The motion characteristic of a discontinuously movable mechanism with special link length condition is analyzed. In different configurations, the discontinuously movable mechanism has one rotational and one translational motions, one translational motion, one rotational motion, respectively. Reconfigurable hybrid limbs are obtained by integrating the discontinuously movable mechanism with serial limbs that have two rotational and two translational motions. The kinematic bonds associated with the hybrid limbs in different configurations are identified based on Lie group theory. A class of reconfigurable parallel mechanisms is constructed with three identical hybrid limbs connecting the moving platform and the fixed base. When all the discontinuously movable mechanisms in the hybrid limbs are in singular position, the reconfigurable parallel mechanisms have instantaneous six degrees of freedom. By actuating the discontinuously movable mechanisms move into different motion branches, the reconfigurable parallel mechanisms have the ability to perform different kinds of motion, including four kinds of motion with three degrees of freedom.