Materials Science and Engineering A 378 (2004) 210–215 Shape memory alloy flexures Yves Bellouard a,∗ , Reymond Clavel b a Center for Automation Technologies, Rensselaer Polytechnic Institute, CII 8211, 110 8th Street, Troy, NY 12180-3590, USA b Laboratoire de Systèmes Robotiques, LSRO, Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland Received in revised form 29 November 2003 Abstract Flexures are used in precision engineering where highly accurate, wear-free, smooth and repeatable motion is desired. Flexures are based on deformation of material to achieve a motion between elastically joined parts. They are used in a variety of precision mechanisms such as high-resolution balances or high accuracy optical positioning stages. Shape memory alloys (SMA) are an attractive option in designing flexures. Superelastic flexures can withstand larger deformations for the same weight as a conventional flexure. In addition, the damping properties of SMA, controllable through the phase transformation, offer new design opportunities for adaptive compliant mechanisms. The martensitic phase transformation can also be used to shift the natural frequency of flexures adding useful functionalities such as vibration rejection. This paper presents design principles of SMA flexures based on non-linear beam theory. Results show a good agreement between mea- sured and predicted data. In addition, experimental results on phase transformation effects on damping behavior are also presented. Both, natural-frequency shift and increased damping were observed in bulk-micro machined flexures using the R-phase transformation. These results demonstrate the feasibility of natural-frequency-tunable flexures. © 2004 Elsevier B.V. All rights reserved. Keywords: Smart material; Shape memory alloy; Flexure; Non-linear beam analysis; Tunable damping 1. Introduction Flexures are an indispensable tool in precision engineer- ing. A simple definition of a flexure or “flexure joint” is a compliant element that links two rigid bodies such that one body moves relative to the other one in a geometrically well-defined manner. In precision machine design, flexures replace traditional multi-part joints to provide a repeatable motion that is free of friction, backlash and wear. Exten- sive literature has been published on the topic, the interested reader may consult Smith [1] for instance, for an overview on flexures. Although flexures offer a dramatic improvement in pre- cision and repeatability as compared to traditional guiding systems, they also have numerous limitations. For a given size and stiffness, flexures have a limited excursion in mo- tion defined by the elastic limit of the material used. Whilst friction-less operation is a decisive advantage, flexures ∗ Corresponding author. Tel.: +1-518-276-6696; fax: +1-518-276-4897. E-mail address: bellouard@cat.rpi.edu (Y. Bellouard). are sensitive to dynamic disturbances and lack significant damping properties. Although the ideal guidance should have only one degree-of-freedom, flexure have several degrees-of-freedom coupled together with various spring stiffnesses. Unwanted vibrations can excite some of the vi- bration modes leading to unacceptable dynamic instabilities. Shape memory alloys (SMA) mostly known for their re- markable shape memory properties (“shape memory effect”) also have unusual elastic properties. In a defined tempera- ture window for which the material is in its austenite phase, SMA have a wide fully reversible deformation several or- ders of magnitude higher than usually observed in common metallic materials. This effect—called superelasticity—is related to the martensitic transformation which is thoroughly described for instance in [2]. In a uniaxial, isothermal ten- sile test, the stress–strain characteristic is characterized by four zones. The first one (typically from 0 to 1% strain) is the elastic domain of the austenite phase. The second one (typically from 1 to 7–8%) corresponds to the stress-induced phase transformation where austenite is gradually trans- formed into martensite. This region is characterized by a constant stress and is often called the “plateau.” The stress 0921-5093/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2003.12.062