This contribution presents a comprehensive theory for the type synthesis of fully parallel platforms. The theory deals with both types of platforms, 6 D.O.F. parallel platforms and lower mobility platforms. The theory is based on an analysis of the subsets and subgroups of the Euclidean group, SE(3). It is likely that the theory can be also developed based on an analysis of the subspaces and subalgebras of the Lie algebra, se(3), of the Euclidean group, SE(3).

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