Chapter1StructuralAnalysis(结构分析)ofMechanisms(机构)课件.ppt

Chapter 2 Structural Analysis(结构分析)of Planar Mechanisms(机构)2-1 Kinematic Pairs(运动副)、Kinematic Chain and MechanismsTo make an inquiry into motion possibility of mechanisms.（探讨机构运动的可能性）To classify mechanisms by different combination of links （按机构组成分类）To represent mechanisms by the Kinematic Diagram of a Mechanism (用机构运动简图表达机构)Purpose of Studying Structural Analysis of Mechanisms一.LinksThe basic elements in kinematic analysis.The motions of links determine the motions of mechanism.CamGearGearGearLinks can be divided into three groups:Frame(机架)The fixed(固定的)link is called the frame(机架)and there is only one frame for each mechanism.Driving links(驱动件）Some moving links have their own independent(独立的)motion characteristics.They are called driving links(驱动件）.Driven links（从动件）.The other moving links are called driven links（从动件）.ExampleLinks Mechanismmobile connection(可动连接)kinematic pair(运动副)二.kinematic pairs1.DefinitionIn order to transmit(传输)and transform(转换)motion,every link must be kept permanently(永久地)in contact(接触)with other links by some kind of connection and have motion relative to them.Such a mobile connection(可动连接)is called a kinematic pair.The mobile connection between the frame and the piston is a kinematic pairThe mobile connection between the coupler 3 and the crank 4 is another kinematic pair.The mobile connection between the two gears is also a kinematic pair.Note:（1）One kinematic pair can connect only two links.（2）Those connections that join two machine elements firmly(牢固地)and do not allow the connected machine elements(零件)to move relative to each other,such as welds(焊接),rivets(铆钉),or nuts(螺母)and bolts(螺栓),are not kinematic pairs.The connection between the coupler body and the big-end cover is not a kinematic pair.The part of the link surface which makes contact with another link and forms a kinematic pair is called a pair element(运动副元素).For example,the cylindrical surfaces of the hole and the shaft in a revolute pair are two pair-elements.The combination of two such elements on the connected links constitutes a kinematic pair2.Types of kinematic pairs:Revolute pair(转动副)Sliding pair or Prismatic pair(移动副)Gear pair(齿轮副)Cam pair(凸轮副)Screw pair(螺旋副)Spherical pair(球面副)Representation of kinematic pairsRevolute pair(转动副):A pair that permits only relative rotation is called a revolute pair(转动副).12BRepresentation of Revolute pair(转动副)A pair that allows only relative rectilinear(直线的)translation(平移)is called a sliding pair or prismatic pair(移动副).Representation of Sliding pair or Prismatic pairNote:The actual shape and dimensions of the cross section(横截面)of the sliding pair has no influence(影响)on the kinematics of the mechanism.The centerline of the sliding pair in the kinematic diagram must be parallel(平行)to the pathway(导路)in the mechanism.The centerline of a sliding pair can be translated(平移).Any one link can be drawn as a sliding block while the other is drawn as a guide bar(导杆).The following five diagrams are equivalent.Gear pairCam pairIt is necessary to draw the actual cam contour(凸轮实际廓线)and the end profile(轮廓)of the follower in the kinematic diagramScrew pair（螺旋副）Spherical pair（球面副）If two links connected by a kinematic pair can move relative to each other only on a plane,the kinematic pair is called a planar kinematic pair,otherwise,spatial kinematic pairplanar cam pair.revolute pairPlanar kinematic pair:sliding pairGear pair.Spatial kinematic pair:spatial cam pair spatial gear pairscrew pairspherical pairIf two links are connected by a surface,the pressure(压强)between the two links is lower.If two elements of a kinematic pair have surface contact(面接触)or its equivalent(等价物),the kinematic pair is known as a lower pair(低副).If the connection