Conceptual Design and Workspace Analysis of an Exechon-inspired Parallel Kinematic Machine

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1 Conceptual Desgn and Workspace Analyss of an Exechon-nspred Parallel Knematc Machne Tang, T., Zhao, Y., Jun, Z., & Jn, Y. (2015). Conceptual Desgn and Workspace Analyss of an Exechonnspred Parallel Knematc Machne. Paper presented at 3rd IEEE/IFToMM Internatonal Conference on Reconfgurable Mechansms and Robots, Bejng, Chna. Document Verson: Early verson, also known as pre-prnt Queen's Unversty Belfast - Research Portal: Lnk to publcaton record n Queen's Unversty Belfast Research Portal Publsher rghts 2015 The Authors General rghts Copyrght for the publcatons made accessble va the Queen's Unversty Belfast Research Portal s retaned by the author(s) and / or other copyrght owners and t s a condton of accessng these publcatons that users recognse and abde by the legal requrements assocated wth these rghts. Take down polcy The Research Portal s Queen's nsttutonal repostory that provdes access to Queen's research output. Every effort has been made to ensure that content n the Research Portal does not nfrnge any person's rghts, or applcable UK laws. If you dscover content n the Research Portal that you beleve breaches copyrght or volates any law, please contact openaccess@qub.ac.uk. Download date:13. Nov. 2018

2 Conceptual Desgn and Workspace Analyss of an Exechon-nspred Parallel Knematc Machne Tang Tengfe 1, Zhao Yanqn 2, Zhang Jun 3,* and Jn Yan 4 1 School of Mechancal Engneerng, Anhu Unversty of Technology, Ma'anshan , Chna, e-mal:tengfe413zm@163.com 2 School of Mechancal Engneerng, Anhu Unversty of Technology, Ma'anshan , Chna, e-mal: zhaoyanqn_91@163.com 3 School of Mechancal Engneerng, Anhu Unversty of Technology, Ma'anshan , Chna, emal: zhang_jun_81@163.com, Correspondng author 4 School of Mechancal and Aerospace Engneerng, Queen s Unversty Belfast, BT9 5HN, Northern Ireland, UK, emal: y.jn@qub.ac.uk Abstract Inspred by the commercal applcaton of the Exechon machne, ths paper proposed a novel parallel knematc machne (PKM) named Exe-Varant. By exchangng the sequence of knematc pars n each lmb of the Exechon machne, the Exe-Varant PKM clams an arrangement of 2UPR/1SPR topology and conssts of two dentcal UPR lmbs and one SPR lmb. The nverse knematcs of the 2UPR/1SPR parallel mechansm was frstly analyzed based on whch a conceptual desgn of the Exe-Varant was carred out. Then an algorthm of reachable workspace searchng for the Exe-Varant and the Exchon was proposed. Fnally, the workspaces of two example systems of the Exechon and the Exe-Varant wth approxmate dmensons were numercally smulated and compared. The comparson shows that the Exe-Varant possesses a compettve workspace wth the Exechon machne, ndcatng t can be used as a promsng reconfgurable module n a hybrd 5-DOF machne tool system. Keywords parallel knematc machne; Exechon; knematcs; workspace

3 1 Introducton Machne tool manufacturers are facng global compettveness characterzed by large fluctuaton n product demands and ncreasng product varetes n recent years [1]. To survve n ths aggressve envronment, the machnng systems and/or facltes are requred to possess reconfgurable ablty [2]. Thanks to the merts of hgh rgdty and dynamcs as well as good flexblty and reconfgurablty, the parallel knematc machnes (PKMs) have found ther compromsng applcatons n aeronautc and automoble ndustres. Ths can be best exemplfed by the 5-DOF Trcept and Exechon wth seral-parallel archtecture. Accordng to the publc reportng, varous versons of the Trcept have been ntegrated as a plug-and-play module n machne tools and/or robots [3-7]. As a newly nvented 5-DOF PKM, the Exechon machne has been expermentally proven to be compettve n terms of accuracy, relablty, and operaton speed [8-12]. Although extensve research and applcaton actvtes have been carred out on the Exechon [13-15], lttle attenton has been pad to ts reconfgurable verson. Generally speakng, a reconfgurable PKM module can be realzed through the reconfgurablty of knematc chans at the component level [16-19]. The basc deal of achevng such reconfgurablty s to use the combnaton of a set of readly made lmbs that enable the formaton of PKM wth specfed types and DOF. Followng ths track, a new reconfgurable PKM named Exe-varant s proposed by exchangng the sequence of knematc pars n each lmb of Exechon machne. To be specfc, ths Exechon-nspred PKM clams an arrangement of 2UPR/1SPR topology and conssts of two dentcal UPR lmbs and one SPR lmb. The remnder of the paper s organzed as follows. The nverse knematcs and conceptual desgn of the Exe-Varant are brefly descrbed n secton 2. In secton 3, an algorthm of reachable workspace searchng s proposed and the workspaces of two example systems of Exechon and Exe-Varant wth approxmate dmensons are numercally smulated and compared. At last, some conclusons are drawn n secton 4.

