1、Mechanisms and Machine Theory (機(jī)械原理)206,mechanical engineering school,NUST Tel:84315623Chapter1 IntroductionChapter2 Structural Analysis of Planar MechanismsChapter3 Kinematic Analysis of MechanismsChapter4 Planar Linkage MechanismsChapter 5 Cam MechanismsChapter 6 Gear MechanismsChapter 7 Gear Trai

2、nsChapter 8 Other Mechanisms in Common UseChapter 9 Balancing of MachineryChapter 10 Motion of Mechanical Systems and Its RegulationChapter 11 Efficiency of MachineChapter 2 Structural Analysis(結(jié)構(gòu)分析) of Planar Mechanisms(平面機(jī)構(gòu)) Planar mechanism平面機(jī)構(gòu)：Spatial mechanism空間機(jī)構(gòu)：All links of a mechanism move

3、in planes that remains parallel to each other各構(gòu)件的相對運(yùn)動(dòng)平面互相平行（常用的機(jī)構(gòu)大多數(shù)為平面機(jī)構(gòu)）。至少有兩個(gè)構(gòu)件能在三維空間中相對運(yùn)動(dòng)。2.1 Purpose of Structural Analysis2.2 Planar Kinematic Pairs(平面運(yùn)動(dòng)副) and Planar Mechanisms2.3 The Kinematic Diagram of a Mechanism(機(jī)構(gòu)運(yùn)動(dòng)簡圖) 2.4 Degree of Freedom of a Mechanism2.5 Points for Attention during

4、the Calculation of DOF機(jī)構(gòu)結(jié)構(gòu)分析的目的 探討機(jī)構(gòu)具有確定運(yùn)動(dòng)的條件機(jī)構(gòu)的分類畫機(jī)構(gòu)的運(yùn)動(dòng)簡圖2.1 Purpose of Structural Analysis2.2 Planar Kinematic Pairs(平面運(yùn)動(dòng)副) and Planar Mechanisms2.2.1 Kinematic Pairs2.2.2. Kinematic Chain(運(yùn)動(dòng)鏈) and Mechanism2.2.1 Kinematic Pairs機(jī)構(gòu)的組成要素Link構(gòu)件Kinematic Pairs運(yùn)動(dòng)副In order to transmit(傳輸) and transform(

5、轉(zhuǎn)換) motion, every link must be kept permanently(永久地) in contact(接觸) with other links by some kind of connection and have motion relative to them. Such a mobile connection(可動(dòng)連接) is called a kinematic pair. Types of kinematic pairs:（根據(jù)兩構(gòu)件接觸方式的不同）Revolute pair(轉(zhuǎn)動(dòng)副)Sliding pair or Prismatic pair(移動(dòng)副)Scr

6、ew pair(螺旋副)Spherical pair(球面副) Gear pair(齒輪副)Cam pair(凸輪副)面接觸lower pair點(diǎn)、線接觸higher pair A pair that permits only relative rotation is called a revolute pair (轉(zhuǎn)動(dòng)副). 面接觸lower pair低副A pair that allows only relative rectilineal(直線的) translation(平移) is called a sliding pair or prismatic pair(移動(dòng)副).點(diǎn)、線接觸高

7、副higher pair Gear pair （齒輪副）Cam pair （凸輪副）A pair element運(yùn)動(dòng)副元素the part of the link surface Which make contact with another linkAttention: （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(

8、零件) to move relative to each other, such as welds(焊接), rivets(鉚釘), or nuts(螺母) and bolts(螺栓), are not kinematic pairs.按兩構(gòu)件間相對運(yùn)動(dòng) planar kinematic pair(平面) Spatial kinematic pair(空間) 面接觸(surface contact) ：lower pair sliding revolute screw spherical 如：移動(dòng)副、轉(zhuǎn)動(dòng)副；螺旋副、球副點(diǎn)、線接觸(point, line contact)：higher pai

