By Litvin F.L., Fuentes-Aznar A., Gonzalez-Perez I., Hayasaka K.

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1 shows the centrodes (as mating circles) of a gear mechanism with circular gears. For the purpose of simplification of drawings, only two profiles of teeth are shown in Fig. 1. The instantaneous point of contact of the tooth profiles is shown in Fig. 1 as I . (1) (2) Points Mi and Mi in Fig. 1 represent points of intersection of neighboring (1) (2) profiles with the centrodes of radii r p and r p . The distance p between two neigh( j) boring points Mi ( j = 1, 2) is measured along the arc of the respective centrode and is determined as p = mπ, where m is the module of the gears.

Such requirements may be fulfilled by: (a) Application of multithread noncircular gears wherein φ1 max ≥ 2π (see Fig. 4). 5). 1 shows polar axis OA and two points M0 and M2 of the polar curve infinitesimally close to each other. Vector t is the tangent to the polar curve at point M0 . 1. For derivation of angle µ formed by extended position vector r (θ ) and tangent t to polar curve. 1) Angle µ (Fig. 1) is formed by extended position vector OM0 and tangent t. 1) is the basic equation for the determination of tangent t to polar curve.

1). The great advantage of application of a multigear drive formed by noncircular gears is the reduction of the pressure angle of the centrodes and their favorable shape (see Chapter 10). 3 Developments Related with Theory of Gearing Teeth of the same noncircular gear have different profiles, and this is the main difference between a circular and noncircular gear. The geometry of teeth and their profiles must be based on the concepts applied in differential geometry for planar curves. 12. 1; (c) shape of textile ball wherein noncircular gears are not applied (ε1 = 0).