ABSTRACT
Flexible hinges with curved/circular axis are employed in applications where coupling between axial and bending deformation, as well as between bending and torsion, are necessary. This chapter formulates the in-plane and out-of-plane compliance matrices of planar flexible hinges that are fully formed of curvilinear-axis segments or combine curvilinear-axis segments with straight-axis segments. It analyzes the class of multiple-segment, curvilinear-axis flexible hinges that are symmetric with respect to an axis. The in-plane and out-of-plane compliance matrices of a generic hinge are derived first based on the corresponding matrices that define half the hinge. In order to formulate the in-plane and out-of-plane compliance matrices of flexible hinges that incorporate curvilinear-axis segments, the local-frame segment compliance matrices need to be transferred to the global frame; this is mainly achieved by matrix translation and rotation, but it can also include mirroring. The serially connected flexible segments composing the hinge have curvilinear centroidal axes, but some of the segments can be of straight longitudinal axis.
