Issue 23

R. Vertechy et alii, Frattura ed Integrità Strutturale, 23 (2013) 47-56 ; DOI: 10.3221/IGF-ESIS.23.05 49 estimated on sacrificial specimen. A voltage difference 1 V ( 2 V ) between the electrode pair of the DE film #1 (#2) generates a rightward (leftward) force on the actuator output. The bias spring has been designed so that the overall actuator in its OFF-state mode (i.e. 1 2 0 V V   ) possesses a rest (stable) position when the actuator output lies exactly in the middle of the rigid frame rings (i.e. when x d  ). Also, the actuator maintains a positive stiffness across the desired stroke (see Sec. Mathematical model of the dielectric elastomer film force ). For each actuator output position, reciprocal activation of the agonist-antagonist DE films enables feed-forward independent regulation of the actuator interaction force. Figure 1 : DE actuator CAD model. Figure 2 : Parallel compliant mechanism. Pseudo-rigid model. Figure 3 : Slider-crank schematic. M ATHEMATICAL MODEL OF THE DIELECTRIC ELASTOMER FILM FORCE et first consider the DE film #1. The expression of the overall external force, F ( f,1) , that must be supplied at O and P (and directed along the line joining these points, Fig. 2) to balance the DE internal reaction force at a given generic configuration x of the actuator, can be split as: ,1 1 ,1 ,1 1 ( , , ) ( , ) ( , ) f ve em F x x V F x x F x V     (1) where F ( ve,1) represents the viscoelastic response of the DE film and F ( em,1) represents an electrically induced term, having the dimension of a force and usually referred to as Maxwell force [11, 12]. As for the electrically induced force, a suitable expression for conically-shaped DEs has been derived in [6] and it is given by: 2 2 2 ,1 1 1 ( , ) ( ) / em M m F V x x V r r       (2) L