The mechanism of original ternary joint robot fingers without drive is analyzed into several component. After its type and number is confirmed , we gain circular topological graph of kinematic chain with topological theory. Based on it, all the generalized kinematic chain is constructed. And so is evolved a series of regenerating kinematic chain and corresponding new type of mechanical graph according to specialized restriction. A designer can choose the new mechanism which is different from original one. The new one has better function, so the designer can realize his innovating design of three-joint robot fingers without drive.