A micro-electro-mechanic actuator device (1; 85; 95) comprising: - a fixed structure; and - a mobile structure configured to move along a driving direction and includes a first deformable band, a second deformable band and a third deformable band which lie, in a first operating condition, in a resting plane and have a respective main extension along a first direction orthogonal to the driving direction, the first deformable band being arranged between the second and third deformable bands (47a, 47b) and being mechanically uncoupled, along said first direction, from the second and third deformable bands (47a, 47b) by respective first and second through trenches, the first, second, and third deformable bands (47c, 47a, 47b) each having respective ends and being joined together at said ends, and wherein the second deformable band is further coupled to the fixed structure by a first supporting element (12; 80; 82), and the third deformable band is coupled to the fixed structure by a second supporting element (14; 81; 84), the first and second supporting elements being aligned to one another, at least in the first operating condition, along one and a same first axis of symmetry orthogonal to said first direction, the first, second, and third deformable bands (47c, 47a, 47b) housing first, second, and third piezoelectrics (50k, 50i, 50j), respectively, wherein the second and third deformable bands (47a, 47b) and the respective second and third piezoelectrics (50i, 50j) are arranged with respect to one another and configured so that, in a second operating condition where the second and third piezoelectrics are biased by a working voltage, the second and third deformable bands (47a, 47b) are subjected to a negative bending that causes a translation of said ends and of the first deformable band in said driving direction; the first deformable band and the respective first piezoelectric being arranged with respect to one another and configured so that, when the first piezoelectric is biased at the working voltage, the first deformable band is subjected to a positive bending that causes a further translation in said driving direction of at least one portion of the first deformable band, which extends between said ends of the first deformable band, wherein the translation of said ends and of the first deformable band and said further translation of at least one portion of the first deformable band are directed with the same orientation as that of said driving direction, adding to one another. - a fixed structure; and - a mobile structure configured to move along a driving direction and includes a first deformable band, a second deformable band and a third deformable band which lie, in a first operating condition, in a resting plane and have a respective main extension along a first direction orthogonal to the driving direction, the first deformable band being arranged between the second and third deformable bands (47a, 47b) and being mechanically uncoupled, along said first direction, from the second and third deformable bands (47a, 47b) by respective first and second through trenches, the first, second, and third deformable bands (47c, 47a, 47b) each having respective ends and being joined together at said ends, and wherein the second deformable band is further coupled to the fixed structure by a first supporting element (12; 80; 82), and the third deformable band is coupled to the fixed structure by a second supporting element (14; 81; 84), the first and second supporting elements being aligned to one another, at least in the first operating condition, along one and a same first axis of symmetry orthogonal to said first direction, the first, second, and third deformable bands (47c, 47a, 47b) housing first, second, and third piezoelectrics (50k, 50i, 50j), respectively, wherein the second and third deformable bands (47a, 47b) and the respective second and third piezoelectrics (50i, 50j) are arranged with respect to one another and configured so that, in a second operating condition where the second and third piezoelectrics are biased by a working voltage, the second and third deformable bands (47a, 47b) are subjected to a negative bending that causes a translation of said ends and of the first deformable band in said driving direction; the first deformable band and the respective first piezoelectric being arranged with respect to one another and configured so that, when the first piezoelectric is biased at the working voltage, the first deformable band is subjected to a positive bending that causes a further translation in said driving direction of at least one portion of the first deformable band, which extends between said ends of the first deformable band, wherein the translation of said ends and of the first deformable band and said further translation of at least one portion of the first deformable band are directed with the same orientation as that of said driving direction, adding to one another.