Coordinate measuring method with two operation modes based on the adjustable articulated arms

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1 Coordnate measurng method wth two operaton modes based on the adjustable artculated arms Lanqng Zhu Wexan L Zhkang Pan Yangkuan Guo Qngshan Chen

2 Optcal Engneerng 53(12), (December 2014) Coordnate measurng method wth two operaton modes based on the adjustable artculated arms Lanqng Zhu, a,b, * Wexan L, a,b Zhkang Pan, a,b Yangkuan Guo, a,b and Qngshan Chen a,b a Bejng Informaton Scence and Technology Unversty, Bejng Key Laboratory of Optoelectronc Measurement Technology, Bejng , Chna b Bejng Engneerng Research Center of Optoelectronc Informaton and Instrument, Bejng , Chna Abstract. A coordnate measurng method wth two operaton modes, based on the adjustable artculated arms, s proposed to keep measurement capablty n global space and mprove the measurement precson n local space. The adjustable artculated arm coordnate measurng machne (AACMM) wth an electromagnetc lockng devce can automatcally swtch between the all-free artculated arms operaton mode and the partally bound artculated arms operaton mode. In the former mode, three arms and sx artculatons can freely move and measure the coordnates of any pont n global space. In the latter mode, the front two artculatons are locked to mprove the measurement precson by decreasng the mportaton of angle errors n the local space. A prototype of the adjustable AACMM has also been desgned and developed. A mathematcal model for the adjustable AACMM has been bult. Theoretcal analyss and numercal smulaton show that the partally bound AACMM performed much better than the all-free AACMM n sngle pont repeatablty and length measurement precson n the local space. Therefore, the proposed coordnate measurng method based on the adjustable artculated arms s verfed as beng effectve. The Authors. Publshed by SPIE under a Creatve Commons Attrbuton 3.0 Unported Lcense. Dstrbuton or reproducton of ths work n whole or n part requres full attrbuton of the orgnal publcaton, ncludng ts DOI. [DOI: /1.OE ] Keywords: artculated arm; coordnate measurng machne; adjustable. Paper SS receved Apr. 1, 2014; revsed manuscrpt receved May 11, 2014; accepted for publcaton May 16, 2014; publshed onlne Jun. 25, Introducton The coordnate measurng machne has been appled extensvely as a key precse tool for guaranteeng product qualty n the automoble and shp manufacturng ndustres. 1,2 Although the tradtonal orthogonal coordnate measurng machne has hgh measurement precson, ts usage n onste applcatons s extremely lmted by ts complex structure, hgh cost, and strct ambent demands. Because of ths, the nonorthogonal coordnate measurng machne has made rapd developments n the last two decades. For example, the flexble artculated arm coordnate measurng machne (AACMM), characterzed wth smple structure, low cost, and portablty, has been broadly appled n those ndustres that have a low measurement precson requrement. 3 6 The artculated arm coordnate measurng machne s desgned as a seral, spatal, open-lnked structure. It usually conssts of three arms and sx artculatons and can move freely n multple degrees of freedom. The error of every arm and artculaton wll be accumulated and transmtted step-by-step toward the end n an amplfcatory way. For years, the measurement precson has mpeded further applcaton of the AACMM. Researchers as well as manufacturers have carred out varous works n the herarches of system structure desgn and system model calbraton. In the former, the tolerances of elements and assembles have been mproved. In the latter, dfferent calbraton methods have also been developed for better precson. 7 9 Hamana et al. proposed a calbraton method for the knematc parameters of the AACMM usng sphercal center *Address all correspondence to: Lanqng Zhu, E-mal: zhulanqng@sna.com coordnates. Santolara et al. presented a new technque for capturng data that allows the subsequent dentfcaton of the AACMM knematc parameters and a new repeatablty error measurement correcton method based on Fourer polynomals. Sładek et al. proposed a descrpton of modelng and the dentfcaton of errors of the AACMM based on a metrologcal model. In addton to the pursut of mprovement n structure desgn and model calbraton, we pay attenton to the real operaton stuaton. Although the AACMM has a large measurement space, most measurement tasks n real applcatons are lmted n a local space, where some, but not all, of the arms and artculatons are needed to move. In those cases, decreasng the system s degrees of freedom of moton obvously can reduce the mportaton of errors and mprove the measurement precson sgnfcantly. From ths pont of vew, the contrbuton of ths paper s not to make an mprovement n structural desgn or model calbraton, but to break the current measurement mode of the AACMM. A new coordnate measurng method based on the adjustable artculated arms for the AACMM n two operaton modes s proposed. Ths measurement method wll mantan the measurement capablty n global space and mprove the measurement precson n local space. 2 Adjustable Strategy and Implementaton 2.1 Adjustable Strategy The authors prevous studes showed that the front artculatons generally have a greater mpact on the measurement precson. 10,11 Thus, f one front artculaton s locked, the front artculaton error s not mported to the measurement, Optcal Engneerng December 2014 Vol. 53(12)

