This paper presents a new family of maximally regular -type parallel manipulators with bifurcated spatial motion. In each branch, the moving platform has two independent translations and one rotation driven by three actuators mounted on the fixed base. The rotation axis is situated in the plane of translation and can bifurcate in two orthogonal directions. This bifurcation occurs in a constraint singularity in which the connectivity between the moving and fixed platforms increases instantaneously, incurring no change in limb connectivity. The Jacobian matrix of the maximally regular solutions presented in this paper is a identity matrix in the entire workspace of each branch. This paper presents for the first time a family of maximally regular -type parallel manipulators with bifurcated spatial motion of the moving platform along with solutions using uncoupled motions.