A variable section beams based Bi-BCM formulation for the kinetostatic analysis of cross-axis flexural pivots

The Cross-Axis Flexural Pivot (CAFP) is a well-established compliant rotational joint characterized by a highly configurable behavior. Its classic form, consisting of two uniform beams that cross at an arbitrary angle, has been thoroughly examined via either theoretical approaches or Finite Element Analysis (FEA). Conversely, the effects of utilizing variable section beams have had minor consideration, possibly due to the more complex modeling phase. The present paper addresses the analysis of CAFPs incorporating beams whose width and thickness are assumed to vary along the axis with either linear or parabolic functions. The CAFP planar behavior is studied resorting to the Beam-Constraint Model (BCM) for different load cases, namely with an ideal rotation applied to one rigid link or a more practicable cable-driven actuation. To extend the use of BCM to large deflections, each CAFP's beam is modeled as a chain of two BCM elements, named Bi-BCM. A preliminary study has been carried out to establish empirical equations that provide the BCM characteristic coefficients for every considered beam shape. Next, these have been used to perform the pivot behavioral analysis and to generate, as an output of the sensitivity studies, the performance maps of stiffness, maximum stress and center shift. These results have been verified with FEA, which confirmed the Bi-BCM accuracy for any tested configuration. Finally, direct comparisons between predicted behaviors of the CAFP actuated via the flexible cable and experimental data obtained with 3D printed specimens further validated the proposed Bi-BCM model.