**5. Conclusion**

The optimum mechanical design of shape memory based actuators is performed by means of analytical description of the governing equations of the system, providing an easy to follow design procedure for engineers working with SMA devices. Since no complex thermomechanical models are involved, the closed form equations developed are based on two simple constitutive models: a linear or a bilinear behaviour for the martensitic phase and a linear relationship for the austenitic phase. Three backup elements are considered to recover the stroke: a constant force, a traditional elastic spring and antagonist SMA element, leaving the designer the opportunity to adopt those which fits the application best. The external load is as general as possible, because a system of both dissipative and conservative forces is taken into account. The actuator performances are improved considering an elastic compensation instead of a backup element. This negative stiffness element can enhance either the stroke or the force of the SMA actuator depending on the needs. The output force design equations both for the SMA actuators and for the compensator are given and the detailed description of the compensated SMA system grants an immediate comprehension of the whole system. In order to give an operative guideline for SMA actuators design, several numerical examples are provided. The proposed procedure is applied to real case studies and to a specific configuration of SMA active elements (wires or springs). The benefits of the described methodology are critically discussed and compared. In terms of mechanical performance the agonist antagonist SMA system gives the best performances both for compensated and uncompensated systems, while optimum values for the non dimensional parameters are provided in order to obtain compact and efficient SMA based actuators. The analytical equations developed in this Chapter allow a SMA based actuator to be correctly designed in order to match the specifications and give useful information to optimize size and mechanical response of the system with no need of complex numerical simulations.
