平面機構自由度計算Calculationofdegrees

平面機構自由度計算Calculationofdegreesoffreedomforplanarmechanisms主講人：周會娜123目錄CONTENTS平面機構自由度計算機構具有確定運動的條件例題解析CalculationofdegreesoffreedomforplanarmechanismsMechanismshaveconditionsfordeterminingmotionReflecExampleanalysistionquestions教學目標Teachingobjectives1.如何使組合起來的構件產生運動并具有運動確定性?2.機構的自由度3.機構具有確定性運動的條件Howtomakethecombinedcomponentsgeneratemotionandhavemotioncertainty?DegreeofFreedomoftheMechanismConditionsforMechanismtoHaveDeterministicMotion1平面機構自由度計算CalculationofdegreesoffreedomforplanarmechanismsONE平面機構自由度與組成機構的構件數目、運動副的數目及運動副的性質有關。Thedegreeoffreedomofaplanarmechanismisrelatedtothenumberofcomponentsthatmakeupthemechanism,thenumberofmotionpairs,andthepropertiesofthemotionpairs.平面機構自由度計算Calculationofdegreesoffreedomforplanarmechanisms1.低副Lowpair在平面機構中每個平面低副(轉動副、移動副等)引入兩個約束平面機構自由度計算Calculationofdegreesoffreedomforplanarmechanisms圖1轉動副Figure1Rotatingpair圖2移動副Figure2MobileSub低副提供約束及自由度情況:引入2個約束，保留1個自由度。Lowpairprovidesconstraintsanddegreesoffreedom:introduce2constraintswhileretaining1degreeoffreedom.1.高副SeniorOfficer平面機構自由度計算Calculationofdegreesoffreedomforplanarmechanisms高副提供約束及自由度情況:限制了沿公法線n-n方向的相對移動保留了沿接觸處切線t-t方向的相對移動和在平面內的相對轉動。引入1個約束，保留2個自由度。Thehighpairprovidesconstraintsanddegreesoffreedom:itrestrictstherelativemovementalongthen-ndirectionofthecommonnormalandretainstherelativemovementalongthetangentt-tdirectionatthecontactpointandtherelativerotationintheplane.Introduceoneconstraintwhileretainingtwodegreesoffreedom.設機構共有N個構件TheestablishmenthasatotalofNcomponents活動構件數:n=N-1Numberofactivecomponents:n=N-1在沒有用運動副聯接之前，這些可動構件的自由度總數應為3n。當各構件用運動副連接起來之后,由于運動副引入的約束使構件的自由度減少Beforeconnectingwiththemotionpair,thetotalnumberofdegreesoffreedomofthesemovablecomponentsshouldbe3n.Aftereachcomponentisconnectedbyamotionpair,thedegreeoffreedomofthecomponentisreducedduetotheconstraintsintroducedbythemotionpair平面機構自由度計算Calculationofdegreesoffreedomforplanarmechanisms低副數:PLLownumberofpairs:PL高副數:PHHighnumberofpairs:PH機構自由度F:F=3n-(2PL+PH)

MechanismdegreeoffreedomF:F=3n-(2PL+PH)平面機構自由度計算Calculationofdegreesoffreedomforplanarmechanisms例1:計算下圖所示的單缸內燃機機構的自由度Example1:Calculatethedegreesoffreedomofthesinglecylinderinternalcombustionenginemechanismshowninthefollowingfigure平面機構自由度計算Calculationofdegreesoffreedomforplanarmechanisms解:活動構件數:n=3Solution:Numberofactivecomponents:n=3低副數:PL=4Lowpairnumber:PL=4高副數:PH=0Highpairnumber:PH=0機構自由度:F=3n-(2PL+PH)=3x3-2x4=1Institutionaldegreeoffreedom:F=3n-(2PL+PH)=3x3-2x4=12機構具有確定運動的條件ThemechanismhascertainconditionsformotionTWO二、機構具有確定運動的條件Themechanismhascertainconditionsformotion機構institution自由度freedom原動件drivinglink結論conclusionF=3×3-2×4=11F=原動件數目，機構有確定運動F=numberoforiginalcomponents,withdefinitemovementofthemechanismF=3×3-2×4=12F<原動件數目，機構有確定運動F<numberoforiginalcomponents,mechanismhasdefinitemotion二、機構具有確定運動的條件Themechanismhascertainconditionsformotion機構institution自由度freedom原動件drivinglink結論conclusionF=3×4-2×5=21F>原動件數目，機構運動不確定F>ThenumberoforiginalcomponentsandthemechanismmotionareuncertainF=3×2-2×3=00F=0，機構為桁架結構，不能運動F=0,themechanismisatrussstructureandcannotmove機構具有確定性運動的條件:F>0，且原動件的數目等于自由度數TheconditionforthemechanismtohavedeterministicmotionisthatF>0andthenumberofactivecomponentsisequaltothenumberofdegreesoffreedom3例題解析ExampleanalysisTHREE例2:計算下圖所示的擺動導桿機構的自由度Example2:Calculatethedegreesoffreedomoftheswingingguiderodmechanismshowninthefollowingfigure三、例題解析Exampleanalysis解:活動構件數:n=5Solution:Numberofactivecomponents:n=5低副數:PL=7Lowpairnumber:PL=7高副數:PH=0Numberofhighpairs:PH=0機構自由度:F=3n-(2PL+PH)=3x5-2x7=1Mechanismdegreeoffreedom:F=3n-(2PL+PH)=3x5-2x7=1例3:計算下圖所示機構的自由度。如果機構中有1個原動件，請判斷機構是否具有確定運動。Example3:Calculatethedegreesoffreedomofthemechanismshowninthefollowingfigure.Ifthereisoneactuatorinthemechanism,pleasedetermineifthemechanismhasadefinitemotion.三、例題解析Exampleanalysis解:活動構件數:n=7Solution:Numberofactivecomponents:n=7低副數：PL=10Lownumberofpairs:PL=10高副數：PH=0Numberofhighpairs:PH=0機構自由度:F=3n-(2PL+PH)=3x7-2x10=1Institutionaldegreeoffreedom:F=3n-(2PL+PH)=3x7-2x10=1F=1，且等于原動件的數目，機構具有確定性運動。F=1andequaltothenumberofactivecomponents,themechanismhasdeterministicmotion.例4:計算下圖所示機構的自由度。如果機構中有1個原動件，請判斷機構是否具有確定運動。Example4:Calculatethedegreesoffreedomofthemechanismshowninthefollowingfigure.Ifthereisoneactuatorinthemechanism,pleasedetermineifthemechanismhasadefinitemotion.三、例題解析Exampleanalysis解:活動構件數:n=3Solution:Numberofactivecomponents:n=3低副數：PL=4Lowpairnumber:PL=4高副數：PH=1Highpairnumber:PH=1機構自由度:F=3n-(2PL+PH)=3x3-2x4-1=0Institutionaldegreeoffreedom:F=3n-(2PL+PH)=3x3-2x4-1=0F=0，且小于原動件的數目，機構不能動。F=0andlessthanthenumberoforiginalcomponents,themechanismcannotmove.自測題——計算題Selftestquestions-CalculationQuestion1計算下圖所示機構的自由度。如果機構中有1個原動件，請判斷機構是否具有確定運動。Calculatethedegreesoffreedomofthemechanismshowninthefigurebelow.Ifthere