The word adjustable means the AACMM has two operaton modes: one wth all-free artculated arms to mantan coordnate measurement ablty n global space (whch s the tradtonal coordnate measurement) and the

3 Zhu et al.: Coordnate measurng method wth two operaton modes... Fg. 1 Scheme of the adjustable measurement method. and the precson may be mproved. Ths paper presents a coordnate measurng method based on the adjustable artculated arms. The word adjustable means the AACMM has two operaton modes: one wth all-free artculated arms to mantan coordnate measurement ablty n global space (whch s the tradtonal coordnate measurement) and the other wth partally bound artculated arms, acheved by lockng the frst two artculatons to mprove the coordnate measurement precson n the local space. In the meanwhle, the adjustable artculated arms could automatcally swtch between the above two operaton modes. Fgure 1 shows the operaton scheme of the adjustable AACMM. The lockng devce, whose essence s to lock the rotatng artculaton of the arms, s the key to the adjustable AACMM. Ths paper develops an electromagnetc lockng devce, whch can precsely and automatcally lock and unlock the artculaton at any poston. As shown n Fg. 2, the lockng devce conssts of an electromagnetc base and an electromagnetc col. They are fxed wth two sdes of one artculaton knematc par. When the lockng devce s powered off, there s no constrant between the base and the col, so the artculatng knematc par can move freely. When the lockng devce s powered on, a force constrant s placed between the base and the col, and the artculatng knematc par wll be locked frmly. The force of the devce can be ncreased by ncreasng the col turns to meet the maxmum force requred. Most mportantly, the lockng devce can be controlled to realze the automatc swtch between the all-free artculated arms operaton mode and the partally bound artculated arms operaton mode. 2.2 Adjustable Measurement System Fgure 3 shows an adjustable AACMM wth the electromagnetc lockng devce desgned and developed n ths paper. The prototype conssts of a base, three arms, sx artculatons, two lockng devces, and a probe. The two lockng devces are placed n artculatons 1 and 2, respectvely. Artculated arm 1 and the base, as the supports of the other parts of the prototype, are made n the shape of barrel by 40Cr steel to reduce dstorton. Artculated arms 2 and 3, whch are supposed to move n any drecton, are made n the shape of thn barrel by carbon fber to reduce weght. The neghborhood artculated arms are connected wth double cross-artculatons, as shown n Fg. 4(a). The cross-artculatons can rotate along two vertcal drectons ndependently. Every artculaton s equpped wth a crcular gratng angle sensor to measure the artculaton angle. Fgure 4(b) shows the M1800 angle sensor from McroE, Bedford, Massachusetts nstalled on the surface of the artculaton bearng. The lockng devces, shown n Fg. 5, have been developed takng nto consderaton the structures and the force requrements of artculatons 1 and 2. 3 Adjustable Mathematcal Model The adjustable AACMM conssts of three arms, sx artculatons, and two lockng devces. Fgure 6 shows the structure and coordnate frames of the adjustable AACMM. {O 0 X 0 Y 0 Z 0 } s the base coordnate frame and {O tp X tp Y tp Z tp } s the probe coordnate frame {O X Y Z }. ( ¼ 1 6) sthe artculaton coordnate frame defned at each artculaton. The D H model, proposed by Denavt and Hartenberg, s used n the mathematcal modelng of the adjustable AACMM. 12 There are four types of structure parameters n the D H model: (1) arm length d s the dstance between Fg. 2 Prncple of lockng devce. Fg. 3 Setup of the prototype. Optcal Engneerng December 2014 Vol. 53(12)

Zhu et al.: Coordnate measurng method wth two operaton modes... Fg. 4 (a) Double cross-artculatons and (b) crcular gratng angle sensor. Fg. 5 Lockng devces: (a) lockng devce 1 and (b) lockng devce 2.

the postve; and (4) artculaton angle θ s the angle between the adjacent X-axs wth the rght hand around the Z 1 -axs as the postve.

