Mechanisms (機構學) - StudyLib

For instance, a pin-in-a-slot joint may become a combination of a revolute ... equation) – n: the number of links M 桿件之自由度 接頭所造成之拘束度j – j: ... Studylib Documents Flashcards Chromeextension Login Uploaddocument Createflashcards × Login Flashcards Collections Documents Lastactivity Mydocuments Saveddocuments Profile Addto... Addtocollection(s) Addtosaved Science Physics Mechanics Mechanisms(機構學) advertisement 機構學 Mechanisms(機構學) 原名: 原名:機動學, 機動學,即機械運動學( 即機械運動學(kinematics)之簡稱 kinematics)之簡稱 Text: K.J.WaldronandG.L.Kinzel,2004,Kinematics, Dynamics,andDesignofMachinery, Machinery2nded.,JohnWiley &Sons.(歐亞) Reference: 1.顏鴻森,機構學,東華書局. 2.G.Bögelsack,F.J.Gierse,V.Oravsky,J.M.Prentis, andA.Rossi,1983,TerminologyfortheTheoryof MachinesandMechanisms,PergamonPress. C.F.Chang,KUASME 1 Contents  BasicConcepts:(基本觀念) –Chapter1Introduction  Linkages:(連桿組,連桿機構) –Chapter2GraphicalPosition,Velocity,andAccelerationAnalysis forMechanismswithRevoluteJointsofFixedSlides –Chapter3LinkageswithRollingandSlidingContactsandJointson MovingSliders –Chapter4InstantCentersofVelocity –Chapter5AnalyticalLinkageAnalysis  CamandGears:(凸輪和齒輪) – – – –  Chapter8ProfileCamDesign Chapter10SpurGears Chapter11Helical,Bevel,andWormGears Chapter12GearTrains Wewillfocusontheso-called“ PlanarMotion” —Motionoflinks whosepointsdescribecurveslocatedinparallelplanes.[桿件上 各點之運動皆在同一平面或其平行平面上] C.F.Chang,KUASME 國立高雄應用科大機械系 2 1 機構學 Chapter1.Introduction Definition ofMechanisms –Mechanismsareassemblagesofrigid memberconnectedtogetherbyjoints.(p.3) –(機構係由機件與接頭所構成之可動組合) C.F.Chang,KUASME 3 MechanismVsMachine Links Joints   Constrained Constrained motion? motion? mechanism Power Mechanisms Mechanismstransfer transfermotion motionto to one or more output members oneormoreoutputmembers  Machine Machinetransfer transfermotion motionand and useful usefulwork workto toone oneor ormore more output outputmembers members  (機器為可輸出有用之功的機構) (機器為可輸出有用之功的機構) Controller Output Output effective effective work? work?     Constrained Constrainedmotion: motion: (各機件皆產生確切且可預期之運動) (各機件皆產生確切且可預期之運動) machine C.F.Chang,KUASME 國立高雄應用科大機械系 4 2 機構學 TerminologyForMMT  Kinematicchain[運動鏈] –Assemblageoflinksandjoints.  Mechanism[機構] –Kinematicchainwithoneofitscomponents(link orjoint)connectedtotheframeandwithdefinite motion 具有確切運動且至少有一桿固連於機架之運動鏈 –Systemofbodiesdesignedtoconvertmotionsof andforcesononeorseveralbodiesinto constrainedmotionsofandforcesonotherbodies (MMT) 一支或多支桿件之運動和受力轉換為其他桿件之拘 束運動和受力  Machine(機器 Machine(機器)) –Deviceperformingmechanicalmotiontotransform andtransferenergy,materialandinformation 是一種執行機械運動的裝置,用來變換和傳遞能量,材料 與資訊 C.F.Chang,KUASME 5 TerminologyForMMT  Link[連桿,機件] 1.Mechanismelement(component)carryingkinematicpairing elements[機構元件,用來帶動以運動對連接之元件] 2.Elementofalinkage.