An Intrinsic Geometric Framework for the Building Block Synthesis of Single Point Compliant Mechanisms

In this paper, we implement a characterization based on eigentwists and eigenwrenches for the synthesis of a compliant mechanism at a given point. For 2D mechanisms, this involves characterizing the compliance matrix at a unique point called the center of elasticity, where translational and rotational compliances are decoupled. Furthermore, the translational compliance may be represented graphically as an ellipse and the coupling between the translational and rotational components as vectors. These representations facilitate geometric insight into the operations of serial and parallel concatenations. Parametric trends are ascertained for the compliant dyad building block and are utilized in example problems involving serial concatenation of building blocks. The synthesis technique is also extended to combination of series and parallel concatenation to achieve any compliance requirements.