DEXTERITY INDICES OF 6-UPS PARALLEL MANIPULATOR

Transcription

1 Internatonal Journal of Mechancal Engneerng and echnology (IJME) Volume 6, Issue 12, Dec 2015, pp , Artcle ID: IJME_06_12_001 Avalable onlne at ISSN Prnt: and ISSN Onlne: IAEME Publcaton DEXERIY INDICES OF 6-UPS PARALLEL MANIPULAOR Sr Rama Jayakrshna Dept of Mechancal Engneerng, Holy Mary Insttute of echnology and Scence, Kesar, R.R Dst, elangana State, Inda G. Satsh Babu Professor, Dept of Mechancal Engneerng, JNUH College of Engneerng Hyderabad, elangana State, Inda ABSRAC he performance evaluaton s one of most mportant ssues n the analyss and desgn of parallel manpulators. Characterstcs such as manpulablty and mnmum sngular value are used to determne the performance of the manpulators. he performance ndces are used to elmnate the sngularty and t s near confguratons. In ths paper 6-UPS spatal parallel manpulator s consdered and ts performance ndces such as condton number, manpulablty and mnmum sngular value are determned for dfferent structures. Based on the performance ndces, the optmum confguraton of the manpulator s determned. A MALAB code s developed and used for the analyss. he results are graphcally presented. Key words: Performance Index, Manpulablty, Mnmum Sngular Value. Cte ths Artcle: Sr Rama Jayakrshna and G. Satsh Babu. Dexterty Indces of 6-UPS Parallel Manpulator, Internatonal Journal of Mechancal Engneerng and echnology, 6(12), 2015, pp INRODUCION Pareds and Khosla (1) proposed a way to deal wth llumnate the knematc outlne of a non repettve controller wth jont confnes that can acheve an arrangement of determned focuses wth requred ntroductons. he ssue was ntally detaled by them numercally by utlzng the dea of the knematc hyper surface. hey have utlzed a worldwde mprovement system to mnmze the punshment of a controller outlne whch results n an deal knematc arrangement. Ro and Lee (2) proposed a get together way calculaton for male and female parts utlzng just vertces of the male and female parts when ther startng and objectve poston are known. A calculaton for the deal poston for two-arm fxtureless get together n the workspace s proposed by them. Stance enhancement of two-arm 1 edtor@aeme.com

2 Sr Rama Jayakrshna And G. Satsh Babu controller for fxtureless usng so as to gather was concentrated on by them the executon fles, manpulablty and calculablty fle. Sngh and Rastegar (3) presented the new dea, the worldwde speed ellpsod, whch speaks to the worldwde movement manpulablty or the speed transmsson qualtes of a controller. he worldwde speed ellpsod s acqured by consderng a weghted dsperson of the end-effector poston over the workspace of the controller. Parameters speakng to the worldwde sotropy and the worldwde sze of the speed transmsson of controllers are utlzed for breakng down and enhancng the knematc structure of controllers. he expanson of ths dea to drve transmsson attrbutes and ts usage for mnmzng mstake engenderng and mprovng precson, assgnment poston and arrangng are talked about by them. Krcansk (4) amplfed the system for typcal SVD n vew of Jacoban deteroraton s stretched out to straghtforward excess controller. he Jacoban s communcated n one of the moderate drecton casngs to get the least complex typcal expressons. General relatons are bult up by hm between the SVD of frameworks J and JJ that apply to any excess robot. He lkewse examned the utlzaton of the proposed strategy for takng care of the converse knematc ssue on low-level poston or constran control calculatons on undertakng drectons. Krcansk (5) decded all the sotropc desgns of planar controllers wth two, three and four degrees of opportunty and 3 DOF spatal controller. he arrangements are gotten as polynomals. he condton numbers are acqured as express nvestgatve elements of jont facltates and connecton length proportons. Gosseln, Lemeux and Merlet (6) proposed and broke down a novel structural plannng of planar 3-DOF parallel controller. hey have determned the stuatng and speed mathematcal statements. he component examned by them can be utlzed as a part of superor automated applcatons, for example, a planar stuatng and ntroducton gadget or vehcle movement test systems. Chablat and Wenger (7) characterzed the movement of angle for parallel controllers wth dfferent converse and drect knematc arrangements. hey have dscovered areas of the workspace and jont space wthout sngulartes. hs strategy can be utlzed to study the moveablty nvestgaton n the workspace of the controller and addtonally way arrangng and control. Stucco, Salcudean and Sassan (8) exhbted another confguraton grd standardzaton strategy to handle the ssue of non homogeneous physcal unts. he undertakng space scale varables are utlzed to set relatve requred qualty or velocty along any tomahawks of end-pont movement whle the jont space scale elements are dealt wth as free outlne parameters to enhance sotropy through non homogeneous actvaton. anev and Stoyanov (9) connected the executon lsts, the smoothness record, manpulablty, condton number and least soltary qualty to a SCARA sort robot and thnk about the lsts. Xn-Jun Ln et al (10) proposed another spatal three-degrees-ofopportunty parallel controller. he lsts to assess the rotatonal capacty of the movng stage of the controller are characterzed and topology buldng desgn of the controller s presented by them. Xn-Jun Lu et al (11) utlzed the assessment crtera, for example, the moldng record, the frmness to choose the connecton lengths of 3-DOF crcular parallel controllers and broke down ther operatonal executon. he chart books of the 2 edtor@aeme.com

