Position analysis of Assur kinematic chains using coupler curves

Abstract

The configurations of several Assur kinematic chains (AKCs) are analysed with the aid of coupler curves. An analysed linkage is dismantled into two constituent linkages. The intersection points of two coupler curves generated by the constituent linkages are the solutions of the dismantling point. All possible configurations of the linkage can then be obtained with the dismantling point being found by solving two coupler curve equations. The coupler curve equations of Watt-I and Stephenson-I six-bar are derived with orders and circularities being emphasized. All three AKCs with seven-link and several AKCs with nine-link and even with 11-link are analysed. The maximum number of solutions can also be determined easily on the basis of the orders and circularities of the coupler curves. The chains with prismatic joints included are also considered.