This paper presents the direct position analysis of the fully-parallel mechanism that features six connection points on the base and four on the platform. The shape of both base and platform is general and, in particular, not restricted to being planar. The analysis is performed first by writing a suitable set of five closure equations in five unknowns. Then, by a specifically-developed elimination scheme, the closure equation set is reduced to a 32nd-order algebraic equation with only one unknown, which proves free from extraneous roots. Hence 32 closure configurations of the 6-4 mechanism do exist in the complex field. A numerical example is reported that confirms the new theoretical results.

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