Mechanisms can 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 common; the criterion which distinguishes the groups, however, is to be found in the characteristics of the motions of the link.

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. 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 follow, and the slider-crank mechanism are familiar examples of planar mechanism. The vast majority of mechanism in use today is planar.

Planar mechanisms utilizing only lower pairs are called planar linkages; they may include only revolve and prismatic pairs. Although a planar pair might theoretically be included, this would impose no constraint and thus be equivalent to an opening in the kinematic chain. Planar motion also requires that axes of all prismatic pairs and all revolute axes be normal to the plane motion.

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; 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 radiap projections, or “shadows”, on the surface of a sphere with properly chosen center.

Spherical linkages are constituted entirely of revolute pairs. A spherical 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 spherical linkages, the axes of all revolute pairs must intersect at a point.

Spatial mechanisms, on the other hand, include no restrictions on the relative motions of the particles. The motion transformation is not necessary coplanar, nor must it be concentric. A spatial mechanism may have particles with loci of double curvature. Any linkage which contain a screw pair, for example, is a spatial mechanism, since the relative motion within a screw pair is helical.