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1、Mechanism Introduction to Mechanism Mechanisms may be categorized in several different ways to emphasize their similarities and differences. One such grouping divides mechanisms into planar, sphe-rical, and spatial categories. All three groups have many things in common; the criterion, which disting
2、uishes the groups, however, is to be found in the characteristics of the motions of the links. 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 single common plane
3、. 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 mechanism is called coplanar. The plane four-bar linkage, the plate cam and follower, and the slide
4、r-crank mechanism are familiar examples of planar mechanisms. The vast majority of mechanisms in use today are planar. A spherical mechanism is one in which each link has some point which remains stationary as the linkage moves and in which the stationary points of all links lie at a common location
5、; i.e., the locus of each point is a curve contained in a spherical surface, and the spherical surfaces defined by several arbitrarily chosen points are all concentric. The motions of all particles can therefore be completely described by their radial projections, or "shadows", on the surf
6、ace of a sphere with properly chosen center. Hooke's universal joint is perhaps the most familiar example of a spherical mechanism.Spherical linkages are constituted entirely of revolute pairs. A spheric pair would produce no additional constraints and would thus be equivalent to an opening in t
7、he chain, while all other lower pairs have nonspheric motion. In spheric linkages, the axes of all revolute pairs must intersect at a point.Spatial mechanisms, include no restrictions on the relative motions of the particles. The motion transformation is not necessarily coplanar, nor must it be conc
8、entric. 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 within a screw pair is helical. Thus, the overwhelming large category of planar mechanisms and the category ofspherica
9、l mechanisms are only special cases, or subsets, of the 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 mechanisms, why is it desirable t
10、o 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, it is possible to observe the motions of all particles of a planar mechanism in true size and shape from a si
11、ngle direction. In other words, all motions can be represented graphically in a single view. Thus, graphical techniques are well suited to their solution. Since spatial mechanisms do not all have this fortunate geometry, visualization becomes more difficult and more powerful techniques must be devel
12、oped for their analysis. 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 why more powerful methods are of value even though the simpler graphical tech
13、niques have been mastered. 1. They provide new, alternative methods, which will solve the problems in a different way. Thus they provide a means of checking results. Certain problems by their nature may also be more amenable to one method than another. 2. Methods which are analytical in nature are b
14、etter suited to solution by calculator or digital computer than graphical techniques.3. Even though the majority of useful mechanisms are planar and well suited to graphical solution, the few remaining must also be analyzed, and techniques should be known for analyzing them. 4. One reason that plana
15、r linkages are so common is that good methods of analysis for the more general spatial linkages have not been available 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.5. We w
16、ill discover that spatial linkages are much more common in practice than their formal description indicates. Consider a four-bar linkage. It has four links connected by four pins whose axes are parallel. This "parallelism" is a mathematical hypothesis; it is not a reality. The axes as prod
17、uced in a shop in any shop, no matter how good will only-be approximately parallel. If they are far out of parallel, there 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 near
18、ly parallel, the mechanism operates because of the looseness of the running fits of the bearings or flexibility of the links. A common way of compensating for small no parallelism is to connect the links with self-aligning bearings, actually spherical joints allowing three-dimensional rotation. Such
19、 a "planar" linkage is thus a low-grade spatial linkage. Degrees of Freedom 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 positions of the links in a four-bar linkage it is
20、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 the links in a five-bar linkage; it has two degrees of freedom. Linkages with one degree of freedom have constrained motion;
21、 i. e., all points on all of the links have paths on the other links that are fixed and determinate. The paths are most easily obtained or visualized by assuming that, the link on which the paths are required is fixed, and then moving the other links in a manner compatible with the constraints. Four
22、-Bar Mechanisms When one of the members of a constrained linkage 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 to the fixed link; the
23、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 relationship, can be obtained with a four-bar linkage. These four mechanisms are said to be inversions o
24、f the basic linkage. Slider-Crank Inversions When one of the pin connections in a four-bar linkage is replaced by a sliding joint, a number of useful mechanisms can be obtained 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
25、 the slot in link 1. It would make no difference, kinematically, if link 1 were sliding in a hole or slot in link 4. 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 the piston
26、; 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. The stroke of the piston in twice AB, the throw of the crank. The slider-crank mechanism
27、provides means for converting the translator motion of the pistons in a reciprocating engine into rotary motion 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 inte
28、rfere with the crank if both 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 eccentric-and-rod mechanism in place of a crank, no offsetting is necessary and very small throws can be obtained. In Fig.1 (bo
29、ttom) the crankpin bearing at B has become 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 drawings of Fig. 1 are kinematically equiva
30、lent. By fixing links 2, 3, and 4 instead of link 1, three other inversions of the linkage in Fig. 1 (top) are obtained. Fig.1譯文:機(jī)構(gòu)機(jī)構(gòu)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。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)。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(shuō),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
31、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)。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(lái)分析,或者稱為“影子” ,位于正確選擇的中心的
32、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。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(kāi)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)。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(lái)說(shuō),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。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
33、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(lái)它們呢?由于用來(lái)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(lái),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(shuō),所有的運(yùn)動(dòng)在一個(gè)方向上可以由圖形來(lái)表示。 因此,圖解技法非常適合去解決它們的問(wèn)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(jué)化變得更加困難,并且必須開(kāi)發(fā)出更強(qiáng)的技術(shù)來(lái)對(duì)它們進(jìn)行分析。 因?yàn)楝F(xiàn)在所使用的絕大多數(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
34、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。 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(wèn)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(wèn)題也可能比其他方法更有效的到解決。2通過(guò)計(jì)算器或數(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(lái)分析問(wèn)題。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。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(méi)有對(duì)他們進(jìn)行分析的方法,它們的設(shè)計(jì)和用途就不一樣。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。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(wú)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(lái)都是不確定的,并且
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