ABSTRACT
This chapter utilizes the finite element method by means of the regular displacement approach to formulate element stiffness and inertia matrices of straight- and circular-axis flexible-hinge line elements. The elements possess axial, torsional and bending capabilities – the latter feature is modeled for both long configurations by means of the Euler–Bernoulli model and short designs that use the Timoshenko model. The free natural and undamped response of hinge mechanisms is also studied, as well as the forced response of compliant devices. Finite element flexible-hinge mechanism examples include serial, parallel, planar and three-dimensional configurations. Planar and spatial mechanisms are most often formed of flexible hinges, which have various orientations/directions. Because the nodal displacements and loads need to be expressed in a unique reference frame, the elemental stiffness and inertia matrices have to be correspondingly transformed into the global frame from their element local frames.
