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# This mathematical problem has not an explicit

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Unformatted text preview: A tooth surface Σ is described by expressing its cartesian coordinates x, y, z in the local coordinate system (S7 substitute surface gear 1 or S8 substitute surface gear 2) as functions of two parameters (φ, θ) or (α, γ) in a certain closed interval. In this paper, only the mathematical models of the active tooth surfaces of the pinion and the gear are expressed and discussed. The position vectors and unit normal vectors of tooth surface of pinion and gear are denoted as rk(i) and nk(i) for part (i) in the coordinate system “k”. The model of the gear box with geometrical variations can be simulated by changing the settings and orientations of the coordinate systems. The odd index are use for the wheel 2 and even one is used for pinion 1. The coordinate systems of part 1 are (Figure 1): S7 is rigidly attached to the first substitute surface of pinion 1, S5 is rigidly attached to one of nominal active surfaces of part 1, Statistical Tolerance Analysis of Gears 257 S3 is rigidly attached to the ho...
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## This note was uploaded on 08/03/2010 for the course DD 1234 taught by Professor Zczxc during the Spring '10 term at Magnolia Bible.

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