3 Dexterty Indces of 6-UPS Parallel Manpulator worldwde moldng fle and the worldwde soldness record are acqured to mprove connecton lengths of 3-DOF SPMS. MEASURES OF KINEMAIC PERFORMANCE Manpulablty he concept of manpulablty of a manpulator was ntroduced by yoshkawa. he manpulablty s defned as the square root of the determnant of the product of the manpulator jacoban by ts transpose,.e, w det( JJ ) he manpulablty w s equal to the absolute value of the determnant of the jacoban n case of a square jacoban. Usng the sngular value decomposton the manpulablty can be wrtten as follows: w ( ) Where are the sngular values of the jacoban matrx J. Mnmum sngular value he mnmum sngular value changes more radcally near sngulartes than the other sngular values. hs suggests that the mnmum sngular value tself can be used as a measure of dexterty. hus the mnmum sngular value drectly shows stuatons where excessve jont veloctes would be requred, whch s a characterstcs of nearness to sngulartes. he mnmum sngular value of the jacoban matrx of the parallel manpulator s consdered as a measure of performance. 6-UPS PARALLEL MANIPULAOR Fgure 1 Knematc model of 6-UPS Parallel manpulator 3 edtor@aeme.com

4 Sr Rama Jayakrshna And G. Satsh Babu he 6 UPS parallel manpulator shown n fg.1 conssts of a fxed platform and movng platform connected by sx dentcal lmbs. he reference frame attached to the fxed platform s O s -x s,y s,z s. and the frame O p -x p,y p,z p s attached to the the movng platform. he dstances between the jonts n movng and fxed platforms are: Fxed Platform: O 1 O 2 =O 3 O 4 =O 5 O 6 = a 1 O 2 O 3 =O 4 O 5 =O 6 O 1 =a 2 Movng Platform: P 1 P 2 =P 3 P 4 =P 5 P 6 = b 1 P 2 P 3 =P 4 P 5 =P 6 P 1 = b 2 Optmal Desgn of 6-UPS Parallel Manpulator usng Performance Indces Jacoban Analyss he nstantaneous twst, P, of the movng platform can be expressed as where for = 1,2..6 1, s1, ( b d ) s 1, 2, s2, ( b d ) s 2, 0 3, s3, 4, 5, s4, b s s5, b s 4, 5, 6, s6, b s 6, Where s j, s a unt vector along the j th jont axs of the th lmb, b PB and d AB d S 3, 3, 4 edtor@aeme.com

