VnSA: Variable negative stiffness actuation based on nonlinear deflection characteristics of buckling beams

We present variable negative stiffness actuation (VnSA), an alternative method of achieving variable stiffness actuation based on the nonlinear deflection characteristics of buckling beams. The approach exploits transverse stiffness variations of axially loaded beams around their critical buckling load to achieve an actuator with adjustable stiffness. In particular, transverse stiffness of buckled beams are positive under tensile loading and for compressive loading below their first critical buckling load, while they display negative stiffness above this critical value. Furthermore, for small deflections transverse stiffness of buckled beams depends linearly on the amount of axial loading. Consequently, the stiffness of a variable stiffness actuator can be modulated (i) by decreasing the transverse stiffness through an increase of the axial compressive loading on a beam, up to values above the first critical buckling load where the overall stiffness of the actuator approaches its lowest negative value, and (ii) by increasing the transverse stiffness through application of tensile axial loading. Capitalizing on the concept of negative stiffness, the lowest stiffness of VnSA can be set arbitrarily close to zero or even to negative values (when counterbalanced), while very high stiffness values are also achievable by tensile loading of the beam. As a result, VnSA can modulate its stiffness over a uniquely large range that includes zero and negative stiffness values. Furthermore, thanks to the negative stiffness characteristics, the stiffness of VnSA can be kept very low without sacrificing the mechanical integrity and load bearing capacity of the actuator. We introduce the design of VnSA, theoretically analyze its stiffness modulation response, and provide implementation details of a prototype. We also provide experimental results detailing range of stiffness modulation and force tracking performance achieved with this prototype and discuss its correspondence with the- theory.