The wheeled-legged mobile platform combines the advantages of wheeled vehicles and legged platforms, allowing for rapid movement in flat terrains and effective navigation through complex environments and unstructured surfaces. The leg’s electric joints must provide both high speed and high torque output, which are crucial for the platform’s superior passability and mobility. This paper begins by establishing precise kinematic and dynamic models for the single leg of the wheeled-legged mobile platform. It analyzes various operating conditions to calculate the speed and torque requirements of the joint motors using the forward and inverse kinematics of the legs. Based on the performance requirements for different operating conditions, an integrated model for the drive joints and gear reducers of the wheeled-legged mobile platform was designed and constructed. Prototyping and testing confirmed the practicality and effectiveness of the joint motor design, which meets the performance demands of the operating conditions.