4 Zhu et al.: Coordnate measurng method wth two operaton modes... Fg. 4 (a) Double cross-artculatons and (b) crcular gratng angle sensor. Fg. 5 Lockng devces: (a) lockng devce 1 and (b) lockng devce 2. adjacent rod length between the X-axs; (2) artculaton length a s the dstance between the adjacent Z-axs; (3) twst angle α s the angle between the adjacent Z-axs wth the rght hand around the X-axs as the postve; and (4) artculaton angle θ s the angle between the adjacent X-axs wth the rght hand around the Z 1 -axs as the postve. Accordng to the D H method, the homogeneous transformaton matrx from {O 1 X 1 Y 1 Z 1 } to the coordnate system {O X Y Z }(¼1 6) s T 1; 2 3 cos θ sn θ cos α sn θ sn α a cos θ sn θ ¼ cos θ cos α cos θ sn α a sn θ sn α cos α d 7 5 : Let the homogeneous coordnates of the probe P n the sxth artculaton coordnate frame {O 6 X 6 Y 6 Z 6 }bex 6 ¼ ½l 1 ;l 2 ;l 3 ; 1Š T and the homogeneous coordnates n the base coordnate frame {O 0 X 0 Y 0 Z 0 } be p 0 ¼½x; y; z; 1Š T. The mathematcal measurement model for the adjustable AACMM s (1) Y 6 p 0 ¼ T 1; X 6 : (2) ¼1 Fg. 6 Structure and coordnate frames of the adjustable artculated arm coordnate measurng machne (AACMM). In the partally bound artculaton arms operaton mode, artculatons 1 and 2 (θ 1 and θ 2 ) are fxed, whle the other four (θ 3 θ 6 ) can rotate freely. In the all-free artculaton arms operaton mode, all sx artculatons can move freely and θ 1 θ 6 can change freely. Therefore, the all-free AACMM has a set of structural parameters ^ξ str ¼ fl 1 ;l 2 ;l 3 ;a ; α ;d g, ¼ 1 6 and a set of extrnsc parameters ^ξ ex ¼fθ g, ¼ 1 6. But the partally bound AACMM has a set of structural parameters ξ str ¼fl 1 ;l 2 ;l 3 ;a ; α ;d ; θ 1 ; θ 2 g, ¼ 1 6 and a set of extrnsc parameters ξ ex ¼fθ g, ¼ 3 6. Both operaton modes and ther parameter sets construct the adjustable AACMM and ts mathematcal model. Optcal Engneerng December 2014 Vol. 53(12)

5 Zhu et al.: Coordnate measurng method wth two operaton modes... Fg. 7 Eghty-eght ponts n a local space. 4 Analyss and Test 4.1 Measurement Precson Analyss The measurement precson of the AACMM s affected by many factors, such as parameter error and envronmental error. The parameter error s one of the most mportant errors, manly produced n the machnng and assembly process. The four types of parameters n the transformaton matrx of the D H model have great nfluence on the measurement precson. Accordng to the structure and extrnsc parameters of the all-free AACMM, the measurement error of the probe can be denoted as Δ^p 0 ¼ ^ξ Δ^ξ str þ str ^ξ Δ^ξ ex ex X 3 ¼ l Δ^l m þ X6 m¼1 m a Δ^a þ ¼1 α Δ^α þ X 6 d Δ^d þ θ Δ^θ : (3) ¼1 angles of the two AACMM operaton modes should have the equal errors Δθ ¼ Δ^θ for ¼ 3 6. Therefore, the dfference of the measurement error between these two operaton modes s Δp 0 Δ^p 0 ¼ θ ðδθ 1 Δ^θ 1 Þþ 1 θ ðδθ 2 Δ^θ 2 Þ: (5) 2 Parameter calbraton s amed at true value, so the error after calbraton should be less than the error before calbraton. Thus, the artculaton angles as the structure parameters are clearly more accurate than the ones as the extrnsc parameters, and Δθ 1 Δ^θ 1, Δθ 2 Δ^θ 2, and Δp 0 Δ^p 0. Therefore, n theory, the measurement error of the partally bound AACMM should be less than the one of the all-free AACMM. That s to say, the partally bound AACMM operated n the local space could mprove the measurement precson. In the same way, the measurement error of the probe for the partally bound AACMM can be denoted as Δp 0 ¼ ξ Δξ strþ str ξ Δξ ex ex X 3 ¼ l Δl m þ X6 m¼1 m a Δa þ ¼1 α Δα þ d Δd þ X2 X 6 θ Δθ Šþ θ Δθ : (4) ¼1 ¼3 Although these two AACMM operaton modes have dfferent model parameters, they have the same model equaton. So, after system calbraton, the same model parameters could be supposed to have equal errors theoretcally, meanng Δl m ¼ Δ^l m for m ¼ 1 3, Δa ¼ Δ^a, Δα ¼ Δ^α,and Δd ¼ Δ^d for ¼ 1 6. Due to structural desgn and assembly error, there s an artculaton angle error between the ndcaton and true angle. As the extrnsc parameters, the same artculaton Fg. 8 Sngle pont repeatablty under the two modes of the adjustable AACMM for the 88 ponts. Optcal Engneerng December 2014 Vol. 53(12)

