Synthesis at the output port of compliant mechanisms through the instantaneous geometric invariants

Recently, the instantaneous geometric invariants have proved to be a fundamental tool for the analysis of the motion generated by flexure hinges. In this paper, the invariants are applied to the synthesis of compliant mechanisms at the output port level. The motion of the moving plane associated to the output port is described through fundamental geometric entities, that are the inflection circle, the cubic of stationary curvature, and its derivative. The proposed synthesis procedure aims to reshape the output port to embody the special points on the plane, that are the Ball's and the Burmester's points, approximating straight and circular paths to the third and to the fourth order, respectively. The method is implemented for the design of a compliant mechanism and numerical simulations are conducted to verify the theoretical results. A discussion of the advantages and disadvantages of the method is presented.