9、r 如：齒輪副，凸輪副gearcamConclusion：Types of kinematic pairs按兩構(gòu)件接觸方式 螺旋副screw球副sphericalDOF of a Link構(gòu)件的自由度 構(gòu)件含有獨(dú)立運(yùn)動(dòng)的數(shù)目剛體作空間運(yùn)動(dòng)時(shí)，則有6個(gè)自由度。an unconstrained link on a plane would have 3 DOF（剛體作平面運(yùn)動(dòng)時(shí)，有3個(gè)自由度） Constraint（約束）：對獨(dú)立運(yùn)動(dòng)的限制one planar lower pairs（低副）sets two constraints （2個(gè)約束，1個(gè)自由度）one planar higher pair

10、s（高副）sets one constraints （1個(gè)約束，2個(gè)自由度）2.2.2. Kinematic Chain(運(yùn)動(dòng)鏈) and Mechanism When a number of links are connected by means of kinematic pairs, the resulting mobile system is a kinematic chain. If every link in a kinematic chain has at least two pair elements, all links form a closed chain.閉鏈If on

11、e or more links in a kinematic chain have only one pair element, then the kinematic chain will be an open chain.開鏈Kinematic chain Closed chain:（閉鏈） 每一構(gòu)件至少含有兩個(gè)運(yùn)動(dòng)副元素,動(dòng)其中幾桿，其余各桿便于傳遞運(yùn)動(dòng)，廣泛使用 Open chain:（開鏈） 一個(gè)以上的構(gòu)件只有一個(gè)運(yùn)動(dòng)副元素應(yīng)用于機(jī)械手，挖掘機(jī)，機(jī)器人，多自由度 Conclusion：Types of kinematic chain If a link of the kinematic

12、 chain is fixed as the frame機(jī)架, then the kinematic chain es mechanism.mechanism driving links:have their own independent motion driven links:generate the expected output motion(output links) 2.3 The Kinematic Diagram of a Mechanism 2.3.1 Definition2.3.2 Representation of a Kinematic Pair 2.3.3 The r

13、epresentation of a link in the kinematic Diagram 2.3.4 Procedures for Drawing the Kinematic Diagram of a Mechanism 2.3.1 Definition不考慮與運(yùn)動(dòng)無關(guān)的因素（外形，尺寸，具體構(gòu)造），僅用簡單線條，符號，按一定比例表示各運(yùn)動(dòng)副的相對位置this diagram is used only to express the relationship between the motions of links, it should be simple but provide all

14、 necessary (but not redundant多余的) information determining the relative motion of all links. Such a diagram is called the kinematic diagram of the mechanism(機(jī)構(gòu)運(yùn)動(dòng)簡圖).Attention： It should be simple but provide all necessary (but not redundant) information determining the relative motion of all links. A

15、ccording to specified symbols(符號). The kinematic diagram should be drawn to scale(按比例). If not, such a diagram is called the schematic diagram(機(jī)構(gòu)示意圖) of the mechanism.2.3.2 Representation of a Kinematic Pair 轉(zhuǎn)動(dòng)副 revolute pair：(關(guān)鍵畫出轉(zhuǎn)軸位置) The shaded(帶陰影線) links represent the frameA revolute is conveni

16、ently(方便地) represented by a small circle placed at the centre of the revolute no matter how large its radius(半徑) is. 移動(dòng)副 sliding pair (關(guān)鍵畫出相對移動(dòng)的方向，導(dǎo)路 )The shaded(帶陰影線) links represent the frame The actual shape and dimensions of the cross section(橫截面) of the sliding pair has no influence(影響) on the

17、kinematics of the mechanism.Attention： The centerline of the sliding pair in the kinematic diagram must be parallel(平行) to the pathway(導(dǎo)路) in the mechanism. Any one link can be drawn as a sliding block while the other is drawn as a guide bar(導(dǎo)桿). The following five diagrams are equivalent.齒輪副gear pa

18、ir：凸輪副cam：need actual cam contour and end profile of follower 2.3.3 The representation of a link in the kinematic Diagram the kinematic function of the link to keep the distance straight line can be used links with two pair elements(雙副構(gòu)件)：A link with more than two pair elements can be represented by

19、 a hatched(陰影線的) or welded(焊接的) polygon(多邊形) with pair elements at corners.Note the differences between the following two groups of figures：The special representative(有代表性的) symbols(符號) used in a kinematic diagram for some common mechanisms are listed in Table 2-1（P9）.2.3.4 Procedures for Drawing th

