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1、mechanisms and machine theory (機械原理)school of mechanical engineering, nust chapter1 introductionchapter2 structural analysis of planar mechanismschapter3 kinematic analysis of mechanismschapter4 planar linkage mechanismschapter 5 cam mechanismschapter 6 gear mechanismschapter 7 gear trainschapter 8

2、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)分析結(jié)構(gòu)分析) of planar mechanisms(平面機構(gòu)平面機構(gòu)) planar mechanism平面機構(gòu)平面機構(gòu):spatial mechanism空間機構(gòu)空間機構(gòu):all links of a mechanism m

3、ove in planes that remains parallel to each other2.1 purpose of structural analysis2.2 planar kinematic pairs(平面運動副平面運動副) and planar mechanisms2.3 the kinematic diagram of a mechanism(機機構(gòu)運動簡圖構(gòu)運動簡圖) 2.4 degree of freedom of a mechanism2.5 points for attention during the calculation of dof機構(gòu)結(jié)構(gòu)分析的目的機構(gòu)結(jié)

4、構(gòu)分析的目的 探討機構(gòu)具有確定運動的條件探討機構(gòu)具有確定運動的條件機構(gòu)的分類機構(gòu)的分類畫機構(gòu)的運動簡圖畫機構(gòu)的運動簡圖2.1 purpose of structural analysis2.2 planar kinematic pairs(平面運動副平面運動副) and planar mechanisms2.2.1 kinematic pairs2.2.2. kinematic chain(運動鏈運動鏈) and mechanism2.2.1 kinematic pairs機構(gòu)的組成要素機構(gòu)的組成要素link構(gòu)件構(gòu)件kinematic pairs運動副運動副in order to transm

5、it(傳輸傳輸) and transform(轉(zhuǎn)換轉(zhuǎn)換) motion, every link must be kept permanently(永久永久地地) in contact(接觸接觸) with other links by some kind of connection and have motion relative to them. such a mobile connection(可動連接可動連接) is called a kinematic pair. types of kinematic pairs:(根據(jù)兩構(gòu)件接觸方式的不同根據(jù)兩構(gòu)件接觸方式的不同) revolute

6、pair(轉(zhuǎn)動副轉(zhuǎn)動副) sliding pair or prismatic pair(移動副移動副) screw pair(螺旋副螺旋副) spherical pair(球面副球面副) gear pair(齒輪副齒輪副) cam pair(凸輪副凸輪副)面接觸lower pair點、線接觸higher pair a pair that permits only relative rotation is called a revolute pair (轉(zhuǎn)動副轉(zhuǎn)動副). 面接觸lower pair低副低副a pair that allows only relative rectilineal(直

7、線的直線的) translation(平移平移) is called a sliding pair or prismatic pair(移動副移動副).點、線接觸高副higher pair gear pair (齒輪副)(齒輪副)xy12ocam pair (凸輪副)(凸輪副)123a pair element運動副元素運動副元素the part of the link surface which make contact with another linkattention: (1)one kinematic pair can connect only two links. (2) thos

8、e connections that join two machine elements firmly(牢固地牢固地) and do not allow the connected machine elements(零件零件) to move relative to each other, such as welds(焊接焊接), rivets(鉚釘鉚釘), or nuts(螺母螺母) and bolts(螺栓螺栓), are not kinematic pairs.按兩構(gòu)件間按兩構(gòu)件間相對運動相對運動 planar kinematic pair(平面平面) spatial kinematic

9、 pair(空間空間) 面接觸面接觸(surface contact) :lower pair sliding revolute screw spherical 如:移動副、轉(zhuǎn)動副如:移動副、轉(zhuǎn)動副;螺旋副、球副點、線接觸點、線接觸(point, line contact):higher pair 如:齒輪副,凸輪副如:齒輪副,凸輪副gearcamconclusion:types of kinematic pairs按兩按兩構(gòu)件構(gòu)件接觸接觸方式方式 螺旋副screw球副sphericaldof of a link構(gòu)件的構(gòu)件的自由度自由度 構(gòu)件含有獨立運動的數(shù)目構(gòu)件含有獨立運動的數(shù)目剛體作空間運

10、動時,剛體作空間運動時,則有則有6 6個自由度。個自由度。an unconstrained link on a plane would have 3 dof(剛體作平面運動時,有剛體作平面運動時,有3 3個自由度)個自由度) constraint(約束):對獨立運動的限制約束):對獨立運動的限制one planar lower pairs(低副)(低副)sets two constraints (2個約束,個約束,1個自由度)個自由度)one planar higher pairs(高副)(高副)sets one constraints (1個約束,個約束,2個自由度)個自由度)2.2.2.

