Methods for shaping the teeth of spherical gears

A method for proportioning the shape of the teeth of a pair of mating gears designed to transmit rotational forces between two elements which are each rotatable about a respective one of two axes that variably intersect with each other when in one of (a) the same plane and (b) parallel planes projected one upon the other, said method comprising the steps of:

• constructing a respective pitch surface and a respective pitch circle for each of said mating gears, each said pitch surface being in the form of a respective pitch sphere, and said two pitch spheres and two pitch circles being constructed in one of the positions:
• (a) wherein said two pitch spheres are concentric and have radii which are substantially identical, and each said pitch circle is, respectively, a great circle on a respective one of said substantially identical spheres so that said pitch circles effectively intersect with each other at two points and said gears share two meshing points separated by 180.degree. when rotating relative to each other at a 1:1 ratio, and
• (b) wherein said two pitch spheres are not concentric and are tangent at only one point, and where each said pitch circle is a great circle on a respective one of said tangent spheres so that said pitch circles intersect with each other at only one point and said gears share only a single meshing point when rotating relative to each other;
• determining the desired diameter of the pitch sphere of one of said gears whose pitch circle is the great circle on one of (a) said concentric pitch spheres and (b) the larger one of said two tangent pitch spheres;
• calculating the diametral pitch necessary to provide each tooth with a normal chordal thickness sufficient to support the rotational forces expected to be transferred between said two rotatable elements;
• and
• forming the central portion of each lengthwise tooth surface of each mating tooth of at least one of said mating gears, when viewed on the respective pitch sphere of said one gear, as an arc of a first single circle with a diameter selected so that, when said gears are rotating in a driving and driven relationship, said intersecting axes can be varied over a continuous range of angles extending from 180.degree. to a predetermined maximum angle differing from 180.degree..