Analysis of the center of rotation in primitive flexures: Uniform cantilever beams with constant curvature

• Large deflection analysis is performed on cantilever beams with uniform cross section and constant curvature.
• Analytical expressions for the position of the center of rotation of the beam free-end section are obtained.
• Analytical expressions show that the center of rotation lies in the axis of symmetry of the beam in neutral configuration.
• Finite element simulations are performed to compare numerical and analytical solutions.
• A final example focuses on the determination of the pseudo-rigid body model.

Precision of rotation is a fundamental characteristic of primitive flexures, especially when compliant mechanisms are designed for micro-scale applications. In case of single leaf flexures, distributed compliance allows flexible beams to undergo large deflections. Nevertheless, the center of rotation changes its position during such deflections. In this paper, large deflection analysis is performed on cantilever beams with uniform cross section and constant curvature, subjected to end-moment loads. Analytical expressions to determine the position of the center of rotation of the flexure are derived. The center of rotation refers to the displacement of the free-end section of the beam, occurring when the flexure, due to the external load application, moves from its neutral configuration to the deformed one. Several examples are considered and the analytical solutions are compared to the results obtained by finite element analysis. A final example focuses on the determination of the pseudo-rigid body model.