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1、<p> Mechanism </p><p> Introduction to Mechanism </p><p> Mechanisms may be categorized in several different ways to emphasize their similarities and differences. One such grouping divi
2、des mechanisms into planar, sphe-rical, and spatial categories. All three groups have many things in common; the criterion, which distinguishes the groups, however, is to be found in the characteristics of the motions of
3、 the links. </p><p> A planar mechanism is one in which all particles describe plane curves in space and all these curves lie in parallel planes; i. e., the loci of all points are plane curves parallel to a
4、 single common plane. This characteristic makes it possible to represent the locus of any chosen point of a planar mechanism in its true size and shape on a single drawing or figure. The motion transformation of any such
5、 mechanism is called coplanar. The plane four-bar linkage, the plate cam and follower, and the </p><p> A spherical mechanism is one in which each link has some point which remains stationary as the linkage
6、 moves and in which the stationary points of all links lie at a common location; i.e., the locus of each point is a curve contained in a spherical surface, and the spherical surfaces defined by several arbitrarily chosen
7、 points are all concentric. The motions of all particles can therefore be completely described by their radial projections, or "shadows", on the surface of a sphere with properly</p><p> Spherical
8、 linkages are constituted entirely of revolute pairs. A spheric pair would produce no additional constraints and would thus be equivalent to an opening in the chain, while all other lower pairs have nonspheric motion. In
9、 spheric linkages, the axes of all revolute pairs must intersect at a point.</p><p> Spatial mechanisms, include no restrictions on the relative motions of the particles. The motion transformation is not ne
10、cessarily coplanar, nor must it be concentric. A spatial mechanism may have particles with loci of double curvature. Any linkage which contains a screw pair, for example, is a spatial mechanism, since the relative motion
11、 within a screw pair is helical. </p><p> Thus, the overwhelming large category of planar mechanisms and the category of</p><p> spherical mechanisms are only special cases, or subsets, of the
12、 all-inclusive category spatial mechanisms. They occur as a consequence of special geometry in the particular orientations of their pair axes: If planar and spherical mechanisms are only special cases of spatial mechanis
13、ms, why is it desirable to identify them separately?Because of the particular geometric conditions, which identify these types, many simplifications are possible in their design and analysis. As pointed out earlier, i<
14、;/p><p> Since the vast majority of mechanisms in use today are planar, one might question the need of the more complicated mathematical techniques used for spatial mechanisms. There are a number of reasons wh
15、y more powerful methods are of value even though the simpler graphical techniques have been mastered. </p><p> 1. They provide new, alternative methods, which will solve the problems in a different way. Thu
