Parallel mechanisms which can realize three rotational motions are very important in the parallel mechanism family. Not the same with the traditional spherical parallel mechanism, a new kind of 3-DOF (degree of freedom) rotational parallel mechanism with no intersecting axes (RPMNIA) are proposed in this paper. This kind of rotational parallel mechanisms have the advantages of easy manufacturing. A new approach using the screw theory and the subchain theory is proposed to design the branches with only one constraint force and some new one-force-branches are found. Using these new branches, a group of 3-DOF rotational parallel mechanisms without intersecting axes are synthesized.

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