# A Morphing Deployable Mechanism for Re-Entry Capsule Aeroshell
## 5 Morphing Tab Concept  
### SMA Modelling Approach  
The structural morphing of the tabs is obtained through the SMA technology. The compactness, jointly to the relatively large energy density, makes this technology a good candidate for this specific steady (<1 Hz) application. This frequency upper limit is strictly related to thermal inertia of the material. In principle, the higher is the power supply, the shorter is the time of activation, and the more efficient is the cooling of the shorter in the de-activation phase. Many works can be found in the literature dealing with the speed  
Figure 8: Deployment angles relative to ring displacement. Figure 9: Variation in the relative rotations of the rib segments relative to deployment angle. of actuation of the SMA material and with strategies aimed at increasing it. A key role is played by the surface of the actuator, being strictly related to the heat transfer. To cite some examples, one recalls the work of [PERSON] et al. [31], focusing on an SMA-based actuator arriving at a frequency of 35 Hz; in this work, the strategy to overcome the above-mentioned upper limitation of 1 Hz is presented. In another work [32], [PERSON] et al. investigated the effect of pre-stress on the actuation speed of an antagonistic SMA system and demonstrated the capability of achieving cyclic actuation in a period of 0.5 s.  
Another critical aspect is the environmental temperature variation that impacts on needed power, time of activation and de-activation, and is, potentially, responsible for undesired activations. The starting activation temperature is kept generally over the upper limit of the operational scenario to avoid undesired activation. Designers can play on two parameters to control the activation temperature: the composition of the alloy and the preload level, the former assuring a wide excursion window for the transformation temperatures (more than one hundred of Celsius degrees), the latter causing an increase in the original activation temperatures regulated by the alloy transformation temperature/stress ratio. To guarantee both inwards and outwards deflections, the antagonistic configuration, shown in Figure 10, was investigated. The original tab, illustrated in the sketch on the left, was milled preserving the root hinge region and the tip while shaping a flat middle plate on most of the chord. Root and tip were then linked to two SMA rods, as illustrated in the scheme on the right. Two SMA rods were connected to the tip of the inner bending beams in an antagonistic way to provide both upward and downward deflections of the flaps. The contraction of one SMA actuator upon heating resulted in the extension of the opposing SMA actuator mechanically. Then, the contraction by heating of the extended actuator will reverse the actuation. The SMA rods were mounted with a certain pre-stress to have enough martensite phase exploitable for the actuation, that is to say, potentially transformable by heating into austenite to produce strain recovery at a macroscopic level. When outwards deflection is required, the upper SMA is heated; its contraction thus causes the upwards movement of the tip. In the same way, when inwards deflection is required, the lower SMA is activated. Although it is possible to imagine the activation of an SMA rod when the other one is still warm and in austenite phase, in this work, only the case of the activation of an SMA when the other one is cold and in martensite phase was considered. The main tab structure is prone only to deflections occurring in the plane containing the SMA elements; no constraint enforces this type of motion other than the geometry of the cross section of the main tab whose lowest inertia moment drives the planar deflection.