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The design of a novel transmission for speed reduction is reported in this paper. The transmission is based on the layout of pure-rolling indexing cam mechanisms, for it is intended to eliminate backlash and friction, which are the main drawbacks of gear transmissions. The design relies on a unified methodology for indexing cam mechanisms, whereby the same procedure is used to design planar, spherical, and spatial mechanisms. Two versions of the speed reducer, that we term Speed-o-Cam, are described here, namely, planar, to couple shafts of parallel axes, and spherical to couple shafts of intersecting axes. By means of a cascade of two planar versions of Speed-o-Cam, moreover, coaxial shafts can be coupled. Moreover, contrary to other alternatives to gear transmissions, such as harmonic drives or epicyclic transmissions, Speed-o-Cam caters to shafts with either parallel or intersecting axes; in the latter case, moreover, the angle at which the axes intersect can vary from 0 degrees to 180 degrees continuously. The design with shaft axes at 0 degrees leads to an internal cam, i.e., one with its axis external to the axes of the follower and the roller in contact; for shaft axes at 180 degrees, the design leads to an external cam, i.e., one with its axis lying between those of the follower and the roller in contact.

In this paper the ruled surfaces of two rigid bodies that are in contact while moving with a prescribed time-varying angular-velocity ratio are generated. These are then used as the contact surfaces of indexing cam mechanisms. In this way, planar, spherical, and spatial mechanisms are synthesized in a unified framework, the pressure angle, for all these cases, being analyzed. The approach is illustrated with various examples.

The solid modeling of bevel gears has been recognized as a major design challenge. Various approaches have been proposed to approximate the theoretical involute-generated contact surface of bevel gears. As a means to accurately represent contact surfaces of these gears, the exact spherical involute is introduced here. The solid models of straight and spiral bevel gears are obtained by applying simple sweeping techniques to their tooth profiles, which are described by the exact spherical involute. Furthermore, the volumetric properties of the modeled bevel gears are readily computed from their piecewise-linear approximation.

A novel method of synthesis of the surface geometry of spherical cam-oscillating roller-follower mechanisms is introduced. The approach aims at zeroing the sliding velocity between the cam and the roller, their respective geometries being thus obtained as conical surfaces. The pressure angle is analyzed in detail. Specific results are presented for the application of this synthesis technique to indexing cam mechanisms.