Two-axis flexure hinges with axially-collocated and symmetric notches

The paper introduces a new class of two-axis flexure hinges with axially-collocated and symmetric notches as an alternative to the existing flexure designs with serially-disposed notches. A generic formulation is developed in terms of the geometric curves defining the two notches which includes assessing the capacity of rotation, precision of rotation, sensitivity to parasitic effects, stress values, motion efficiency and shearing effects by means of compliance factors. Closed-form compliance equations are derived for a two-axis flexure hinge that is defined by two non-identical parabolic profiles. The analytical model predictions are confirmed by finite element data. A numerical comparison is made of the parabolic flexure with a constant rectangular cross-section flexure hinge in terms of several performance criteria.