11、kinematic chain(運動鏈運動鏈) and mechanism1122334421343124 when a number of links are connected by means of kinematic pairs, the resulting mobile system is a kinematic chain.1122334421343124 if every link in a kinematic chain has at least two pair elements, all links form a closed chain.閉鏈閉鏈1122334421343

12、124if one or more links in a kinematic chain have only one pair element, then the kinematic chain will be an open chain.開鏈開鏈kinematic chain closed chain:(閉鏈)(閉鏈) 每一構(gòu)件至少含有兩個運動每一構(gòu)件至少含有兩個運動副元素副元素,動其中幾桿,其余各動其中幾桿,其余各桿便于傳遞運動,廣泛使用桿便于傳遞運動,廣泛使用 open chain:(開鏈)(開鏈) 一個以上的構(gòu)件只有一個運動副一個以上的構(gòu)件只有一個運動副元素應(yīng)用于機械手,挖掘機,機元素

13、應(yīng)用于機械手,挖掘機,機器人,多自由度器人,多自由度 conclusion:types of kinematic chain if a link of the kinematic chain is fixed as the frame機架機架, then the kinematic chain becomes mechanism.mechanism driving links:have their own independent motion driven links:generate the expected output motion(output links)abcddriving li

14、nkframedriven linkdriven link 2.3 the kinematic diagram of a mechanism 2.3.1 definition2.3.2 representation of a kinematic pair 2.3.3 the representation of a link in the kinematic diagram 2.3.4 procedures for drawing the kinematic diagram of a mechanism 2.3.1 definition不考慮與運動無關(guān)的因素(外形,尺寸,具體構(gòu)造),不考慮與運動

15、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動副的相對僅用簡單線條,符號,按一定比例表示各運動副的相對位置位置.this diagram is used only to express the relationship between the motions of links, it should be simple but provide all necessary (but not redundant多余的多余的) information determining the relative motion of all links. the kinematic d

16、iagram of the mechanism 機構(gòu)運動簡圖機構(gòu)運動簡圖attention: it should be simple but provide all necessary (but not redundant) information determining the relative motion of all links. according to specified symbols(符號符號). the kinematic diagram should be drawn to scale(按比例按比例). if not, such a diagram is called th

17、e schematic diagram(機構(gòu)示意圖) of the mechanism.2.3.2 representation of a kinematic pair 轉(zhuǎn)動副轉(zhuǎn)動副 revolute pair:(關(guān)鍵畫出轉(zhuǎn)軸位置關(guān)鍵畫出轉(zhuǎn)軸位置) the shaded(帶陰影線帶陰影線) links represent the frame.a revolute is conveniently(方便地方便地) represented by a small circle placed at the centre of the revolute no matter how large its ra

18、dius(半徑半徑) is. xy121111122222122211移動副移動副 sliding pair (關(guān)鍵畫出相對移動的方向,導(dǎo)路關(guān)鍵畫出相對移動的方向,導(dǎo)路 )the shaded(帶陰影帶陰影線線) links represent the frame121212(a)(b)(c)121212(a)(b)(c)121212(a)(b)(c) the actual shape and dimensions of the cross section(橫截面橫截面) of the sliding pair has no influence (影響影響) on the kinematics

19、 of the mechanism.attention: the centerline of the sliding pair in the kinematic diagram must be parallel(平行平行) to the pathway(導(dǎo)路導(dǎo)路) in the mechanism. aaaaabbbbb1111122222 any one link can be drawn as a sliding block while the other is drawn as a guide bar(導(dǎo)桿導(dǎo)桿). the following five diagrams are equi

20、valent.齒輪副齒輪副gear pair:凸輪副凸輪副cam:need actual cam contour (輪廓輪廓) and end profile (外外形形)of follower(從動件從動件). 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)件雙副構(gòu)件):a link with

21、 more than two pair elements can be represented by a hatched(陰影線的陰影線的) or welded(焊焊接的接的) polygon(多邊形多邊形) with pair elements at corners.note the differences between the following two groups of figures:abcabcabcbac32211abcabcabcbac32211the special representative(有代表性的有代表性的) symbols(符符號號) used in a kin

22、ematic diagram for some common mechanisms are listed in table 2-1(p9).2.3.4 procedures for drawing the 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

