Integrated type and dimensional synthesis of planar four-bar mechanisms

Abstract

A novel approach to integrated type and approximate dimensional synthesis of planar four-bar mechanisms (i.e. linkages comprised of any two of RR, PR, RP, and PP dyads) for rigid-body guidance is proposed. The essence is to correlate coordinates of the coupler attachment points in two different coordinate frames, thereby reducing the number of independent variables defining a suitable dyad for the desired rigid-body motion from five to two. After applying these geometric constraints, numerical methods are used to size link lengths, locate joint axes, and decide between RR, PR, RP and PP dyads that, when combined, guide a rigid body through the best approximation, in a least-squares sense, of n specified positions and orientations, where n5. No initial guesses of type or dimension are required. An example is presented illustrating the effectiveness and robustness of this new approach.