[連桿組之元件]  Joint[接頭] –Thephysicalembodimentofkinematicpair.[運動對之具體化身]  Kinematicpair[運動對] –Contactingelementsoflinkspermittingtheirconstrainedrelative motion.[桿件間之接觸部份,它使桿件之間產生拘束的相對運動] –Lowerpair—Kinematic pairwhichisformedbysurfacecontactof pair itselements.[經由面接觸所構成之可動連接] –Highpair—Kinematic pairwhichisformedbypointorlinecontact pair ofitselements[經由點或線接觸所構成之可動連接] –Connectivity(Degree Connectivity(Degreeoffreedomofajoint): jointthenumberof independentcoordinatesneededtodescribetherelativepositions ofpairingelements[確定兩桿件之相對位置所需之獨立參數的數目] C.F.Chang,KUASME 國立高雄應用科大機械系 6 3 機構學 LowerPairJoints[六種常見之低對接頭] C.F.Chang,KUASME 7 1.RevolutePair(R)[旋轉對]  Name: Revolutehinge 2.turningpair 1.  Lettersymbol: –  R Connectivity(DOF): 1 Dof Dofof ofkinematic kinematicpair pair(connectivity) (connectivity) ==the thenumber numberof ofindependent independent coordinates coordinatesneeded neededto todescribe describethe the relative relativepositions positionsof ofpairing pairing elements elements 接頭之自由度 接頭之自由度==確定兩桿件之相對 確定兩桿件之相對 位置所需之獨立參數的數目 位置所需之獨立參數的數目 C.F.Chang,KUASME 國立高雄應用科大機械系 8 4 機構學 2.PrismaticPair(P)[滑行對]  Name: 1. 2. 3.  Prismaticjoint Slider Slidingpair Lettersymbol: P  Connectivity(DOF): 1 C.F.Chang,KUASME 9 3.HelicalPair(H)[螺旋對]  Name: 1. 2. 3.  Screwjoint Helicaljoint Helicalpair Lettersymbol: H  Connectivity(DOF): 1 C.F.Chang,KUASME 國立高雄應用科大機械系 10 5 機構學 4.CylindricalPair(C)[圓柱對]  Name: CylindricalJoint 2.Cylindricalpair 1.  Lettersymbol: C  Connectivity(DOF): 2 C.F.Chang,KUASME 11 5.SphericalPair(S)[球面對]  Name: 1. 2. 3.  Sphericaljoint Balljoint Sphericalpair Lettersymbol: S  Connectivity(DOF): 3 C.F.Chang,KUASME 國立高雄應用科大機械系 12 6 機構學 6.PlanarPair(R)[平面對]  Name: 1. 2.  Planarjoint Planarpair Lettersymbol: R  Connectivity(DOF): 3 C.F.Chang,KUASME 13 ReplacementofaLowerPairJointbyacombinationofHigherPair PairJoints  Inordertoreducethefrictioninlowerpairjoints,asimplejoint maybereplacedbyakinematicallyequivalentcompoundjoint. Forinstance, C.F.Chang,KUASME 國立高雄應用科大機械系 14 7 機構學 AntifrictionBearings C.F.Chang,KUASME 15 SomeHigherPairJoints C.F.Chang,KUASME 國立高雄應用科大機械系 16 8 機構學 1.CylindricalRoller[圓柱形滾子,滾動對]  Name: 1.Cylindricalroller 2.RollingPair  Connectivity(DOF): 1 C.F.Chang,KUASME 17 2.CamPair[凸輪對]  Name: CamPair  Connectivity(DOF): 2 C.F.Chang,KUASME 國立高雄應用科大機械系 18 9 機構學 3.RollingBall  Name: RollingBall  Connectivity(DOF): 3 C.F.Chang,KUASME 19 4.BallinCylinder  Name: BallinCylinder  Connectivity(DOF): 3+1=4 C.F.Chang,KUASME 國立高雄應用科大機械系 20 10 機構學 5.SpatialPointContact  Name: Spatialpointcontact  Connectivity(DOF): 3+2=5 C.F.Chang,KUASME 21 