A generalized analytical approach to the coupled effect of SMA actuation and elasticadeflection

Abstract

A compliant miniature parallel manipulator made of superelastic nitinol pipe as its centralpillar and actuated by three symmetrically attached shape memory alloy (SMA)wires is under development. The mobility for the platform is obtained by theselective actuation of one or two wires at a time. If one wire is actuated, theother two unactuated wires provide the counter effect. Similarly, if two wiresare actuated simultaneously or in a differential manner, the third unactuatedwire resists the movement of the platform. In an earlier work of the authors,the static displacement analysis was presented without considering the effect ofunactuated wires. In this contribution, the force–displacement analysis is presentedconsidering the effect of both actuated and unactuated wires. Subsequently, anattempt has been made to obtain a generalized approach from which six types ofactuation methods are identified using a group of conditional parameters. Eachmethod leads to a set of large deflection expressions suitable for a particularactuation method. As the large deflection expressions derived for the mechanism arenonlinear and involve interdependent parameters, their simplified form using aparametric approximation have also been obtained using Howell’s algorithm. Thegeneralized approach and the solution algorithm developed can be applied toany kind of compliant mechanism having large deflection capabilities, includingplanar and spatial MEMS devices and stability analysis of long slender columnssupported by wires or cables. The procedure developed is also suitable for the staticanalysis of spatial compliant mechanisms actuated by multiple SMA actuators.