This work demonstrates universal dynamic perching capabilities for quadrotors of various sizes and on surfaces with different orientations. By employing a non-dimensionalization framework and deep reinforcement learning, we systematically assessed how robot size and surface orientation affect landing capabilities. We hypothesized that maintaining geometric proportions across different robot scales ensures consistent perching behavior, which was validated in both simulation and experimental tests. Additionally, we investigated the effects of joint stiffness and damping in the landing gear on perching behaviors and performance. While joint stiffness had minimal impact, joint damping ratios influenced landing success under vertical approaching conditions. The study also identified a critical velocity threshold necessary for successful perching, determined by the robot's maneuverability and leg geometry. Overall, this research advances robotic perching capabilities, offering insights into the role of mechanical design and scaling effects, and lays the groundwork for future drone autonomy and operational efficiency in unstructured environments.