The conveyor chain model which include constrained and free pin is established.Through analyzing each position of pin in static and the movement velocity and displacement of pin in one period are calculated according to its coordinate.The mathematical model of each pin in the state of motion is established and the motion trajectory of free pin should include two parts because of the polygonal action of the chain is proposed.Aiming at the problem of the nonlinear equations in the mathematical model of chain is hard to calculate,a kind of solution method based on fundamental theorem of calculus is presented.Finally,motion trajectory of top and bottom edge free pin is obtained by using the MATLAB point depiction method.A computation method is provided for the analysis of trajectory constrained conveyor chain and the design of constrained trajectory.