ReplacementofaHigherPairJointwithLowerPairJoints  Inordertoreducethecontactstressinhigherpairjoints,ajoint maybereplacedbysomekinematicallyequivalentlowerpair joints. Forinstance,apin-in-a-slotjointmaybecomeacombinationof arevolutejointandaprismaticjoint. + C.F.Chang,KUASME 國立高雄應用科大機械系 22 11 機構學 SomeExamplesofCompoundJoints C.F.Chang,KUASME 23 Mechanism&Linkage(p.8)     Alinkageisaclosedkinematicchainwithonelink selectedastheframe. Aframeorbasememberisalinkthatisfixed. Thetermmechanismissomewhatinterchangeable withlinkage. Innormalusage, –mechanismissomewhatmoregenerictermencompassing systemswithhigherpairs,orcombinationsoflowerand higherpairjoints,whereas –thetermlinkagetendstoberestrictedtosystemsthathave onlylowerpairjoints. C.F.Chang,KUASME 國立高雄應用科大機械系 24 12 機構學 PlanarLinkages   Aplanarlinkageisoneinwhichthevelocitiesofall pointsinallmembersaredirectedparalleltoaplane, calledtheplaneofmotion. 機構上各點之速度若皆與運動平面平行,則稱其為平面 機構 C.F.Chang,KUASME 25 RepresentationofLinksandframe  Binarylinks( links(二接頭桿) 二接頭桿) –thosethathavetwojointsmountedonthem  Ternarylinks(三接頭桿) 三接頭桿) –thosethathavethreejointsmountedonthem Slider-cranklinkage  Quaternarylinks(四接頭桿) 四接頭桿) –thosethathavefourjointsmountedonthem C.F.Chang,KUASME 國立高雄應用科大機械系 26 13 機構學 SymbolicDesignationofSingleSingle-LoopLinkages  RRRRLinkage(4R)  RRRPLinkage(3R-P)  RPRPLinkage(2R-2P) C.F.Chang,KUASME 27 VisualizationoftheMotionofLinkages Modelling withwoods,papercards,… Modelling withcomputergraphicssystems C.F.Chang,KUASME 國立高雄應用科大機械系 28 14 機構學 ConstraintAnalysisofPlanarLinkages(pp.1111-18)    Mobility(Degreesoffreedomofalinkage) –Theminimumnumberofcoordinatesneededtospecifythe positionsofallmembersofthemechanism –確定機構各桿件之相對位置所需之獨立參數的數目 Ifthemobilityiszeroornegative,theassemblageisastructure. structure. –Ifthemobilityiszero,thestructureisstaticallydeterminate(靜定結 構) –Ifthemobilityisnegative,thestructureisstaticallyindeterminate (靜不定結構) Themobilityofplanarlinkages:(constraintcriterionequation) –n:thenumberoflinks M桿件之自由度接頭所造成之拘束度 j –j:thenumberofjoints 3(n1)(3fi) i 1 –fi:theconnectivityofjointi(dofofjointi) –thedofalinkwithplanarmotion=3 j M3(nj1)fi i1 C.F.Chang,KUASME 29 DegreeofFreedomofaBody(Link)  Thedofofabodyisthenumberofindependent coordinatesneededtospecifyitsposition –Abodymovingfreelyinaplanehasthreedegreesof freedom.2translation+1rotation –Abodymovingfreelyinspacehassixdegreesoffreedom.3 translation+3rotation(pitch-yaw-roll) C.F.Chang,KUASME 國立高雄應用科大機械系 30 15 機構學 Examples j M3(nj1)fi i1  Mobilityanalysisofaplanarfour-barlinkage  Mobilityanalysisofaplanarfour-barlinkage C.F.Chang,KUASME Examples(cont.) Examples(cont.)pp.1414-15 31 j M3(nj1)fi i1  whenmorethantwomemberscometogetheratasinglepoint