Kinetostatic Analysis of a Spatial Compliant Mechanism Actuated by Three Shape Memory Alloy Wires in Differential Form

摘要

This contribution presents the kinetostatic analysis of a spatial compliant mechanism actuated by three Shape Memory Alloy (SMA) wire actuators. This mechanism exploits both shape memory and superelastic effects of SMA actuators. The moving platform of the mechanism is mounted on a pillar made of superelastic SMA and its mobility is obtained from the large deflection of the pillar by the selective actuation of any one or two wires in differential manner. The deflection expressions obtained are basically force-displacement kinematic relationships, derived after incorporating follower forces and variable moments developed by the actuators. Two sets of geometric parameters, related to deflected and undeflected conditions, have been utilized to solve the coupled relationship between the force developed by the SMA actuation and the force required for the elastica deflection. The deflection expressions are solved using Romberg integration method and the numerical results obtained have been validated by comparing them with those obtained from FEM simulation. The results show that, for the design of compliant mechanisms exhibiting large displacements the force-displacement relationships in linear form, as applicable to small deflections, are no longer valid.