported b the Natonal Natural Scence Foundaton of Chna (NSFC#78) and the Open Foundaton of State Ke Laborator of Precson Measurng Technolog and Instruments (Tanjn Unverst and Tsnghua Unverst). References. Santolara Jorge, Agular Juan-Jose, Yague Jose-Antono, et al. Knematc parameter estmaton technque for calbraton and repeatablt mprovement of artculated arm coordnate measurng machnes. Precson Engneerng. 8, (), pp I. Kovac, A. Frank. Testng and calbraton of coordnate measurng arms. Precson Engneerng., (), pp Wanl Lu, Janfe Ouang, Xnghua Qu, et al. Msalgnment error calbraton of faro retro probe for laser tracker sstem. Chnese Optcs Letters. 7, (), pp Wanl Lu, Xnghua Qu, Janfe Ouang, et al. Desgn and CAD-drected Inspecton Plannng of Laser Gude measurng robot. Computer & Graphcs. 8, (6), pp Curran Emmett, Phelan Pat. Quck check error verfcaton of coordnate measurng machnes. Journal of Materals Processng Technolog., (), pp J.-P. Kruth, L. Zhou, C. Van den Bergh, et al. A Method for Squareness Error Verfcaton on a Coordnate Measurng Machne. Internatonal Journal of Advanced Manufacturng Technolog., (), pp