## 1 Introduction  
In civil aviation, morphing flaps are garnering increased attention from the technological and scientific communities. This interest is driven by the potential advantages offered at the aircraft level, particularly in enhancing high-lift performance and reducing fuel consumption. By exploiting morphing capabilities, it becomes feasible to adopt a single-flap configuration and adjust its shape to meet the aerodynamic take-off and landing requirements. By avoiding multiple-part high-lift architectures, the design is largely simplified. Those systems (such as Fowler/Kruger flaps, slats, droops, etc.) play a crucial role at low-velocity regimes; in that case, the wing's performance requirements are pursued by increasing max lift coefficient (C\({}_{\text{L,max}}\)) and stall angle, resulting in increased carried-loadcapacity. Their deployment requires an intricate design of the mechanism system that is in line with the flight parameters, also accounting for mobility constraints due to possible limited range of motion. For instance, in the case of the common triple-slotted fowler flap [1], only three rotations shape the camber variations. Furthermore, negative rotation (upper-wise) is usually not permitted. Recently, there has been significant interest in morphing structures to better adapt to different flight conditions [2; 3; 4; 5; 6; 7; 8; 9]. In reference [5], the study therein reported comparing different morphing flap (MF, in what follows) architectures through 2D and 3D simulations to define an optimal configuration. Predictions indicated that lift and efficiency could increase by several percentage points, with notable differences observed between take-off and landing, as expected. The selected morphing trailing edge could modify its shape in several ways, adding degrees of freedom, if compared to a conventional one, to face different environments. Combined with adaptive control technologies, these morphing structures offer unprecedented potentialities for next-generation aircraft, enabling rapid responses to operational changes, safer take-offs and landings, and improved fuel efficiency. Research by [PERSON] et al. [10] showed that high-lift devices equipped with multiple elements and slits can significantly enhance lift for wings. This is why double- and triple-slotted flaps were initially implemented in large commercial aircraft, such as B707, B737, and A300. The complexity of multi-element high-lift systems is, however, strictly related to maintenance and repair costs. To simplify deployment mechanisms, with the aim of facilitating the production and operation aspects, single-slotted flap configurations have recently gained popularity in commercial aviation. For example, the Adaptive Dropped Hinge Flap (ADHF) [11] was introduced on the A350 XWB-900 to decrease the weight and complexity of the devices while using a slotted camber tab configuration. Adaptive camber is among the most promising concepts of morphing technologies, particularly suitable for adjusting the airfoil curvature to foster high-lift aerodynamic performances. Over the years, various experimental approaches have been proposed and tested to achieve that goal by using flexible skins connected to rigid mechanisms, including rigid levers and kinematic joints, with initial developments originating from Boeing and NASA (National Aeronautics and Space Administration) [12]. In relation to the trailing edge, [PERSON] (1995) [13] proposed a finger-like concept as part of the ADIF project, which utilized ribs made of multiple plates connected by revolute joints and attached to the skin via sliding joints. Years later, [PERSON] also explored a morphing solution to replace the conventional droop nose device on typical Airbus aircraft (2010) [14], designed by employing optimization techniques. The design of this high-lift device is aimed at realizing a seamless and gapless wing structure to minimize acoustic emissions and drag while ensuring laminarity.