In this paper, two new parallel mechanisms (PMs) with fewer active inputs than the degrees of freedom (DOFs)are proposed: (i) an nSPS (n = 7, 8, 9) six‐DOF PM with n‐6 active inputs and six lockable joints. and (ii) a 3RPS‐SPS 3‐DOF PM with one active input and three lockable joints. Compared with the traditional PMs, the difference is that the proposed PMs can achieve the same mobility by using a minimal number of active joints. Moreover, the load‐carrying capacity is also improved compared with the original standard mechanisms, since the new PMs become statically redundant when all the branches are locked. For this purpose, a sequential motion control principle is introduced that requires both inverse and forward kinematics of PMs. Kinematic modeling, dimensional optimization, and structural design are carried out for the 7SPS and 3RPS‐SPS mechanisms, and the two prototypes are constructed for experimental validation. Both simulation and experiment results have shown that the proposed hybrid PM can achieve the original mobility while significantly reducing the number of actuators.