In order to improve the accuracy of a solar-powered punch card car’s movement on a designated route and reduce positional deviations during its operation, a solar-powered punch card car with a single cam as the steering guidance mechanism was designed. The car adopts a three-wheel structure. The transmission mechanism, steering mechanism, driving mechanism, and regulating mechanism of the car were analyzed. The kinematics model of the car was established and the motion characteristics of the car were obtained. By analyzing the relationship between the steering angle of the car and the curvature radius of its travel route, the front wheel angle of the car at each position was calculated using MATLAB R2020a. This allowed us to establish the relationship between the front wheel angle and the displacement of the steering push rod, which was further converted into the theoretical contour line of the cam. Subsequently, the theoretical contour line of the cam was completed and envelope correction was performed. Finally, through mechanical analysis and experimental verification using a prototype, the results indicated that the single-cam steering guidance mechanism calculated using this fast path fitting method exhibited excellent mechanical performance and a smooth and accurate trajectory, and the traveling path of the theoretical cam contour curve was basically consistent with the actual trajectory route.