In this paper, a general method for kinematic analysis of complex gear mechanisms, including bevel gear trains and noncollinear input and output axes, is presented. This new approach is based on the nullspace of the kinematic constraint matrix computed from the mechanism graph or its adjacency matrix. The novelty is that the elements of the adjacency matrix are weighted with complex coefficients allowing bevel gears to be taken into account and the angular velocity of each link to be directly expressed using polar coordinates. This approach is illustrated on a two-degree-of-freedom car differential and applied to a helicopter main gear box. A MATLAB open source software was developed to implement this method.

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