For lacking of theoretical basis of the structural design of forging hydraulic cylinder′s connection spherical hinge, the status of spherical hinge friction was confirmed by analyzing lubrication conditions of spherical hinge surface. Then, the stress state of working cylinder was studied by setting up the mechanics model of working cylinder under the eccentric forging of the self-locked single and double spherical hinges，and the side force of plunger on guide sleeve was obtained. Based on Hertz contact theory, the contact condition between plunger and guide sleeve was analyzed, and the calculation method of allowed friction circle radius for spherical hinge was studied through limiting the friction torque transmitted by the working cylinder to satisfy the guide sleeve strength condition. However, composited eccentric forging conditions, the spherical hinge friction circle radius was  confirmed, and the methods of determining spherical hinge structural parameters were put forward according to the relationship between friction circle radius and structure of spherical hinge. According to the above methods, the spherical hinge structure of four existing working cylinders were designed and calculated. The theoretical calculation results indicate that the anti-eccentric load capacity of the single-ball hinge cylinder is weaker than that of the double-ball hinge cylinder, and the design of single-ball hinge structure is with hidden troubles.