By Faydor L. Litvin, Alfonso Fuentes

This revised, increased version covers the idea, layout, geometry, and manufacture of all kinds of gears and kit drives. a useful reference for designers, theoreticians, scholars, and brands, the second one variation comprises advances in apparatus idea, equipment production, and laptop simulation. one of the new issues are: new geometry for gears and pumps; new layout techniques for planetary equipment trains and bevel apparatus drives; an stronger strategy for pressure research; new equipment of grinding and equipment shaving; and new concept at the simulation and its program. First version released by means of Pearson schooling Hb (1994): 0-132-11095-4

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3) where ρ is drawn to point M from an arbitrary point on the line of action of ω (2) , for instance, from point O2 . An alternative equation for v(2) is based on the substitution of the sliding vector ω (2) with the line of action O2 − O2 by an equal vector that passes through Of and by the vector-moment, m = R × ω (2) . 4) Here, R is a position vector that is drawn from Of to an arbitrary point O2 on the line of action of ω (2) . For instance, we may choose that O2 coincides with O2 and R = Of O2 = E.

In some cases, the gear ratio is given by a function m21 = f (φ1 ) where φ1 is the input parameter, the angle of rotation of body 1. Then, the instantaneous center of rotation translates along O1 O 2 in the process of transformation of rotation. The centrode i is the locus of instantaneous centers of rotation in coordinate system Si (i = 1,2). We may imagine that point I (it translates along O1 O 2 or it is at rest) traces out the centrode while coordinate system S i rotates about Oi . 2: Rotation between parallel axes in the same direction.

According to Eq. 30), matrix Lma is  1 0  Lma =  0 cos γ 0 sin γ  0  − sin γ  . 25) cos γ Coordinate systems S n and S b which are rigidly connected to each other are rotated about cm = km through angle φ. Matrix Lnm , in accordance with Eqs. 30), is represented by  cos φ  Lnm =  − sin φ sin φ cos φ 0 0 0   0. 26) 1 Matrix product Lnm Lma = Lna is  cos φ  Lna =  − sin φ 0 sin φ cos γ cos φ cos γ sin γ − sin φ sin γ   − cos φ sin γ  . 5: General case of coordinate transformation.

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