A forward acceleration of the kinematic limbs for the redundant serial–parallel manipulators is studied. The relationships between the input velocity/acceleration and the output general velocity/acceleration of the kinematic limbs are discovered. The forward kinematic Jacobian matrices and the forward kinematic Hessian matrices are derived. A unified forward acceleration of the kinematic limbs is established for solving the output general acceleration of the kinematic limbs by only giving the input general velocity/acceleration of every parallel manipulator. A novel 2(RPS + SPR + UPS + SPU) type serial–parallel manipulator is constructed, several formulas are derived for solving the full forward general acceleration of the kinematic limbs in the redundant serial–parallel manipulator based on the unified forward acceleration model. The theoretical solutions are proved to be correct by the simulation solution of the novel serial–parallel manipulator.