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 surface of a sph
6、ere with properly chosen center. Hookes 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 the chain, while
7、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 concentric. A spati
8、al 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 of spherical mechanisms a
9、re 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 to identify the
10、m 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 single direction
11、. 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 developed for their
12、 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 techniques have be
13、en 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 better suited t
14、o 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 planar linkages ar
15、e 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 will discover
16、 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 produced in a shop in any sh
17、op, 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 nearly parallel, the mechanism operates
18、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 a planar linkage is thus a low-grad
19、e 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 necessary only to know the angle between any two
20、 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； i. e., all points on all of the links have path
21、s 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-Bar Mechanisms When one of the members of a con
22、strained 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 connecting links (couplers) are usually neither
23、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 of 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
