A type of three-degree-of-freedom parallel mechanism with a redundant link that can realize one-dimensional translation and two-dimensional rotation is proposed. A novel wave power generating device is then designed based on this mechanism. The kinematics of a floater in this device are analyzed, and the effects of the shape and size of the floater on wave energy acquisition efficiency are analyzed quantitatively. The inverse displacement formulas of this mechanism are then derived, its velocity and acceleration mapping relations are established, and a kinematics simulation is performed. In addition, the workspace of this mechanism is analyzed, a kinematic performance evaluation index is defined that combines the actual applications of the wave power generating device, and performance index distribution maps in the working space are drawn. The results show that the cylindrical and spherical floats are suitable for sea areas with small and large variation ranges of the wave period, respectively. The working space of the mechanism meets the motion requirements of the float of the wave energy conversion device, and the kinematics character is good. This study provides theoretical foundations for kinematic analysis, structural scale optimization, and prototype development of the mechanism.