【正文】
nisms may be categorized in several different ways to emphasize their similarities and differences. One such grouping divides mechanisms into planar, spherical, and spatial categories. All three groups have many things in mon。 the criterion, which distinguishes 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。 ., 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 pletely described by their radial projections, or shadows, on the surface of a sphere with properly chosen center. Hooke39。 it is not a reality. The axes as produced in a shop — in any shop, no matter how good — will onlybe 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 because of the looseness of the running fits of the bearings or flexibility of the links. A mon way of pensating for small no parallelism is to connect the links with selfaligning bearings, actually spherical joints allowing threedimensional rotation. Such a planar linkage is thus a lowgrade spatial linkage. Degrees of Freedom A threebar linkage (containing three bars linked together) is obviously a rigid frame。 it has two degrees of freedom. Linkages with one degree of freedom have constrained motion。 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 inputoutput relationship, can be obtained with a fourbar linkage. These four mechanisms are said to be inversions of the basic linkage. SliderCrank Inversions When one of the pin connections in a fourbar 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 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 fixe