4 2 Inverse Knematcs and Conceptual Desgn 2.1 Inverse Knematcs From the topologcal pont of vew, the parallel knematc part of the Exechon machne s a 2RPU/1RPS parallel mechansm whle that of the Exe-Varant s a 2UPR/1SPR parallel mechansm. The schematc dagrams of the two parallel mechansms are depcted n Fg. 1. As the knematc analyss of the Exechon can be referred to our prevous paper [9], the followng wll only explore the nverse knematcs of the Exe-Varant. d s 1 1 B 1 z 1 x 1 b 10 y 1 r w r p B u v B 3 B 2 q w 1 1 A 1 a 10 r w r a A u A 3 v A 2 A 1 a 1 z A y A 2 B 1 b 1 z B y B 2 C 1 x C 2 C 1 x C 3 r b r b A 3 B 3 C 3 C 2 (a) Fg. 1 Schematc dagrams of (a) Exechon; (b) Exe-Varant (b) As shown n Fg. 1 (b), B (=1, 2, 3) represents the center of R jont. A (=1, 2) denotes the center of U jont and A 3 s the center of S jont. For the convenence of dervaton, some reference frames need to be defne at the frst place. A global coordnate frame B-xyz s fxed at the center of B 1 B 2, wth x axs parallelng to BB 3, y axs parallelng to B 1 B 2, whle z axs s determned by the rght hand rule. Smlarly, a movng coordnate frame A-uvw s assgned to the movng platform, wth the u axs parallelng to AA 3, v axs parallelng to A 1 A 2. r a and r b represent the crcumcrcle rad of the movng platform and the fxed base, respectvely.

5 Assume the transformaton matrx of A-uvw wth respect to B-xyz can be expressed as cc css sc cs c ss R sc sss cc ss c cs (1) s s c cc where s and c denote sn and cos functons, respectvely;, and φ are Euler angles n terms of precesson, nutaton and rotaton. The vector of pont A measured n B-xyz can be expressed as a = Ra + r = b + q w (2) 0 where a denotes the poston vector of pont A 0 n the frame A-uvw; r represents the poston of pont A n the frame B-xyz; b denotes the vector of pont B n the frame B-xyz; q and w represent the dstance between A and B and unt vector of the th lmb. And there exst a = r, b rcos sn T, 0 x, y, z T where a 0 cos sn 0 T b r= (3) denotes the poston angle, and 1 /2, 2 /2, 3 0. Takng z, θ and as ndependent coordnates and consderng the constraned condtons arsen by R jonts, one can obtan the parastc moton of the Exe-Varant x= 0 y = ra snφcosθ (4) = arctan tan / snθ Substtutng Eq. (4) nto Eq. (2), the nverse knematc can be solved q a b a b, w = (5) q 2.2 Conceptual Desgn In ths subsecton, the conceptual desgn for the Exe-Varant s carred out at the nspraton of that of Exechon machne. As shown n Fg. 2(a), the Exechon machne s a hybrd PKM, whch conssts of a parallel structure to locate the poston of the movng platform and a seral structure to orent the machnng tool. The movng platform s supported by three lmbs denoted as lmb 1, lmb 2, and lmb 3, respectvely. At the home poston, lmb 1 and lmb 2 are symmetrcal wth

respect to lmb 3. Lmb 1 (lmb 2) connects the base to the movng platform by a unversal (U) jont, a prsmatc (P) jont and a revolute (R) jont n sequence.

fxed base lmb 1 lmb 2 U jont fxed base lmb 2 R jont R jont lmb 1 lmb 3 lmb 3 U jont spndle movng platform spndle movng platform (a) (b) Fg.

Fg. 2(b). Heren, Lmb 1 (and lmb 2) connects the fxed base to the movng platform by a revolute (R) jont, a prsmatc (P) jont and a unversal (U) jont n sequence.

