A troublesome problem in flat belt transmission is a phenomenon known as skew, where the belt moves along the axial direction of the pulleys in operation. Skew usually is caused by angular misalignment of pulleys. Angular misalignment can be classified in two types, in-plane misalignment and out-of-plane misalignment. The former is where the axes of a pulley pair, driving and driven, are in the same plane but not parallel. The latter is where the axes of pulleys are not in the same plane. In this paper, both cases of the belt skew caused by out-of-plane and in-plane misalignment are addressed. Theoretical analyses are provided following discussions of the simulation results by finite element method. It is found: (1) in case of out-of-plane misalignment, the skew ratio, an index describing the degree of skew, is determined by a very simple formula in which only three geometrical parameters are required; (2) in case of in-plane misalignment, the skew is much more complicated than that in case of out-of-plane misalignment, and the skew ratio is determined by a system of nonlinear simultaneous equation. An iteration method for solving the system of nonlinear simultaneous equations is proposed. The theoretical analyses for both cases are verified with the FEM results and factors that influence the skew are discussed.

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