Abstract: The Position analysis of plane mechanisms with many links is one of the most diffcult problems in the theory of mechanisms and machines. All known methods to this problem are very complicated, because we ought to solve a set of nonlinear or trigonometric equations with many variables. This paper gives a simpler "method of successive approximation of link length" to determine the positions of Assur’s three arm group. This method may be also extended to the solution of the more complex groups The method is simple and 0onvenient, the solution of this problem can reach to any given accuracy. At last, as an example, ell 24 positions of thirteen-Link mechanism with varied construction are obtained by this method on the digital computer.