5 Dexterty Indces of 6-UPS Parallel Manpulator he recprocal screw, denoted as r,1, s pontng n a drecton perpendcular to the jont axes of the unversal jont. 0 r,1, n 0 r,1, Where J C 0 P J c n n n n n n Recprocal to all passve jont screws of the th lmb can be dentfed as zero ptch screw along the lne passng through the two unversal jonts Where J ( b s ) s ( b s ) s ( b s ) s ( b s ) s ( b s ) s 1 3,1 3,1 2 3,2 3,2 3 3,3 3,3 x ( b4 s3,4 ) s 3,4 5 3,5 3,5 6 3,6 3,6 5 edtor@aeme.com

6 Sr Rama Jayakrshna And G. Satsh Babu Where J ( b s ) s ( b s ) s n 0 n ,1 3,1 6 3,6 3, RESULS Usng Matlab the followng results have been obtaned for 6 UPS spatal manpulators. he results regardng optmum structures based on the performance ndces were dentfed have been presented n ths secton. Fgure 2 manpulablty vs reach 6 edtor@aeme.com

7 Dexterty Indces of 6-UPS Parallel Manpulator Fgure 3 mnmum sngular value Vs reach CONCLUSION he 6-UPS parallel manpulator has been analyzed for ts performance ndces. Based on the performance ndces, the optmum confguratons are dentfed. All the obtaned results for the performance ndces are graphcally plotted. REFERENCES [1] Chrstaan J.J. Pareds and Pradeep K. Khosla. Knematc Desgn of Seral Lnk Manpulators from ask Specfcatons, he Internatonal Journal of Robotcs Research, Vol. 12, No. 3, pp , June [2] Paul I. Ro and Byung R. Lee. An Optmum Path and Posture Plannng for Fxtureless Assembly, IEEE, Proc. Int. Conf. Adv. Robot., pp (1993). [3] J.R. Sngh and J. Rastegar. Optmal Synthess of Robot Manpulators Based on Global Knematc Parameters, Mechansm and Machne heory, Vol. 30, No. 4, pp (1995). [4] ManjaKrcansk. Symbolc Sngular Value Decomposton for Smple Redundant Manpulators and ts Applcaton to Robot Control, he Internatonal Journal of Robotcs Research, Vol. 14, No. 4, pp , August [5] ManjaKrcansk. Knematc Isotropy and Optmal Knematc Desgn of Planar Manpulators and a 3-DOF Spatal Manpulator, he Internatonal Journal of Robotcs Research, Vol. 15, No. 1, pp 61-77, Feb [6] Clement M. Gosseln et al. A new archtecture of planar three-degree-offreedom parallel manpulator, IEEE, proc. Int. Conf. Robotcs and Automaton, pp , Mnneapols, Mnnesota, Aprl [7] Damen Chablat and Phlppe Wenger. Workng modes and aspects n fully parallel manpulators, IEEE Proc. Int. Conf. Adv. Robot., pp (1998). [8] Leo J. Stocco et al. On the Use of Scalng Matrces for ask-specfc Robot Desgn, IEEE rans. Robotcs and Automaton, Vol. 15, No. 5, October [9] anoanev and BogdanStoyanov. On the performance Indexes for Robot Manpulators, Journal of Bulgaran Academy of scences, Problems of Engneerng Cybernetcs and Robotcs 49, pp (2000). 7 edtor@aeme.com

8 Sr Rama Jayakrshna And G. Satsh Babu [10] Xn-Jun Lu et al. On the Analyss of a New Spatal hree-degrees-of-freedom Parallel Manpulator, IEEE rans. on Robotcs and Automaton, Vol. 17, No. 6, pp , December [11] A. Chandrashekhar and G. Satsh Babu, Force Isotropy of hree-lmb Spatal Parallel Manpulator. Internatonal Journal of Mechancal and Engneerng echnology 6(6), 2015, pp [12] Xn-Jn Lu et al. Optmum desgn of 3-dof sphercal parallel manpulators wth respect to the condtonng and stffness ndces, mechansm and machne theory 35, pp (2000). 8 edtor@aeme.com