16、s they provide a means of checking results. Certain problems by their nature may also be more amenable to one method than another. </p><p> 2. Methods which are analytical in nature are better suited to sol
17、ution by calculator or digital computer than graphical techniques.</p><p> 3. Even though the majority of useful mechanisms are planar and well suited to graphical solution, the few remaining must also be a
18、nalyzed, and techniques should be known for analyzing them. </p><p> 4. One reason that planar linkages are so common is that good methods of analysis for the more general spatial linkages have not been ava
19、ilable until quite recently. Without methods for their analysis, their design and use has not been common, even though they may be inherently better suited in certain applications.</p><p> 5. We will discov
20、er that spatial linkages are much more common in practice than their formal description indicates. </p><p> Consider a four-bar linkage. It has four links connected by four pins whose axes are parallel. Thi
21、s "parallelism" is a mathematical hypothesis; it is not a reality. The axes as produced in a shop — in any shop, no matter how good — will only-be approximately parallel. If they are far out of parallel, there
22、will be binding in no uncertain terms, and the mechanism will only move because the "rigid" links flex and twist, producing loads in the bearings. If the axes are nearly parallel, the mechani</p><p&
23、gt; Degrees of Freedom </p><p> A three-bar linkage (containing three bars linked together) is obviously a rigid frame; no relative motion between the links is possible. To describe the relative positio
24、ns of the links in a four-bar linkage it is necessary only to know the angle between any two of the links. This linkage is said to have one degree of freedom. Two angles are required to specify the relative positions of
25、the links in a five-bar linkage; it has two degrees of freedom. Linkages with one degree of freedom have const</p><p> Four-Bar Mechanisms </p><p> When one of the members of a constrained l
26、inkage is fixed, the linkage becomes a mechanism capable of performing a useful mechanical function in a machine. On pin-connected linkages the input (driver) and output (follower) links are usually pivotally connected t
27、o the fixed link; the connecting links (couplers) are usually neither inputs nor outputs. Since any of the links can be fixed, if the links are of different lengths, four mechanisms, each with a different input-output re
28、lationship, can be</p><p> Slider-Crank Inversions </p><p> When one of the pin connections in a four-bar linkage is replaced by a sliding joint, a number of useful mechanisms can be obtaine
29、d from the resulting in Fig. 1 (top) the connection between links 1 and 4 is a sliding joint that permits block 4 to slide in the slot in link 1. It would make no difference, kinematically, if link 1 were sliding in a ho
30、le or slot in link 4. </p><p> If link 1 in Fig. 1 (top) is fixed, the resulting slider-crank mechanism is shown in Fig. 1 (center). This is the mechanism of a reciprocating engine. The block4 represents th