23、) draw the schematic diagram機構(gòu)示意圖機構(gòu)示意圖4) measure kinematic dimensions5) select scale )( )( mmdiagraminlengthmlengthactual= 6)draw the kinematic diagram of the mechanism.oscillating guide-bar mechanismoscillating guide-bar mechanismoscillating guide-bar mechanismcrank and oscillating block mechanismc

24、rank and oscillating block mechanismcrank and oscillating block mechanismbacd4dacb123123ex. : circular disk 1 rotates relative to the frame 4 about a fixed axis(軸軸) a. the link 3oscillates(擺動擺動) about a fixed axis d. the circular disk 1 matches(配合配合) with a hole on circular disk 2. the circular disk

25、 2 matches with a large hole on the link 3. bacd4dacb1231232.4 degree of freedom 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 motionabcd1234123f=1=3 2.4.1 definition機構(gòu)中各構(gòu)件相對于機架所能有的獨立運動的數(shù)目機構(gòu)中各構(gòu)件相對于機架所能有的獨立運

26、動的數(shù)目 the dof of the mechanism ordof : the number of independent coordinates required to define its position.2.4.2 structural 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

27、 planar mechanism f=3n-2pl-phexample1:2.4.3 condition for a mechanism to have a determined motion104233fabcd2341如果有兩個原動件,那么該機構(gòu)會從最弱構(gòu)件處損壞。如果有兩個原動件,那么該機構(gòu)會從最弱構(gòu)件處損壞。 the number of the driving linksthe dof of mechanism, it will be broken example2:鉸鏈五桿機構(gòu):鉸鏈五桿機構(gòu):205243fabcde1234514abcd1234441a15eb2d32cc3d如果

28、只給一個如果只給一個原動件,機構(gòu)原動件,機構(gòu)運動不確定運動不確定 the number of the driving links 0,f0,原動件數(shù)原動件數(shù)=f=f,運動確定,運動確定原動件數(shù)原動件數(shù)fff,機構(gòu)破壞,機構(gòu)破壞conclusion:2.5.1 compound hinge 2.5.2 passive dof ( 局部自由度局部自由度 )2.5.3 redundant constraints2.5 points for attention during the calculation of dof2.5.1 compound hinge the number of revolut

29、es in a compound hinge=one less than the number of links joined at that hinge. 由由m個構(gòu)件組成的復(fù)合鉸鏈應(yīng)按照個構(gòu)件組成的復(fù)合鉸鏈應(yīng)按照 m-1個轉(zhuǎn)個轉(zhuǎn)動副計算。動副計算。multiple joints(compound hinge)example:1010273fa ab bd dc ce ef f2.5.2 passive dof ( 局部自由度局部自由度 )213233f112223f2 21 1a ac cb b4 43 32 21 1a ac cb b3 3 delete the passive dof

30、by welding the roller to the follower, then calculate the dof of mechanism. 將滾子將滾子“焊接焊接”在從動件上,消除局部自由在從動件上,消除局部自由度,再計算機構(gòu)自由度。度,再計算機構(gòu)自由度。2.5.3 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,這種不起獨立限制作用的約束稱為虛約束。復(fù)的,這種不起獨立限制作用的約束稱為虛約束。 006243f104233f delete the redundant constraints

31、during the calculation of dof. 去除虛約束,再計算機構(gòu)自由度。去除虛約束,再計算機構(gòu)自由度。虛約束常出現(xiàn)的場合虛約束常出現(xiàn)的場合(1) two links are connected by more than one parallel sliding pairs(2)two links are connected by more than one revolute pair whose axes coincide(重合)。(重合)。(3)two links are connected by more than one higher pair whose commo

32、n normals passing through the points of contact coincide.3aobnn12 however, if their common normals (公法線公法線) do not coincide(重合重合), then both higher pairs should be counted. nnnnnnnnaabb(4) the distance between two points on two links remains constant during the motion of the mechanism,adding one lin

33、k and two revolutes create a redundant constraints.(5) the locus of a point is a straight line,adding one link with one 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=1a4312bcedab=bc=bdba4123ce5dfa4312bcedab=

34、bc=bdba4123ce5df(6) symmetrical or duplicated structurein order to transmit(傳輸傳輸) more power, many pinions(小齒輪小齒輪) are distributed(分布分布) symmetrically in space. only one pinion should be counted.note:gear 1, gear 3, and link 4 constitute(組成組成) a compound hinge(復(fù)合鉸復(fù)合鉸鏈鏈). 齒輪a243c5d16bexample2 n=7,pl=

35、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 shou

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