Zhu et al.: Coordnate measurng method wth two operaton modes... maxmum sngle pont repeatablty of the all-free AACMM s 0.5342 mm, whle the maxmum sngle pont repeatablty of the partally bound AACMM s 0.

6 Zhu et al.: Coordnate measurng method wth two operaton modes... maxmum sngle pont repeatablty of the all-free AACMM s mm, whle the maxmum sngle pont repeatablty of the partally bound AACMM s mm. Therefore, the sngle pont repeatablty of the partally bound AACMM s mproved by about 10 tmes that of the all-free AACMM n the local space. Fg. 9 Length measurement error under the two modes of the adjustable AACMM for 100 dstances. 4.2 Measurement Precson Test To llustrate the mprovement n precson from the all-free AACMM to the partally bound AACMM, precson tests for sngle pont repeatablty and length measurement precson are performed through numercal smulaton. Under the partally bound operaton mode, artculatons 1 and 2 are fxed at the angles of 0 and 60 deg, respectvely. Under the all-free operaton mode, all sx artculatons can rotate freely. Table 1 shows the parameters and ther errors to be set n smulaton. A set of 88 ponts are tested under these two modes, respectvely, and each pont s measured by 50 dfferent sets of artculaton orentatons. As shown n Fg. 7, these 88 ponts le n a local space of 1 1 1m Sngle pont repeatablty test After the adjustable AACMM s calbrated by the method presented n Ref. 13, the sngle pont repeatablty of each test pont s defned as rffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff P n¼1 ½ðx σ ¼ 2 xþ 2 þðy ȳþ 2 þðz zþ 2 Š : (6) n 1 For our work, n s equal to 50. Fgure 8 shows the sngle pont repeatablty errors of the 88 ponts calculated based on the calbrated partally bound and all-free AACMM. The Length measurement precson test Centerng on the dstance between any two ponts of the above 88 ponts, the length measurement error s defned as rffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff P n¼1 ðd RMS ¼ 2 DÞ 2 ; (7) n where d s the dstance between two ponts by the th measurement, D s the true value dstance between these two ponts, and n ¼ 50. The length test performed over the 3828 dstances of the 88 ponts n the local space shows that the maxmum length measurement error of the all-free and partally bound AACMM s and mm, respectvely. Fgure 9 shows the length measurement error under the two modes of the adjustable AACMM for any 100 dstances chosen from the 3828 dstances. The length measurement precson of the partally bound AACMM s mproved by about seven tmes compared to that of the all-free AACMM n the local space. Addtonally, the length measurement error of the longer dstance s not meant to be bgger. Accordng to prevous research, 10,11 the dstrbuton of the length error n the AACMM s nonlnear and related to the artculaton orentaton. 5 Concluson In ths paper, a coordnate measurng method wth two operaton modes based on the adjustable artculated arms s proposed. The adjustable AACMM wth two electromagnetc lockng devces can automatcally swtch between the allfree artculated arms and the partally bound artculated arms operaton mode. In the all-free artculated arms mode, three arms and sx artculatons can rotate freely n global space. In the partally bound artculated arms mode, the front two artculatons are locked to decrease the mport of angle errors. A mathematcal model for the adjustable AACMM s also bult n ths paper. Theoretcal analyss and numercal smulaton show that the partally bound artculated arm coordnate measurng machne s more precse than the all-free one n the local space. Therefore, the proposed coordnate measurng method based on the adjustable artculated arms s verfed as beng effectve. Future work wll be Table 1 Smulaton parameters and ther errors of the adjustable AACMM. Smulaton parameters Errors of smulaton parameters d (mm) a (mm) α (deg) l (mm) Optcal Engneerng December 2014 Vol. 53(12)

