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This paper sets forth a method of arriving analytically at a pair of gear tooth curves which will fulfill certain prescribed conditions. The method may also be used to find a curve which will mesh with a given curve and produce a constant angular velocity ratio, e.g., the mating curve for a circular pin tooth.

The senior authors are to be congratulated on the excellence of their teaching and research, as witness the junior author, and this, and other publications. Their forthcoming book, Kinematic Synthesis, will be the first of its kind in English and will fill a long-felt need. The present paper nicely avoids the ambiguities which arise from the multiple values of the inverse trigonometric functions, by use of the iterative method. For example, in analyzing a fourbar linkage by ordinary means, one in general obtains both the "open" and "crossed" forms of the mechanism. This avoidance of ambiguity is emphasized by the fact that the erroneous statement following equation (34) does not invalidate any of the results. The submatrix referred to is the direction cosine matrix between the coordinate systems fixed in adjacent members of the mechanism. If onty three members are specified, an ambiguity of sign remains which is removed by specifying four elements, not all in the same row, or column, or minor.

Mathematicians of the previous generation would have called the results obtained in this paper by Professor Yang "elegant" and I can think of no better word to describe them. His equation (8), which gives both the acceleration of a point A fixed in a rigid body and the rate of change of the momentum of the body