Download Gear Geometry and Applied Theory, Second Edition by Faydor L. Litvin, Alfonso Fuentes PDF
By Faydor L. Litvin, Alfonso Fuentes
This revised, extended version covers the idea, layout, geometry, and manufacture of every kind of gears and equipment drives. a useful reference for designers, theoreticians, scholars, and brands, the second one variation comprises advances in equipment concept, equipment production, and computing device simulation. one of the new subject matters are: new geometry for gears and pumps; new layout techniques for planetary equipment trains and bevel apparatus drives; an improved strategy for rigidity research; new tools of grinding and kit shaving; and new thought at the simulation and its software. First variation released through Pearson schooling Hb (1994): 0-132-11095-4
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Extra resources for Gear Geometry and Applied Theory, Second Edition
Example text
1) The rotational matrix M f 1 describes rotation about the z f axis with the unit vector, c f = [0 1]T . 2) The rotation from S 1 to S 2 is performed clockwise and the lower sign in Eq. 30) must be chosen. Taking into account that c 1 = c 2 = 0, c 3 = 1, we obtain the following expression for the rotational matrix M f 1 : cos φ − sin φ 0 0 sin φ cos φ 0 0 . 1: Centrodes in translation– rotation motions. The drawings of Fig. 1 yield that (O2 Of ) f = [ρφ and the translational matrix is M2 f 1 0 = 0 0 0 1 0 0 0 0 1 0 −ρ 0]T , ρφ −ρ .
4 ROTATIONAL AND TRANSLATIONAL 4 × 4 MATRICES Generally, the origins of coordinate systems do not coincide and the orientations of the systems are different. In such a case the coordinate transformation may be based on the application of homogeneous coordinates and 4 × 4 matrices that describe separately rotation about a fixed axis and displacement of one coordinate system with respect to the other. Consider that the same point must be represented in coordinate systems S p and S q (Fig. 1). The origins of S p and S q do not coincide and the orientations of coordinate axes in these systems is also different.
2 shows the axial section of the surface. The generating curve [Fig. 3(a)] is represented in coordinate system S a (xa , ya , z a ) by equations xa = xa (θ), ya = 0, z a = z a (θ ). 6) The angle of rotation ψ [Fig. 3(b)] lies within the interval 0 ≤ ψ ≤ 2π . Applying the matrix method of surface generation, derive the equations of the generated surface. 3: Generation of surface of revolution: (a) representation of planar curve L in coordinate system S a ; (b) illustration of coordinate systems S a and S 1 .