7 Zhu et al.: Coordnate measurng method wth two operaton modes... conducted on the calbraton and real measurement applcatons of ths prototype. Acknowledgments Ths work was supported by the Natonal Natural Scence Foundaton of PR Chna (Grant Nos and ), the General Program of Scence and Technology Project of Bejng Muncpal Educaton Commsson (No. KM ), and the Program for Changjang Scholars and Innovatve Research Team n Unversty of IRT1212. References 1. J. A. Bosch, Coordnate Measurng Machnes and Systems, Marcel Dekker, Inc., New York (1995). 2. G.-x. Zhang, Development orentatons of coordnate measurng technques [In Chnese], Infrared Laser Eng. 37(S), 1 5 (2008). 3. B. Monsarrat et al., Workspace analyss and optmal desgn of a 3-leg 6-DOF parallel platform mechansm, IEEE Trans. Rob. Autom. 19(6), (2003). 4. K. Furutan et al., Multple degrees-of-freedom arm wth passve jonts for on-the-machne measurement system by calbratng wth geometrc solds, Precs. Eng. 23(2), (1999). 5. P. Carbone, D. Mac, and D. Petr, Measurement uncertanty and metrologcal confrmaton n qualty-orented organzatons, Measurement 34(4), (2003). 6. W. Gao, S. Kyono, and E. Satoh, Precson measurement of mult-degree-of-freedom spndle errors usng two-dmensonal slope sensors, Ann. CIRP 51(1), (2002). 7. H. Hamana et al., Calbraton of artculated arm coordnate measurng machne consderng measurng posture, Int. J. Autom. Technol. 5(2), (2011). 8. J. Santolara et al., Knematc parameter estmaton technque for calbraton and repeatablty mprovement of artculated arm coordnate measurng machnes, Precs. Eng. 32(4), (2008). 9. J. Sładek, K. Ostrowska, and A. Gąska, Modelng and dentfcaton of errors of coordnate measurng arms wth the use of a metrologcal model, Measurement 46(1), (2013). 10. C. Yajun et al., Study on error of ntal poston of mult-jont coordnate measurng machne [In Chnese], Tool Eng. 46(7), (2012). 11. J. Xu et al., The smulaton research of the jont angles error of artculated arm coordnate measurng machne [In Chnese], Manuf. Technol. Mach. Tool 4, (2013). 12. J. Denavt and R. S. Hartenberg, A knematc notaton for lowerpar mechansm based on matrces, Trans. ASME J. Appl. Mech. 77, (1955). 13. L. Zhu et al., Research on parameter self-calbraton method for partly-bonded artculated arm coordnate measurng machne, Chn. J. Sc. Instrum. 35(3), (2014). Lanqng Zhu receved hs master s degree of control scence and engneerng n HeFe Unversty of Technology n 1989 and earned hs PhD degree n Harbn Insttute of Technology n Now, he s a professor at the Bejng Informaton Scence and Technology Unversty. Hs man research nterests focus on bologcal medcne nspecton technology and nstrument, precse optcal-electrcal test technology, and so on. Wexan L receved her bachelor s degree and PhD degree of precson nstrument and machnery n Behang Unversty n 2007 and 2013, respectvely. Now, she s a lecturer at Bejng Informaton Scence and Technology Unversty. Her man research nterests focus on machne vson, optcal-electrcal test technology, and so on. Zhkang Pan receved hs master s degree n technology and nstrument measurement from Bejng Insttute of Technology n 2003, and now he s a lecturer at Bejng Informaton Scence and Technology Unversty. Hs man research nterests focus on precse optcalelectrcal test technology. Yangkuan Guo receved hs PhD degree of nstrument scence and technology n Tsnghua Unversty n Now, he s a professor at Bejng Informaton Scence and Technology Unversty. Hs man research nterests focus on precse optcal-electrcal test technology and so on. Qngshan Chen receved hs PhD degree of physcal electroncs from Bejng Unversty of Posts and Telecommuncatons n Now, he s a senor engneer at Bejng Informaton Scence and Technology Unversty. Hs man research nterests focus on precse optcalelectrcal test technology and so on. Optcal Engneerng December 2014 Vol. 53(12)

Quick error verification of portable coordinate measuring arm

Quick error verification of portable coordinate measuring arm 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 [] 7-8-99