20、e Kinematic Diagram of a Mechanism 1) Run the mechanism slowly,study the structure of the mechanism, How many links? Types of all kinematic pairs?2) stop at a suitable position ,Chose a drawing plane3) Draw the schematic diagram機(jī)構(gòu)示意圖4) Measure kinematic dimensions5) Select scale = 6)draw the kinemat

21、ic diagram of the mechanism.Ex. ： Circular disk 1 rotates relative to the frame 4 about a fixed axis(軸) A. The link 3oscillates(擺動(dòng)) about a fixed axis D. The circular disk 1 matches(配合) with a hole on circular disk 2. The circular disk 2 matches with a large hole on the link 3. 2.4 Degree of Freedom

22、 of a Mechanism2.4.1 the definition of DOF2.4.2 Structural Formula of a planar Mechanism2.4.3 Condition for a mechanism to have a determined motion 2.4.1 Definition機(jī)構(gòu)中各構(gòu)件相對于機(jī)架所能有的獨(dú)立運(yùn)動(dòng)的數(shù)目 the DOF of the mechanism ORDOF : The number of independent coordinates required to define its position.2.4.2 Stru

23、ctural Formula of a Planar MechanismN :the number of moving links (does not include the frame!) PL: the number of planar lower pairs Ph:the number of planar higher pairs The DOF of a Planar Mechanism F=3N-2PL-PhExample1:2.4.3 Condition for a mechanism to have a determined motion如果有兩個(gè)原動(dòng)件，那么該機(jī)構(gòu)會(huì)從最弱構(gòu)件處

24、損壞。 The number of the driving linksthe DOF of Mechanism, it will be broken Example2:鉸鏈五桿機(jī)構(gòu)：如果只給一個(gè)原動(dòng)件，機(jī)構(gòu)運(yùn)動(dòng)不確定 the number of the driving links 0,原動(dòng)件數(shù)=F，運(yùn)動(dòng)確定原動(dòng)件數(shù)F，機(jī)構(gòu)破壞Conclusion:2.5.1 Compound Hinge 2.5.2 Passive DOF ( 局部自由度 )2.5.3 Redundant Constraints2.5 Points for Attention during the Calculation of

25、 DOF2.5.1 Compound Hinge The number of revolutes in a compound hinge=one less than the number of links joined at that hinge.m - m-1Multiple joints(compound hinge)Example:ABDCEF2.5.2 Passive DOF ( 局部自由度 )21ACB4321ACB32.5.3 Redundant Constraints在特殊的幾何條件下，有些約束所起的限制作用是重復(fù)的，這種不起獨(dú)立限制作用的約束稱為虛約束。 解決方案虛約束常出現(xiàn)的

26、場合(1) Two links are connected by more than one parallel sliding pairsTwo links are connected by more than one revolute pair whose axes coincideTwo links are connected by more than one higher pair whose common normals passing through the points of contact coincide. However, if their common normals (公

27、法線) do not coincide(重合), then both higher pairs should be counted. (4) The distance between two points on two links remains constant during the motion of the mechanism,adding one link and two revolutes create a redundant constraints.(5) The locus of a point is a straight line,adding one link with on

28、e fixed guide way parallel to the line and one revolute with its centre at that point will create a redundant constraint. F=3n-2PL-Ph=33 -24=1(6) Symmetrical or duplicated structureIn order to transmit(傳輸) more power, many pinions(小齒輪) are distributed(分布) symmetrically in space. Only one pinion shou

29、ld be counted.Note：gear 1, gear 3, and link 4 constitute(組成) a compound hinge(復(fù)合鉸鏈). Example2 n=7，pl=9，ph=1 F=3n-2pl-ph=37-29-1=2 n=5，pl=7，ph=0 F=3n-2pl-ph=35-27-0=1 n=5，pl=6，ph=2 F=3n-2pl-ph=35-26-21=1 Attention：(1) Redundant constraints can improve the rigidity(剛度) of a mechanism, improve the force condition in links, etc. and are widely used. (2) Deleting the redundant constraints during the calculation of DOF does not mean that the redundant constraints should b