takes place only at a point or along a line(assuming the materials to be rigid),it is known as a higher pair(高副),e.g.,the gear pair and the cam pair.In this book,we are concerned only with planar kinematic pairs.3.Functions of kinematic pairsThe number of independent(独立的)parameters needed to define uniquely(唯一地)the locations of a link with respect to(相对于)the frame is called the degree of freedom(DOF)of the linkIf a moving link in a plane is not connected to any other link,three independent(独立的)parameters are required to completely define its exact location,e.g.XA,YA,and ,therefore,an unconstrained(未约束的)link on a plane would have 3 DOFYXRevolute pair:When the two links are connected by a kinematic pair,their independent motion will be constrained,their DOF will decreaseIf two links are connected by means of a revolute pair,three parameters(XA,YA,and 1)are required to define the location of link 1 first,and another parameter(21)is required to define the position of link 2 relative to link 1.Connecting two planar links with a revolute pair has the effect of removing two DOF from the system.In other words,a revolute pair has two constrains(x and y).Sliding pair：A sliding pair constrains(约束）relative translation(平移)along the common normal(公法线)and relative rotation,permitting only a rectilinear(直线的)relative motion along the path of the slide way.Thus,one planar lower pair sets two constraints,or eliminates two DOF.Planar higher pair:If two links are connected by a planar higher pair,the two links cannot have relative motion along their common normal n-n at the point of contact.Otherwise,the two links will separate(分离)or interfere(干涉).This higher pair is also called a roll&slide pair.Thus,a planar higher pair has only one constraint（约束）or eliminates(消除)only one DOF.三.Kinematics Chain(运动链)When a number of links are connected by means of kinematic pairs,the resulting mobile system is a kinematic chain.LinkKinematic pairLinkKinematic pairLinkType of Kinematics Chain(运动链)closed chain(闭式链)If every link in a kinematic chain has at least two pair elements,all links form a closed chain If one or more links in a kinematic chain have only one pair element,then the kinematic chain will be an open chain四.Mechanism(机构)In order to transmit motion,one of the links in the kinematic chain must be fixed as frame,the other moving links have certain motion,thus Kinematics Chain become mechanism Types of mechanismsplanar mechanism.If all links of a mechanism move in planes that remain parallel(平行)to each other,we say that the mechanism is a planar mechanismspatial mechanism(空间机构）.Some spatial mechanisms If all kinematic pairs in a mechanism are lower pairs,the mechanism is called a lower pair mechanism,or more often,a linkage mechanism(连杆机构).If a mechanism has one or more higher pairs,it is called a higher pair mechanism(高副机构).All kinematic pairs in a planar mechanism must be planar kinematic pairs,while the mechanism containing only planar kinematic pairs may be a spatial mechanism.The universal joint(万向联轴节),which contains only revolutes(planar kinematic pairs),is a spatial mechanism.1-3 The Kinematic Diagram of a Mechanism(机构运动简图)一.Definition and Functions1.Definition:Since this diagram is used only to express the relationship between the motions of links,it should be simple but provide all necessary(not redundant(多余的)information determining the relative motion of all links.Such a diagram is called the kinematic diagram of the mechanism(机构运动简图).2.The ability to draw the kinematic diagram of mechanisms is a basic technical skill for engineers.2.Functions of The Kinematic Diagram of a MechanismExpress transmission theory and motions relationship between the links of a mechanismKinematic analysis and dynamic analysisNote：It