# Bio-Inspired Morphing Tail for Flapping-Wings Aerial Robots Using Macro Fiber Composites
## 2 MFC Tail Actuator Characterization
### MFC Actuator Structure  
The MFC actuator is composed of four layers of different materials. The center layer is the piezoelectric material, which is the most important one, because it performs the actuation. This layer is sandwiched by the rest.  
Surrounding the central layer is the one that is composed of copper electrodes and epoxy. The epoxy guarantees the position of the copper electrodes. These electrodes per form the electric field that produces the movements of the piezoelectric material. The orientation of the copper electrodes is crucial, as they are the ones that produce the deformation.  
In the case of the MFC used in this work, the electrodes are positioned transversely, which generates a deformation in the longitudinal direction. The uniform distribution of the electrodes generates a continuous displacement.  
The next layer is made of an acrylic material that protects and isolates the previous layers.  
Finally, there is a layer made out of Kapton. Kapton is a material with excellent thermal properties. It is usually used to isolate the electronic components when soldering is needed. In this case, the terminals of the electrical power should be welded, but, due to the isolation with Kapton on the rest of the surfaces, the MFC can be used in thermal applications. Figure 2 presents an image of the separated layers.  
The previously described MFC composition was the one that was developed and patented by NASA. Actually, MFC actuators can not produce vertical displacement by themselves, and they need to be attached to a host material for performing this deformation or morphing. This will be further detailed in Section 3.  
The properties and capabilities of the MFC actuator are based on its composition. The different layers add their properties to the final actuator. The MFC selected for this work can actuate in a longitudinal direction. The actuation is based on the electric field that is generated by the copper electrodes and the influence on the piezoelectric material.  
In practice, the actuation is based on the properties of passive materials. These materials add stiffness to the actuator, and this stiffness generates internal forces. Accordingly, these forces directly affect the performance of the MFC, generating deformations in different directions, not only in the longitudinal one.  
In this work, it is intended to maximize the vertical displacement of the actuator by properly managing the internal forces.  
Additionally to the vertical displacement, maximizing the blocking force of the system is also needed. The blocking force opposes the forces of the wind and other external forces, making the deformation stable. A stable actuation is very important in maintaining control over the system. In this work, a balance between the blocking force and the displacement of the actuator is intended. These variables are related with the stiffness of the actuator. This is an equilibrium problem: a major displacement can be achieved by reducing the stiffness of the actuator, but this reduction of stiffness also reduces the blocking force. Several experiments were carried out and the best equilibrium point was chosen, having a good displacement for controlling the robot while maintaining the needed blocking force.