Recirculating-ball epicyclic gear train

A recirculating-ball epicyclic gear train comprising three coaxial cylindrical cages (2, 3, 4) of which one cage (2) is fixed stationary and the inner cage (4) and the outer cage (2) are provided with helical tracking grooves (5, 6) and ball escape grooves oriented oppositely to the direction of the grooves (5, 6), and the intermediate cage (3) has open end recesses (9), and balls (1) accommodated in the recesses (9) and adapted to interact with the grooves of the cages (2, 4), wherein the ball escape groove 7 on the inner cage 4 and between the conjugation points 01 and 02 on the entrance and exit areas thereof is arranged along an axis 11 passing through the center of the balls 10 and appears as two similar mirror-opposed portions of curves 12 and 13 which are described by an equation of the type y1,2=axn1,2 in a local coordinate system;

• one of said curves is associated with the coordinate system (x1, y1) disposed on an extension of the helical tracking groove 5, while the other curve is associated with the coordinate system (x2, y2) disposed on an extension of the helical return groove 7, while the reference points 01 and 02 of both coordinate systems are spaced apart from the point C of mutual intersection of the extension of the center lines of the helical tracking groove 5 and of the helical ball escape groove 7 at the entrance and exit, respectively, by the value of L≧D/Zr cos φ, and the same angle of slope of tangent lines to the curves 12, 13 in local coordinates is maintained at the point T of conjugation of said curves, here x1,2 relative local coordinates read from their origins in fractions of the length of segment L, n an integer exceeding 2 which is the same for both curves being conjugated, D diameter of the center circumference of the balls 10, φ angle of helix of the tracking groove 5 on the inner cage 4 relative to the circumferential direction, Zr number of recesses 9 in the intermediate cage 3.