The kinematic synthesis of steering mechanisms

We propose a computational-kinematics approach based on elimination procedu res to synthesize a steering four-bar linkage. In this regard, we aim at mi nimizing the root-mean square error of the synthesized linkage in meeting t he steering condition over a number of linkage configurations within the li nkage range of motion. A minimization problem is thus formulated, whose nor mality conditions lead to two polynomial equations in two unknown design va riables. Upon eliminating one of these two variables, a monovariate polynom ial equation is obtained, whose roots yield all locally-optimum linkages. F rom these roots, the global optimum, as well as unfeasible local optima, ar e readily identified. The global optimum, however, turns out to be impracti cal because of the large differences in its link lengths, which we refer to as dimensional unbalance. To cope with this drawback, we use a kinematical ly-equivalent focal mechanism, i.e., a six-bar linkage with an input-output function identical to that of the four-bar linkage. Given that the synthes ized linkage requires a rotational input, as opposed to most existing steer ing linkages, which require a translational input. we propose a spherical f our-bar linkage to drive the steering linkage. The spherical linkage is syn thesized so as to yield a speed reduction as close as possible to 2:1 and t o have a maximum transmission quality.