<p>This paper proposes a design idea based on the kinematic coupling of mechanism to integrate a mobile platform and a robotic arm. Based on this idea, a novel serial-parallel manipulator(S-P manipulator) is presented for an alternating walking parallel hexapod robot (AWPHR) with dual-operation modes. This PM has two end-effectors, with 3T/1T2R operation mode, which can output two linearly related motions with different characteristics of degrees of freedom through a set of input parameters. The kinematics performance of the S-P manipulator with 3T/1T2R operation mode is analyzed. The position analytical model and workspace are established using vector method, the singularity of the S-P manipulator is analyzed by Jacobian matrix, and the evaluation index of dexterity is established. The evaluation index of motion/force transmission performance is established using screw theory. According to the proposed evaluation index, the optimization design space of the S-P manipulator is obtained based on the performance atlas method. The final kinematic optimal dimension combination of the S-P manipulator is obtained. A 3D printing prototype was made to verify the effectiveness of the theoretical method. The results show that the S-P manipulator with 3T/1T2R operation mode has excellent kinematics performance, and as the main mechanism of the AWPHR with dual-operation modes, it can adapt to the change of task requirements.</p>