Isotropic point synthesis of flexures and of compliant mechanisms

In this paper, the point compliance synthesis method is applied at the output port of a compliant mechanism to determine the points that satisfy the isotropy property. The kinetostatics of the compliant system is described using the ellipse of elasticity theory. According to the proposed modeling approach, based on projective geometry, the position of the isotropic points depends solely on the conic eccentricity, and their coordinates can be obtained through a simple arithmetic expression. Since any compliant system can be modeled by an ellipse of elasticity, the results obtained are of general validity. The synthesis procedure is applied to three case studies: two uniform flexures having axes with constant and variable curvature, and a closed-chain compliant mechanism. Numerical simulations and experimental testing are carried out to validate the procedure and to confirm the isotropy property.