31、e piston; link 1, shown shaded, is the block that contains the crankshaft bearing at A and the cylinder; link 2 is the crankshaft and link 3 the connecting rod. The crankpin bearing is at B, the wrist pin bearing at C. T
32、he stroke of the piston in twice AB, the throw of the crank. </p><p> The slider-crank mechanism provides means for converting the translator motion of the pistons in a reciprocating engine into rotary moti
33、on of the crankshaft, or the rotary motion of the crankshaft in a pump into a translator motion of the pistons. In Fig. 1 (center), when B is in position B', the connecting rod would interfere with the crank if both
34、were in the same plane. This problem is solved in engines and pumps by offsetting the crankpin bearing from the crankshaft bearing. By using an ecc</p><p> In Fig.1 (bottom) the crankpin bearing at B has b
35、ecome a large circular disk pivoted at A with an eccentricity or throw AB. The connecting rod has become the eccentric rod with a strap that encircles and slides on the eccentric. The mechanisms in the center and bottom
36、drawings of Fig. 1 are kinematically equivalent. </p><p> By fixing links 2, 3, and 4 instead of link 1, three other inversions of the linkage in Fig. 1 (top) are obtained.</p><p><b> Fi
37、g.1</b></p><p><b> 譯文:</b></p><p><b> 機(jī)構(gòu)</b></p><p><b> 機(jī)構(gòu)</b></p><p> 機(jī)構(gòu)可用幾種不同的方式進(jìn)行分類。以強(qiáng)調(diào)其相近與差異之處。其中一種分類法將機(jī)構(gòu)分為平面、球面與空間三類。
38、所有這三類有許多共同之處;然而從連桿運(yùn)動(dòng)的特性可以看出區(qū)分這幾類機(jī)構(gòu)的標(biāo)準(zhǔn)。</p><p> 平面機(jī)構(gòu)是這樣一種機(jī)構(gòu),其所有質(zhì)點(diǎn)在空間描出的是平面曲線,并且所有這些曲線都在平行平面上,也就是說,所有點(diǎn)的軌跡都與一個(gè)單一公共平面相平行的平面曲線。這一特點(diǎn)使得有它可能代表的軌跡所選擇的任何質(zhì)點(diǎn)的平面機(jī)構(gòu)的位置,這個(gè)平面機(jī)構(gòu)在一個(gè)單一的圖形或模型中有其真實(shí)的大小和形狀。任何這類機(jī)構(gòu)的轉(zhuǎn)變,就是所謂的共面。平面四連桿
39、機(jī)構(gòu)、凸輪、導(dǎo)桿機(jī)構(gòu),以及曲柄滑塊機(jī)構(gòu)是我們所熟悉的平面機(jī)構(gòu)。在今天所使用的絕大多數(shù)的機(jī)構(gòu)是平面機(jī)構(gòu)。</p><p> 一種球形機(jī)構(gòu)是平面機(jī)構(gòu)之一,在各個(gè)桿件有一些質(zhì)點(diǎn),這仍然是平穩(wěn)傳動(dòng),就像是聯(lián)結(jié)的移動(dòng)而且在其中的所有桿件的固定質(zhì)點(diǎn)的各個(gè)連接,都處于一個(gè)共同的位置,即每一點(diǎn)的運(yùn)動(dòng)軌跡是一個(gè)曲線并處于一個(gè)球面內(nèi),幾個(gè)任意選擇的質(zhì)點(diǎn)所確定的球面都是同心的。因此,所有質(zhì)點(diǎn)的運(yùn)動(dòng)都可以完全由它們的徑向向外的方向來分
40、析,或者稱為“影子” ,位于正確選擇的中心的球的表面?;⒖说钠毡槁?lián)結(jié),就是一個(gè)球形的機(jī)構(gòu)最熟悉的例子。</p><p> 球形的聯(lián)結(jié),構(gòu)成了完整的運(yùn)動(dòng)副。一個(gè)球形聯(lián)結(jié)一個(gè)運(yùn)動(dòng)副不會(huì)產(chǎn)生任何額外的約束,并會(huì)因此等于鏈中的開環(huán),而所有其他低副,則不是球形運(yùn)動(dòng)。在球形的聯(lián)結(jié)中,所有運(yùn)動(dòng)副的軸必須相交于一點(diǎn)。</p><p> 在相對(duì)運(yùn)動(dòng)的質(zhì)點(diǎn)中,空間機(jī)構(gòu)不包括約束。機(jī)構(gòu)運(yùn)動(dòng)的傳動(dòng),并不一定是
41、共面,也不一定是同心。一個(gè)空間的機(jī)構(gòu)可能有質(zhì)點(diǎn)的運(yùn)動(dòng)軌跡發(fā)生雙面彎曲。任何帶有螺旋副的聯(lián)結(jié),舉例來說,它是一個(gè)空間的機(jī)構(gòu),因?yàn)槁菪钡南鄬?duì)運(yùn)動(dòng)是螺旋狀的。</p><p> 因此,絕大多數(shù)的大的平面機(jī)構(gòu)和類似球形的機(jī)構(gòu),只有在特殊情況下,或者在亞特殊情況下,包含各方的類似空間的機(jī)構(gòu)。在兩個(gè)軸上的特殊方向上,它們作為特殊幾何關(guān)系作用的結(jié)果: 如果平面和球形機(jī)構(gòu)僅僅是空間機(jī)構(gòu)的特殊情況,為什么要分別分析來它們呢?由
