This paper introduces a novel design and static optimization for a two-degrees-of-freedom transformable wheel based on a geared linkage mechanism. Overcoming obstacles, including stairs, with small wheels is a major challenge in the field of mobile robotics research. Among various robots, the transformable wheel, which can change the shape of the wheel to overcome steps and optimize the path, was presented and has undergone many improvements. Nevertheless, problems such as asymmetry and structural strength remain. Therefore, the design of this paper aims to address the structural inefficiencies identified in the previous research model, which were attributed to the asymmetric placement of the linear motion guide. Through the implementation of this mechanism, the linear motion of the lobe can be segregated, enabling each input motor to share the workload effectively. The optimization process focus on determining the optimal linkage length under static conditions, resulting in improved structural characteristics and force distribution of linkage within the designated workspace. As a result, asymmetry of motion is eliminated, required intervention angle of the driving motor and stress of linkage was reduced by 36.24% and 8.35%, respectively.