In this paper, we determine all nontrivial self-motions of triangular symmetric simplified manipulators (TSSMs) with two parallel rotary axes which equal the determination of all flexible octahedra where one vertex is an ideal point. This study also closes the classification of these motions for the whole set of parallel manipulators of TSSM type. Our approach is based on Kokotsakis meshes and the reducible compositions of spherical coupler motions with a spherical coupler component.

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