42、于用來區(qū)分這些類型的特殊幾何條件,在他們的設(shè)計(jì)和分析中,許多是可能得到簡(jiǎn)單化的。 若能更快的指出來,從一個(gè)單一的方向去觀察一個(gè)在真實(shí)的大小和形狀的平面機(jī)構(gòu)的所有質(zhì)點(diǎn)的運(yùn)動(dòng)是可能的。換句話說,所有的運(yùn)動(dòng)在一個(gè)方向上可以由圖形來表示。 因此,圖解技法非常適合去解決它們的問題。 因?yàn)榭臻g機(jī)制不可能全部都有這種幾何關(guān)系,將其視覺化變得更加困難,并且必須開發(fā)出更強(qiáng)的技術(shù)來對(duì)它們進(jìn)行分析。</p><p> 因?yàn)楝F(xiàn)在所使用
43、的絕大多數(shù)機(jī)構(gòu)是平面機(jī)構(gòu),也許有的人對(duì)于空間機(jī)制更復(fù)雜的數(shù)學(xué)技術(shù)的需要會(huì)表示懷疑。雖然更簡(jiǎn)單的圖解法已經(jīng)為我們所掌握,但是有很多的原因可以告訴我們?yōu)槭裁锤訌?qiáng)有力的方法是有價(jià)值。 </p><p> 1.它們提供新的、可交替的方法,這些方法可以用不同的方式解決問題。 因而他們能提供檢驗(yàn)結(jié)果的方法。具有它們的屬性的某些問題也可能比其他方法更有效的到解決。</p><p> 2.通過計(jì)算器
44、或數(shù)字計(jì)算機(jī),分析它們性質(zhì)的方法比圖解法更合適來分析問題。</p><p> 3.雖然大多數(shù)有用的機(jī)構(gòu)是平面機(jī)構(gòu)和非常適合對(duì)圖形分析,剩下的少數(shù)機(jī)構(gòu)也必須得到分析,并且也應(yīng)該有針對(duì)它們進(jìn)行分析的方法。</p><p> 4.平面聯(lián)結(jié)如此普遍的一個(gè)原因是在這之前能為更廣泛的空間聯(lián)結(jié)進(jìn)行分析的好方法還未得到應(yīng)用。雖然空間機(jī)構(gòu)也許在本質(zhì)上能更適合于某些應(yīng)用,但是沒有對(duì)他們進(jìn)行分析的方法,它們
45、的設(shè)計(jì)和用途就不一樣。</p><p> 5.我們發(fā)現(xiàn)空間連接比他們的外部結(jié)構(gòu)的描述在實(shí)踐應(yīng)用上是更加普遍的。</p><p> 考慮到四桿連接, 它由四個(gè)桿件相連,這些鏈接由四個(gè)軸為平行的銷連接。 這里的“平行性”只是一個(gè)數(shù)學(xué)假設(shè); 并不是真實(shí)的。 軸如果是由同一家生產(chǎn)的,無論有多好,都將只是近似平行。如果他們離平行差的太遠(yuǎn),組合起來都是不確定的,并且這種機(jī)構(gòu)只能移動(dòng),因?yàn)閯傂枣溄赢a(chǎn)
46、生彎曲和扭曲,會(huì)將負(fù)荷作用于銷軸上。如果銷軸是接近平行的,由于軸的松動(dòng)配合的松散性或聯(lián)結(jié)的靈活性,機(jī)械裝置同樣能夠運(yùn)轉(zhuǎn)。一個(gè)為非平行做微小補(bǔ)償?shù)钠毡榉椒ㄊ钦{(diào)用帶有自動(dòng)對(duì)準(zhǔn)軸的聯(lián)結(jié),實(shí)際上球形聯(lián)接允許三維旋轉(zhuǎn)。 因此,這樣的“平面”聯(lián)接是低級(jí)的空間聯(lián)接。</p><p><b> 自由度</b></p><p> 三桿機(jī)構(gòu)(包含在一起的三桿機(jī)構(gòu))明顯是一個(gè)剛性框架;
47、 在鏈接之間的相對(duì)運(yùn)動(dòng)是不可能的。 要分析四桿機(jī)構(gòu)的桿件的相對(duì)位置,就有必要明確任何兩個(gè)桿件的角度。 這種聯(lián)結(jié)有一個(gè)自由度。 在五桿機(jī)構(gòu)中,要求二個(gè)角度來指定桿件的相對(duì)位置; 它有二個(gè)自由度。只有一個(gè)自由度的聯(lián)結(jié)有強(qiáng)制運(yùn)動(dòng); 即桿件上的所有質(zhì)點(diǎn)在其他的桿件上的軌道是固定和確定的。通過假設(shè),質(zhì)點(diǎn)的運(yùn)動(dòng)軌跡最容易得到或形象化,運(yùn)動(dòng)軌道所在的桿件是固定的,然后在限制條件下以一種協(xié)調(diào)的方式移動(dòng)其他的桿件。</p><p>
48、;<b> 四桿機(jī)構(gòu)</b></p><p> 當(dāng)受約束的聯(lián)結(jié)的其中一個(gè)聯(lián)結(jié)件受固定時(shí),聯(lián)結(jié)成為機(jī)器中能起到一個(gè)有用的機(jī)械作用的機(jī)構(gòu)。在銷聯(lián)結(jié)中,輸入件(主動(dòng)件)和(輸出桿件)從動(dòng)件聯(lián)結(jié)與固定桿件連接,這種連接常常起到很關(guān)鍵的作用; 管道桿件(連接件)通常既不是輸入件也不是輸出件。 因?yàn)槠渲腥我粋€(gè)桿件都可以是固定的,如果桿件具有不同的長(zhǎng)度,四根桿中其中每一個(gè)都有不同的輸入-輸出關(guān)系,可以
49、由四桿連接來實(shí)現(xiàn)。 這些四桿機(jī)構(gòu)被認(rèn)為是基本連接的倒置。</p><p><b> 滑塊-曲柄轉(zhuǎn)換</b></p><p> 當(dāng)四桿連接中的其中一個(gè)銷連接由滑塊接頭所替代時(shí),大部分有用的機(jī)構(gòu)可以由圖1(上)中桿1和桿四的連接來實(shí)現(xiàn)。桿1與桿4的連接是一個(gè)滑動(dòng)連接,由滑塊4在桿1上滑動(dòng)。如果桿1在一個(gè)孔上滑動(dòng)或者在滑塊4的槽上滑動(dòng),從運(yùn)動(dòng)學(xué)的角度來說,是沒有什么區(qū)別
50、的。</p><p> 如果在圖1 (上)的桿1是固定的,使得滑塊-曲柄轉(zhuǎn)換機(jī)構(gòu)得以形成,如圖1(中)所示,它是往復(fù)式發(fā)動(dòng)機(jī)的機(jī)構(gòu)。 滑塊4代表活塞; 連接1封閉,它包含有A處的軸和發(fā)動(dòng)機(jī)汽缸; 桿2是發(fā)動(dòng)機(jī)曲柄以及桿3為連桿。曲柄軸位于B處,活塞中的銷位于C處。轉(zhuǎn)動(dòng)AB轉(zhuǎn)動(dòng)兩次,活塞完成一次沖程。 </p><p> 滑塊-曲柄轉(zhuǎn)換機(jī)構(gòu)為往復(fù)式發(fā)動(dòng)機(jī)的活塞運(yùn)動(dòng)轉(zhuǎn)換成發(fā)動(dòng)機(jī)軸的轉(zhuǎn)動(dòng)或在
51、泵的軸的轉(zhuǎn)動(dòng)轉(zhuǎn)換為活塞的運(yùn)動(dòng)提供理論依據(jù)。 在圖1 (中)中,當(dāng)B在位置B'時(shí),如果連桿與曲柄在同一平面上,它們將發(fā)生干涉。這個(gè)問題在引擎和泵中可通過偏置曲柄銷和機(jī)軸銷得以解決。 通過使用在曲柄位置的偏心桿機(jī)構(gòu),就沒必要使用偏置法來解決,而且投入少卻能獲得同樣的效果。</p><p> 圖1(下)中,B處的曲柄銷軸承變成了一個(gè)鉚接在A點(diǎn)的大圓盤。具偏心率或行程AB。連接桿變成了偏心桿,它帶有一條在偏心輪
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