static balancing, stiffness elements, torque compliant mechanisms, pre-buckled beams


The concept of a statically balanced mechanism with a single rotational degree of freedom is presented. The proposed device achieves static balancing by combining positive stiff- ness elements and negative stiffness elements within a nuclear domain. Two designs are discussed. The first is composed of an Archimedean spiral and two pinned-pinned pre-buckled beams. The overall mechanism is modeled via an analytical approach and the element dimensions are optimized. The optimal configuration is then tested through finite element analysis (FEA). A second approach replaces the spiral beam with elastic custom-shaped spline beams. An FEA optimization is performed to determine the shape and size of such spline beams. The behavior of the negators is used as a reference for the optimization so as to achieve complete balancing. A physical prototype of each configuration is machined and tested. The comparison between predicted and acquired data confirmed the efficacy of the design methods.

Original Publication Citation

Bilancia, P., Smith, S.P., Berselli, G., Magleby, S.P., Howell, L.L., “Zero Torque Compliant Mechanisms Employing Pre-Buckled Beams,” ASME Journal of Mechanical Design, Vol. 142, 113301-1 to 13301-12, DOI: 10.1115/1.4046810, 2020.

Document Type

Peer-Reviewed Article

Publication Date



ASME Journal of Mechanical Design




Ira A. Fulton College of Engineering


Mechanical Engineering

University Standing at Time of Publication

Full Professor