Stair climbing is one of critical issues for field robots to widen applicable areas. This paper presents optimal design on kinematic parameters of a new robotic platform for stair climbing. The robotic platform climbs various stairs by body-flip locomotion with caterpillar type main platform. Kinematic parameters such as platform length, platform height, and caterpillar rotation speed are optimized to maximize stair-climbing stability. Three types of stairs are used to simulate typical user conditions. The optimal design process is conducted based on Taguchi methodology, and resulting parameters with optimized objective function are presented. In near future, a prototype is assembled for real environment testing.