Closed-form displacement analysis of 10-link 1-DOF mechanisms: part 1 – general framework

This paper presents a closed-form approach, based on the theory of resultants, to the displacement analysis problem of planar 10-link 1-DOF mechanisms. It is shown that the displacement problem for each and every “non-trivial” mechanism resulting from 230 10-link kinematic chains can be classified as one of 22 distinct structures. Using the methods of successive and repeated elimination presented herein, it is also shown how each of these structures can be reduced into a univariate polynomial devoid of any extraneous roots. This univariate polynomial is the input–output (I/O) polynomial of the mechanism. Based on the results presented, it is seen that the displacement analysis problem for all 10-link 1-DOF mechanisms is completely solvable, in closed-form, devoid of any extraneous roots.