Abstract: To improve the supporting capability of the hinged canopy of the four-leg shield powered support and to address the common perception of inadequate support provided by these canopies, a rod system model for the four-leg shield powered support was developed. This model was employed to determine the bearing capacity zone of the powered support based on the loading conditions. It yields the maximum load that the powered support can withstand and identifies its specific action location on the canopy. Two methods of the hinged canopy support force method and the hinged cylinder diameter methodfor solving this problem are presented. The simplified resolution method transforms the external load acting on the canopy into various distribution forms, including quadratic polynomial, triangular, trapezoidal and rectangular shapes, depending on the position of the external load, as described by Taylor's formula. By integrating the hinged structure of the canopy with the assumption of continuous load distribution above it, the magnitude and point of action of the external load on the hinged canopy are determined using the principle of force synthesis. This analysis allows for the derivation of the required diameter for the hinged cylinder based on static equilibrium conditions and specific formulas for solving the problem are provided. The support forces at the front end of the hinged canopy is compared with those of the overall top canopy under identical working resistance conditions. The findings indicate that a larger diameter hinged cylinder significantly enhances the support capacity of the hinged canopy, establishing that the support capacity of a well-designed hinged canopy-powered support surpasses that of an equivalent overall canopy-powered support under the same conditions. Using the mining practices of Shandong Energy Zhengtong Coal Industry Company's four-leg shield-powered support as the primary application context, a continuous load distribution model for the hinged canopy of the ZF20000/26/48 four-leg shield-powered support was established. Based on the continuous load distribution conditions above the canopy, the size and location of the external load on the hinged canopy were determined using the principles of force synthesis and decomposition. Furthermore, the theoretical diameter of the hinged cylinder was derived from static equilibrium conditions. Engineering practice demonstrates that the improved hinged canopy structure is rational, exhibiting significant front-end support force and pronounced support effects. It has been widely applied in various mining faces without encountering issues such as insufficient front-end support force leading to roof collapse or coal layer spalling, thereby validating the accuracy of the theory and effectively meeting the support needs of the mining face.