The conveyor chains bear a periodically impact loading due to the polygonal effect. The model of constrained trajectory of conveyor chains with long pitch is built toward this issue. The model is divided into two parts: chain wheel and top edge. The kinematics models of the two parts are established based on the Lagrange equation to calculate the generalized moment. In order to calculate the contact stress between the pins and other parts more precise,the models of chain wheel-pitch and pitch-pins are built by using the ABAQUS.The generalized moment is used to calculate the maximum contact stress and its position on pins. The consequence may provide some reference for the selection of material and the method of heat treatment.