6 respect to lmb 3. Lmb 1 (lmb 2) connects the base to the movng platform by a unversal (U) jont, a prsmatc (P) jont and a revolute (R) jont n sequence. Lmb 3 s slghtly dfferent from lmb 1 and lmb 2 n that t s allowed to spn by tself. fxed base lmb 1 lmb 2 U jont fxed base lmb 2 R jont R jont lmb 1 lmb 3 lmb 3 U jont spndle movng platform spndle movng platform (a) (b) Fg. 2 Conceptual desgn of (a) Exechon; (b) Exe-Varant By exchangng the sequence of knematc pars n each lmb of the Exechon, a conceptual desgn of the Exe-Varant can be completed and presented n Fg. 2(b). Heren, Lmb 1 (and lmb 2) connects the fxed base to the movng platform by a revolute (R) jont, a prsmatc (P) jont and a unversal (U) jont n sequence. Lmb 3 connects the fxed base to the movng platform by a revolute (R) jont, a prsmatc (P) jont and a sphercal (S) jont n sequence. In order to mprove the reconfgurablty and enhance the rgdty, the structure of the lmb especally the jonts should be delcately desgned. For nstance, a potental desgn of the lmb structure n Exechon and Exe-Varant are compared as shown n Fg. 3. lead screw U/S jont R jont slder servomotor

7 lead screw (a) R jont servomotor U/S jont slder (b) Fg. 3 Structural desgn of lmb (a) Exechon; (b) Exe-Varant 3 Workspace Analyses Workspace s one of the most mportant performance ndces of parallel mechansms reflectng ther poston-orentaton capabltes. In ths secton, an algorthm s proposed to search the reachable workspace for the Exe-Varant whch s then compared wth that of the Exechon wth approxmate dmensons. To facltate the comparson, the orgn of the movng coordnate system s set as the reference pont n ths paper. The basc dea s slce the workspace nto dscrete peces of work plane and then partton the work plane nto grds wth dfferent orentaton angles. When the three ndependent coordnates are gven, the dstance between two jonts A and B n an ndvdual lmb and rotaton angles of lmbs can be calculated through the nverse knematcs as demonstrated n Eq. (5). Then the obtaned analytcal values are compared to the correspondng allowable values of jonts. If the analytcal values are less than the allowable ones, the gven ndependent coordnates are wthn the reachable workspace of the movng platform. Otherwse, they are beyond the reachable workspace. The detaled process for the reachable workspace search s shown n the Fg. 4. For the convenence of comparson, parameters of the Exechon and Exe-Varant example systems are set to be approxmate as shown n Table 1. Heren, q mn and q max denote the mnmum and maxmum dstance between the two jonts n an ndvdual lmb; θ S, θ U and θ R denote the allowable rotaton angles of S jont, U jont and R jont, respectvely.

8 start parameter ntalzaton = +1 =0 z= z + z 0 j= j+1 z z z mn Y j=0 max N = 0+j N mn max Y k=0 k= k+1 = 0+k N mn max Y nverse knematcs d d d, mn max max N Y output z,θ,φ workspace mappng end Fg. 4 Procedure of searchng for the reachable workspace

9 Table 1 Dmensonal parameters of the module. r a r b q mn q max θ S θ U θ R 0.34 m 0.45 m 0.8 m 1.5 m The reachable workspace of the Exechon and the Exe-Varant s depcted n Fg. 5. One can fnd that the reachable workspace of Exechon decreases monotonously wth the ncrement of z, whle that of Exe-Varant s very dfferent n that t ncreases frstly wth the ncrement of z, then almost keeps unchanged and at last decreases wth the ncrement of z. Further calculaton reveals that there are 9659 and 9563 feasble ponts wthn the reachable workspace of the Exechon and the Exe-Varant, respectvely. Ths ndcates that the Exe-Varant possess a compettve reachable workspace wth the Exechon. From the perspectve of orentaton ablty, the Exe-Varant seems to own a better performance than that of the Exechon. z(m) () () z(m) () () (a) Fg. 5 Reachable workspace (a) for Exechon; (b) for Exe-Varant (b) In order to clarfy the orentaton characterstcs of the reachable workspace, the cross-secton of the Exechon and the Exe-Varant at the work plane of z=1.2 m are demonstrated and compared n Fg. 6. Clearly, t can be found that the cross-secton s symmetrc about the lne 0for the two PKMs, whch s concdent wth ther structure features that lmb 1 and lmb 2 are symmetrc about

10 lmb 3. As can be seen, the Exe-Varant demonstrates a larger cross-secton area at ths work plane, ndcatng a better reachable ablty () () () () (a) (b) Fg. 6 Cross-secton of reachable work plane when z=1.2 m: (a) Exechon; (b) Exe-Varant 4 Conclusons To summarze the contrbutons of ths paper, the followng conclusons can be drawn. (1) A conceptual desgn of a new confgurable module s proposed at the nspraton of the Exechon machne by exchangng the sequence of knematc pars n each lmb. (2) A knematc model of the Exe-Varant s establshed wth whch the nverse poston analyss of the PKM s derved. (3) An algorthm s presented to numercally predct the reachable workspace of Exe-Varant and compared wth that of the Exechon PKM. The comparson between the two PKMs ndcates that the proposed Exe-Varant possesses a compettve workspace wth the Exechon. (4) Further nvestgatons on the sngularty analyss, stffness formulaton and structural enhancement wll be carred out n the next step followed by vrtual prototype valdatons.

