Four-Pose Synthesis of a Generalized Rapson Slide Mechanism

In this paper, a novel, robust and reliable design procedure is proposed in order to synthesize a generalized Rapson slide mechanism that is able to reach four assigned poses. In particular, the four-pose synthesis problem is reduced to four three-pose synthesis problems and then imposing the satisfying of the whole conditions. This rigid body guidance synthesis problem gives just one solution, a generalized Rapson slide mechanism, while the corresponding more common case of a three-pose problem can give infinite solutions. In fact, one has just one point that is able to reach four aligned positions and just one straight line that passes through the same fixed point in the four assigned poses. In the synthesis problem of the infinitesimal kinematics, the corresponding points are the Ball and the inverse Ball points, respectively. Therefore, the proposed robust and reliable design procedure is described in depth and then validated by means of significant examples and using the Geogebra dynamic mathematics software.