Multi-legged robots with rigid-flexible coupling grippers have appealing applications to asteroid exploration with the microgravity. However, these robots usually have significantly complicated structures, which leads to a great challenge for the kinematic design.This paper proposes the kinematic design method for a novel multi-legged robot with the microspine gripper. First, the structure of the multi-legged asteroid exploration robot and the microspine gripper are demonstrated. Second, four performance evaluation indices, which are used to evaluate the stiffness, velocity, motion / force transfer efficiency and gripper attachment efficiency of the robot, are derived from the kinematic model. Non-dimensional design spaces of parameters to be optimized are drawn, and performance atlases are presented in design spaces. Third, the stiffness model of the microspine is derived. In addition, the constraint condition of the restoring spring is established, and the stiffness of restoring springs are optimized using the genetic algorithm. Several experiments are conducted to verify the stiffness model of the microspine. Finally, the prototype is developed and the experimental results validates the kinematic design method.