A stepwise discrete actuator (10; 30; 40; 50) comprising: • a stationary support (11; 41; 51; 91), • a movable toothed element (12; 32; 42; 52) with a constant tooth pitch P defining a step distance for the actuator discrete steps, • a slider (13; 33; 43; 53; 73; 83; 93) for moving said movable toothed element (12; 32; 42; 52) through two fingers (131, 132; 331, 332; 431, 432; 531, 532) that alternately engage its teeth, • a stationary finger lifter (14; 34; 44; 54) configured to lift that of said two slider fingers (131, 132; 331, 332; 431, 432; 531, 532) that does not engage the movable toothed element (12; 32; 42; 52), • two shape memory alloy wires (15, 15'; 35, 35'; 45, 45'; 55, 55'; 75, 75'; 85, 85'; 95, 95') connected in an antagonistic configuration, each of which is connected between a stationary terminal (150, 150'; 350, 350'; 450,450'; 550, 550'; 750, 750'; 850, 850'; 950, 950') at a first end and said slider (13; 33; 43; 53; 73; 83; 93) or an intermediate element (78; 88, 89; 96, 97) connected to the slider (13; 33; 43; 53; 73; 83; 93) at a second end, so as to drive the slider (13; 33; 43; 53; 73; 83; 93), wherein - said stationary support (11; 41; 51; 91) is coupled to the movable toothed element (12; 32; 42; 52) by means of releasable locking structures (16, 17; 46, 46',..., 46 n; 56, 57) arranged at said step distance P from each other, - the slider (13; 33; 43; 53; 73; 83; 93) is structured such that it can only deform so as to move away from the movable toothed element (12; 32; 42; 52) but not towards it, - the lift performed by said stationary finger lifter (14; 34, 34'; 44; 54) is caused by the movement of the slider (13; 33; 43; 53; 73; 83; 93) upon actuation of one of the two shape memory alloy wires (15, 15'; 35, 35'; 45, 45'; 55, 55'; 75, 75'; 85, 85'; 95, 95') and is allowed by a gap G along the direction of movement of the slider (13; 33; 43; 53; 73; 83; 93) between said slider finger (131, 132; 331, 332; 431, 432; 531, 532) that is being lifted and the tooth upstream therefrom along said direction, such that said slider finger (131, 132; 331, 332; 431, 432; 531, 532) can clear the teeth of the movable toothed element (12; 32; 42; 52), and wherein said gap is calculated as G=n ∗ P+T-F where n is the number of teeth contained between the slider fingers (131, 132; 331, 332; 431, 432; 531, 532) at rest, P is the tooth pitch/step distance, T is the distance between two adjacent teeth, and F is the distance between the slider fingers (131, 132; 331, 332; 431, 432; 531, 532) at rest. • a stationary support (11; 41; 51; 91), • a movable toothed element (12; 32; 42; 52) with a constant tooth pitch P defining a step distance for the actuator discrete steps, • a slider (13; 33; 43; 53; 73; 83; 93) for moving said movable toothed element (12; 32; 42; 52) through two fingers (131, 132; 331, 332; 431, 432; 531, 532) that alternately engage its teeth, • a stationary finger lifter (14; 34; 44; 54) configured to lift that of said two slider fingers (131, 132; 331, 332; 431, 432; 531, 532) that does not engage the movable toothed element (12; 32; 42; 52), • two shape memory alloy wires (15, 15'; 35, 35'; 45, 45'; 55, 55'; 75, 75'; 85, 85'; 95, 95') connected in an antagonistic configuration, each of which is connected between a stationary terminal (150, 150'; 350, 350'; 450,450'; 550, 550'; 750, 750'; 850, 850'; 950, 950') at a first end and said slider (13; 33; 43; 53; 73; 83; 93) or an intermediate element (78; 88, 89; 96, 97) connected to the slider (13; 33; 43; 53; 73; 83; 93) at a second end, so as to drive the slider (13; 33; 43; 53; 73; 83; 93), - said stationary support (11; 41; 51; 91) is coupled to the movable toothed element (12; 32; 42; 52) by means of releasable locking structures (16, 17; 46, 46',..., 46 n; 56, 57) arranged at said step distance P from each other, - the slider (13; 33; 43; 53; 73; 83; 93) is structured such that it can only deform so as to move away from the movable toothed element (12; 32; 42; 52) but not towards it, - the lift performed by said stationary finger lifter (14; 34, 34'; 44; 54) is caused by the movement of the slider (13; 33; 43; 53; 73; 83; 93) upon actuation of one of the two shape memory alloy wires (15, 15'; 35, 35'; 45, 45'; 55, 55'; 75, 75'; 85, 85'; 95, 95') and is allowed by a gap G along the direction of movement of the slider (13; 33; 43; 53; 73; 83; 93) between said slider finger (131, 132; 331, 332; 431, 432; 531, 532) that is being lifted and the tooth upstream therefrom along said direction, such that said slider finger (131, 132; 331, 332; 431, 432; 531, 532) can clear the teeth of the movable toothed element (12; 32; 42; 52), n is the number of teeth contained between the slider fingers (131, 132; 331, 332; 431, 432; 531, 532) at rest, P is the tooth pitch/step distance, T is the distance between two adjacent teeth, and F is the distance between the slider fingers (131, 132; 331, 332; 431, 432; 531, 532) at rest.