location(multiplejoint複接頭) n=6,j=7,fi=7 M=3(6-7-1)+7=1 n=11,j=14,fi=15 M=3(11-14-1)+15=3 C.F.Chang,KUASME 國立高雄應用科大機械系 32 16 機構學 Remarkonthoselinkages withalljointshavingconnectivityone j M3(nj1)fi i1 Sincealljointshavingconnectivityone(fi=1),wehave –fi=j=numberofjoints Moreover,ifthemobilityofplanarlinkagesissetto one,theconstraintcriterionequationleadsto –1=3(n-j-1)+j –3n=2j+4 –nmustbeaevennumber,sayn=2,4,6,…   C.F.Chang,KUASME 33 ConstraintAnalysisofSpatialLinkages(pp.1818-22)  Thedofofalinkwithspatialmotion=6 M桿件之自由度接頭所造成之拘束度 j 6(n1)(6fi) i 1 j 6(nj1)fi i1  Where –M=Mobilityofspatiallinkages –n:thenumberoflinks –j:thenumberofjoints –fi:theconnectivityofjointi(dofofjointi) ThisequationisknownastheKutzbachcriterion C.F.Chang,KUASME 國立高雄應用科大機械系 34 17 機構學 Example1 j M6(nj1)fi i 1 n =4(桿數) j=4(接頭數)  fi=3+3+1+2=9(接頭之總自由度) M=6(4-4-1)+9=-6+9=3 C.F.Chang,KUASME 35 Example2  n=7 j=6 Fiverevolutejoints:1,2,4,5,6 Oneprismaticjoint:3 1 link joint   fi=51+11=6(接頭之總自由度) M=6(7-6-1)+6=6 C.F.Chang,KUASME 國立高雄應用科大機械系 36 18 機構學 Example3       n=4 j=4(RSSR) Tworevolutejoints(fi=1) Twosphericaljoint(fi=3) fi=21+23=8(接頭之總自由 度) M=6(4-4-1)+8=-6+8=2  Theresultseemstoconflictwithourpracticalexperiencesincethereisa uniquevalueofforanygivenvalueof.i.e.,theorientationoflink4canbe determinedwhentheorientationoflink2isspecified. Examiningthemechanismcarefullywillrevealthatweneedanextra parametertoidentifytheorientationoflink3.Becausethisparameterdoesn't affecttheinput-outputrelationshipofthelinkage,sowecallitanidledegree offreedom. freedom C.F.Chang,KUASME 37 IdleDegreesofFreedom(Redundant (RedundantDOF多餘自由度) 多餘自由度)  Anidledofisonethatdoesnotaffecttheinput-output relationshipofthelinkage.  ProceduresforLocatingtheIdledofareasfollowing: –Identifytheinputlinkandoutputlink. –Checktodetermineifasinglelinkoracombinationof connectedlinkscanmovewithoutalteringtherelative positionoftheinputandoutputlinks.Iftheansweris positive,therearesomeidledof’ s. C.F.Chang,KUASME 國立高雄應用科大機械系 38 19 機構學 IdleDegreesofFreedom&StewartPlatform  ForaStewartplatform,wehave  n=14 (2 6limbs+1baselink+1outputlink) j=18  –Sixprismaticjoints(fi=1) –Twelvesphericaljoint(fi=3)   fi=61+123=42(接頭之總自由度) M=6(14-18-1)+42=-30+42=12   Indeed,thismechanismhassixidledof. Thisisbecauseeachlimbisfreetospinaboutthelinejoining thecentersofitssphericaljoints. C.F.Chang,KUASME 39 PlanarMechanismwithanIdleDegreesofFreedom  Fortheplanarmechanismasshownin thefigure,wehave  M=1ifthekinematicpairatCisarolling pair(fi=1)  M=2ifthekinematicpairatCisacam pair(fi=2)  However,theextradegreeof freedomdoesnotaffectthetheinputoutput(link6vs.link2)relationshipof thelinkage.So,theextradofisanidle dof. C.F.Chang,KUASME 國立高雄應用科大機械系 40 