should be simple but provide all necessary(not redundant)information determining the relative motion of all links.According to specified symbols(符号).The kinematic diagram should be drawn to scale(按比例).If not,such a diagram is called the schematic diagram(草图)of the mechanism.Consider only kinematics dimensions(运 动学尺寸).The representation(表示法)of a Link in the Kinematic Diagram The kinematic function of a link is to hold the relative position of all pair elements on the link unchanged during the motion of the mechanism.Only the value of the distance LAB between the centers of the two revolutes is necessary for all kinematic analysis.A link with more than two pair elements can be represented by a hatched(阴影线的)or welded(焊接的)polygon(多边形)with pair elements at corners.Link in Fig.(a)can be represented by any one kinematic diagram below.Note the differences between the following two groups of figures：symbols(符号)used in a kinematic diagram for some common mechanisms Rack and pinionWormRatchet MechanismInner-meshed Cylindrical Gear DriveOuter-meshed Cylindrical Gear DriveProcedures（步骤）for Drawing the Kinematic Diagram of a Mechanism (1)Study carefully the structure of mechanism.How many links?Types of all kinematic pairs?(2)Choose a drawing plane.Sometimes,a local view may be drawn to clarify the structure.(3)First,draw all fixed pair elements!(4)Draw the drivers first and then draw driven links according to route of transmission(传 递 路 线).(5)The links are numbered while the kinematic pairs are lettered.Each link,no matter how many machine elements it has,can have only one serial number.All machine elements belonging to the same link in the kinematic diagram must be connected firmly by welding(焊接)symbols.(6)Calculate and check degree of freedom(自由度）.(7)Measure all and only kinematic dimensions.(8)Select a suitable scale(比例尺),then draw the kinematic diagram of the mechanism.Fig.2-44：偏心油泵。圆盘2与壳体4的相切与运动无关，不是运动副。34142Fig.2-46：偏心盘1绕固定轴转动，通过构件2，使滑块3相对于机架4往复移动。12344Fig.2-45：偏心盘1绕固定轴转动，迫使滑块2在圆盘3的槽中来回滑动，而圆盘3又相对于机架4转动。21234412344orFig.2-43：油泵。偏心盘1绕固定轴A转动。构件2套在偏心盘1的外面，组成转动副。构件2在圆盘3的槽中滑动，组成移动副。圆盘3相对于机架4绕其圆心C转动。12344颚颚式式破破碎碎机机机机构构运运动动简简图图Fig.2-42：Kinematic diagram of punch(打孔机)ABCDE123 45Fig.2-41：Draw the Kinematic diagram of small press(压力机).441-3 Degree of Freedom of a Mechanism一一.Definition The number of independent(独立的)parameters needed to define uniquely(唯一地)the locations of all moving links within mechanism with respect to(相对于)the frame is called the degree of freedom(DOF)of the mechanism.LinksKinematic Pairs MechanismDOFconstrainsRemain DOFLinksKinematic PairsMechanismDOFconstrainsRemain DOF3N(2PL+PH)F=Each unconstrained(无约束的)link has 3 DOF.Each planar lower pair eliminates(消除)two DOF and each planar higher pair eliminates(消除)one DOF.DOF=3N-2PL-PH Conditions for a Mechanism to have Motion?Answer:DOF=1DOF=3N-2PL-PH Where:N=Numbers of moving links (does not include the frame!)PL=Numbers of planar lower pair PH=Numbers of planar higher pair 二.Conditions for a Mechanism to have a Determined Motion（机构有确定运动的条件）Provide one independent parameter，all moving links can have determined motions(提供一个独立运动，能运动，确定);Provide two independent parameters，can not move at all(提供二个独立运动，不能运动).In extreme(极端)cases,the weakest link in the chain may be broken.If the number of driving links is less than the DOF of the mechanisms,some driven(从动的)links will not have determined motion.Provide two independent parameters，all moving links have determined motion(提供二个独立运动，所有构件有确定相对运动)N=3PL=4PH=0F=3n-2PL-PH =3X3-2X4=1 N=4PL=5PH=0F=3n-2PL-PH =3X4-2X5=2 F=1.F=Number of the driving links.the condition for a mechanism to have a determined(确定的)motion is:Independent(独立的)parameters(参数)are supplied(提供)only by the driving links.Since the driving links are always connected to the frame by lower pairs,one driving link(together with the corresponding lower pair)will provide only one independent parameter.Examples:N=4,PL=6F=3N-2PL-PH =3X4-2X6=0N=2,PL=3F=3N-2PL-PH =3X2-2X3=0N=3,PL=5F=3N-2PL-PH=3X3-2X5=-1 truss(绗架)Examples:N=2;PL=2PH=1F=3N-2PL-PH =3X2-2X2-1X1 =1N=5;PL=7F=3N-2PL-PH =3X5-2X7 =1N=2;PL=2PH=1F=3N-2PL-PH =3X2-2X2-1X1 =113245F=3n-2PL-Ph=36-28=2 两自由度的刹车机构可使两片刹车片均匀地抱紧在轮毂上，自动调节刹车片的均载，刹车效果比单一刹车片（单自由度）的更好。