A parallel mechanism comprises legs with kinematically redundant actuation for a parallel mechanism. Each of these legs comprises a first sub-leg and a second sub-leg each with a proximal end and a distal end. A link has a proximal end and a distal end. A joint with a rotational degree of freedom (DOF) is between and common to the distal ends of the sub-legs, and the proximal end of the link. A joint provides two or more rotational DOFs at the distal end of the link and connects the distal end of the link to one end of the parallel mechanism. Joints in the sub-legs provide DOFs to the sub-legs and connect the proximal ends of the sub-legs to the other end of the parallel mechanism. A degree of actuation (DOA) is provided for each of the sub-legs to control movement of the link.