11 Acknowledgement Ths work was jontly supported by Open Research Fund of Key Laboratory of Hgh Performance Complex Manufacturng (Central South Unversty) wth Grant No. Kfkt , Open Fund of Shangha Key Laboratory of Dgtal Manufacture for Thn-walled Structures wth Grant No and Open Fund of State Key Laboratory for Manufacturng Systems Engneerng(X an Jaotong Unversty) wth Grant No. sklms The forth author would lke to acknowledge for the fundng support from Engneerng and Physcal Scence Research Councl (EPSRC, ref. EP/K004964/1) of Unted Kngdom and Investment Northern Ireland PKAAA project. References 1. Koren, Y., Hu, S. J., Weber, T. W.: Impact of manufacturng system confguraton on performance. CIRP Annals-Manufacturng Technology 47(1), pp (1998) 2. L, M., Huang, T., Zhang, D., et al.: Conceptual desgn and dmensonal synthess of a reconfgurable hybrd robot. Journal of manufacturng scence and engneerng, 127(3), pp (2005) 3. Landers, R. G., Mn, B. K. and Koren, Y.: Reconfgurable Machne Tools. CIRPAnn. 50(1), pp (2001) 4. Unsay, C., Klccote, H., and Khosla: A 3-D Modular Self Reconfgurable Bpartte Robotc System: Implementaton and Moton Plannng. Auton. Rob. 10(1), pp (2001) 5. Neumann, K.-E.: "Trcept Applcatons," Proc. 3rd Chemntz Parallel Knematc Semnar, Verlag Wssenschafrlche Scrpten, Zwckau, Germany, PP (2002) 6. Neumann, K, E.: System and method for controllng a robot. U.S. Patent 6,301, 525(2001) 7. Caccavale, F., Sclano B., Vllan, L.: The Trcept robot: dynamcs and mpedance control. Mechatroncs, IEEE/ASME Transactons on, 8(2) pp (2003) 8. Huang, T., Wang, P.F., Zhao, X.M., et al: Desgn of a 4-DOF hybrd PKM module for large structural component assembly. CIRP Annals-Manufacturng Technology, 59(1): (1999)

12 9. Huang, T., Lu, H.-T., L, M., Zhao, X.-M., and Me, J.-P.: A 5-DOF Hybrd Robot wth Redundant DOF. CN Patent, No. CN (2006) 10. B. Z. M.: Knetostatc modelng of Exechon parallel knematc machne for stffness analyss.internatonal Journal of Advanced Manufacturng Technology, pp (2014) 11. Neumann, K. E.: Exechon concept. Parallel Knematc Machnes n Research and Practce, 33, pp (2006) 12. Zopp, M., Zlatanov, D., Molfno, R.: Knematcs analyss of the Exechon trpod[c]//asme 2010 Internatonal Desgn Engneerng Techncal Conferences and Computers and Informaton n Engneerng Conference. Amercan Socety of Mechancal Engneers, pp (2010) 13. B. Z.M., Jn, Y.: Knematc modelng of Exechon parallel knematc machne. Robotcs and Computer-Integrated Manufacturng, pp (2011) 14. Neu, Mann K-E: Adaptve Exechon machnng &assembly technology. SAE Internatonal, Paper No. 08AMT-0044(2008) 15. Chang, T.-H., Inasak, L, Morhara, K., and Hsu, J.-J.: The development of a parallel mechansm of 5-dof hybrd machne tool. In PKM Internatonal Conference, Ann Arbour, Mchgan, pp (2000) 16. Wang, Z., Wang, Y.B., L, J. et al: Performance analyss and comparson of three knds of confguratons for 3-R//R//C parallel mechansms. Proceedngs of 2014 IFToMM Asan Conference on Mechansm and Machne Scence, Tanjn, Chna (2014) 17. B. Z.M., Lang, S.Y.T., Shen, W. M.: Reconfgurable manufacturng systems: the state of the art. Internatonal Journal of Producton Research, 46(4) pp (2008) 18. B. Z.M., Wang, L. In: Lhu Wang, Jeff Xe, edtors: Desgn of a reconfgurable trpod machne system and ts applcaton n web-based machnng, n smart devces and machnes for advanced manufacturng. Sprnger: Olazagota, J.L., Wyatt, S.: New PKM Trcept T9000 and ts applcaton to flexble manufacturng at aerospace ndustry. SAE Internatonal Paper No. 07ATC-94 (2007)

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