三.Points for Attention during the Calculation of DOF（计算自由度时应注意的事项）In the development of the structural formula of mechanism Eq.：F=3N-2PL-PH no consideration was given to the link dimensions.It is not surprising to find many exceptions to the formula in practical cases with special geometric features.1.Compound Hinge(复合铰)If the axes(轴)of two revolutes coincide(重合),they constitute a compound hinge.The number of revolutes in a compound hinge is equal to one less than the number of links joined at that hinge.Note：In many cases,compound hinge(复合铰链)does not show clearly.Attention must be paid to it.All machine elements belonging to the same link in the kinematic diagram must be connected firmly by welding(焊接)symbols.In a mechanism having gears(齿轮)or cams(凸轮),careful attention must be paid to the existence(存在)of compound hinges.Ex.1:Calculate the DOF of the gear-linkage mechanism(齿轮连杆机构).In the mechanism,there are three moving gears(1,2,and 3)and two moving rods(杆)(4 and 5).C is a compound hinge of links 2、4、5D is a compound hinge of links 3、5、6.F=3N-2PL-PH=35-26-2=1 2.Passive DOF(局部自由度)The DOF which does not change the output motion of the mechanism is called a passive DOF.F=3N-2PL-PH=33-23-1=2123演示演示Any passive DOF should be deleted(删除)by welding the roller(滚子)to the follower before the calculation of the DOF of mechanism.F=3N-2PL-PH=32-22-1=1123123动画动画动画动画have exactly the same kinematic function as other constraints.N=,PL=,PH=0F=3N-2PL-PH=3X-2X=3.Redundant(多余的、虚的)Constraints约束ABCDN=3,PL=4,PH=0F=3N-2PL-PH=3X3-2X4=1动画演示动画演示1234ABCDEFABCDEF(1)When two links are connected by more than one parallel(平行的)sliding pair,only one sliding pair can be counted during the calculation,others are redundant constraints and must not be counted.Redundant constraints must not be counted during the calculation(2)When two links are connected by more than one revolute pair whose axes coincide(重合),(3)When two links are connected by more than one higher pair whose common normals(公法线)passing through the points of contact coincide(重合)F=3N-2PL-PH =32-22-1=1 3 2-23-2=-2However,if their common normals(公法线)do not coincide(重合),then both higher pairs should be counted.(4).When the distance between two points on two links remains(保持)constant(常数)during the motion of the mechanism,adding one link and two revolutes with their centers at these two points will create a redundant constraintDuring the motion of the mechanisms,the distance between two points A and B on two links 2 and 4 remains constant,link 1,revolute A,and revolute B create a redundant constraintF=3n-2PL-PH=33-24=1 34-26=0(5).When the locus(轨迹)of a point is a straight line,adding one link with one fixed guide way parallel to the straight line and one revolute with its centre at that point will create a redundant constraint.(6)Symmetrical(对称的)structure In order to transmit(传输)more power,many pinions(小齿轮)are distributed(分布)symmetrically in space.Only one pinion should be counted.Note：gear 1,gear 3,and frame 4 constitute(组成)a compound hinge(复合铰链).F=3N-2PL-PH =33-23-2=1 Note Redundant constraints can improve the rigidity(刚度)of a mechanism,improve the force condition in links,etc.and are widely used.“Deleting the redundant constraints during the calculation of DOF”does not mean that the redundant constraints should be omitted(省略)from