Aiming at the multi-hinge spatial motion mechanism of pantograph, the relative coordinate method of local coordinate system was used to express the parameters of hinge position in two-dimensional space, and the optimization Latin square method was used to optimize and reliability analysis of the bow-head rotation angle. The bow-head angle was significantly reduced, and the bow-head sliding plate could achieve excellent translation state and reliability index, which could rapidly and effectively provide technical support for the design of hinge pantograph mechanism.