20 機構學 ParadoxicalMechanism(矛盾機構) 矛盾機構) refpp.2525-29overover-constrainedlinkage  Aspatial4Rlinkageis,ingeneral,immovablebecauseM=-2. However,itmayhavemobilityoneifspecialgeometryaremet. Therearetwowell-knowparadoxicalmechanisms: –Sphericalfour-barmechanism(Theaxesofrevolutejointsall passthroughasinglepoint) –Bennettmechanism asin=bsin C.F.Chang,KUASME 41 KinematicInversion  KinematicInversionisthetransformationofonemechanismto anotherbychoosingadifferentmembertobetheframe Forexample, Toothbrush mechanism Walking mechanism Water pump C.F.Chang,KUASME 國立高雄應用科大機械系 42 21 機構學 AnPracticalApplication—WaterPump C.F.Chang,KUASME 43 Classificationof4-barMechanisms& Grashof’ srule(pp.32-37)    s:linklengthoftheshortestlink l:linklengthofthelongestlink p,q:linklengthsoftheothertwolinks Type Grashof condition s+l<p+q Shortestlink mechanism Sidelink Crank-rocker Coupler Double-rocker Base,frame Double-crank ChangePoint s+l=p+q Anylink Change-point Non-Grashof s+l>p+q Anylink Triple-rocker Papercsme2001csmmt2001 國立高雄應用科大機械系 C.F.Chang,KUASME 44 22 機構學 Example  AB=1.14in,BC=2.26in,AD=1.74in AF=2.00in,DE=2.68in,c=1.09in DeterminetheregionforjointEthatwillallowfullrotationoflink 6,i.e.,EF=? Sol: LinkABinloopABCcanmakeafullrotation (BC-AB>c) LinkAFisnottheshortestone(AF<DE) Four-barFEDAmustbeacrank-rocker s=EFl=DE 1.74 2.68 2.0 E s+l<p+q EF+DE<AF+AD EF+2.68<2.00+1.74 EF<1.06inANS C.F.Chang,KUASME 45 Analysisoffour-barlinkages-Centrodes C.F.Chang,KUASME 國立高雄應用科大機械系 46 23 機構學 Limitpositions(ofDrivenLink) C.F.Chang,KUASME 47 Analysisoffourfour-barlinkageslinkages-LimitPositions ref:csme2001.pdf csme2001.pdf C.F.Chang,KUASME 國立高雄應用科大機械系 48 24 機構學 ClassificationofSpherical44-barMechanisms Ref:csmmt2001 C.F.Chang,KUASME 49 Interference ref:csmeconf1995,1996,CSMMTconf2000 .pdf csmeconf1995,1996,CSMMTconf2000.pdf C.F.Chang,KUASME 國立高雄應用科大機械系 50 25 機構學 Actuators C.F.Chang,KUASME 51 Stable&UnstableOperation load>drivingtorque angularvelocityisdecreaseduntilstateAisreached End ofChapter1 C.F.Chang,KUASME 國立高雄應用科大機械系 52 26 Relateddocuments EliteStudyinTaiwanProgramOfficevisitedour Teachingplan MachineLearninginInformationandNetworkSecurity St.PetersburgTimesOct.1996BOUNDFEET&WESTERNDRESS Thewillowpatternstory-YsgolGymraegGwenllian Download advertisement Addthisdocumenttocollection(s) Youcanaddthisdocumenttoyourstudycollection(s) Signin Availableonlytoauthorizedusers Title Description (optional) Visibleto Everyone Justme Createcollection Addthisdocumenttosaved Youcanaddthisdocumenttoyoursavedlist Signin Availableonlytoauthorizedusers   SuggestushowtoimproveStudyLib (Forcomplaints,use anotherform ) Youre-mail Inputitifyouwanttoreceiveanswer Rateus 1 2 3 4 5 Cancel Send