*2.1.3. Interfaces*

The forces and strokes generated by the actuator must be suitably transmitted to the patient's limb, so connective or fastening elements have to be carefully considered in relation to local anatomical constraints, such as the size of the limbs or body parts and the available surrounding space. In particular, when designing a wearable device, additional dimensional and weight constraints must be taken into account. Generally, the device should be attached to the limb segments that articulate at the target joint, in order to promote their reciprocal movement. Designing such connections should take into account the dimensions of limb segments (that strongly depend on age, sex and pathology) and the available space (determined primarily by joint position and orientation relative to the rest of the body, sex and malformation, etc.). For example, a device to move the shoulder should be designed taking into account the sex of the patient, especially if a frontal strap is required; in the case of a knee device, on the other hand, the lateral aspect of the joint could provide more free space for attachment than the medial one, so that interference with the other leg can be avoided. Another important factor linked to the transmission of forces and movement is the device-skin interface. This must be carefully designed so that no excessive pressure, friction or relative motion occurs during activation of the actuator. Some of these problem can arise due to misalignment of the actuator rotation axis with respect to the corresponding anatomic joint axis. In case of wearable applications, also the weight and stability of the device on the limb should be taken into account.

### *2.1.4. Other issues*

94 Smart Actuation and Sensing Systems – Recent Advances and Future Challenges

suppressed (paresis, coma, castings, etc).

stability of the device on the limb should be taken into account.

*2.1.3. Interfaces* 

Apart from a passive response, joints can resist imposed movement also through the activation of the associated muscle groups. Muscular power can be delivered voluntarily (active motion) or by reflex activation. Involuntary active motion can also be produced by neurological conditions such as cloni, dystonia, chorea, etc. During limb and joint passive mobilisation muscle stretching can occur: a dedicated physiologic reflex produces instantaneous muscular contraction when the muscle fibres are elongated over a certain limit. This so called *stretch reflex* is much exasperated in spastic syndromes and may produce an involuntary, uncontrolled increase of resisting loads. Spasticity strongly depends on the speed of stretching; preconditioning the limb by a few cycles of slow manual stretching can help reduce momentarily the intensity of stretch reflex. Very severe spasticity, however, may correspond to the absolute impossibility of mobilising a joint.

Furthermore it must be remembered that the limbs adjacent to a joint possess a mass, and are therefore subjected to gravity and inertial forces connected to accelerations produced even in different parts of the body. One important case is gait. Where and when any or all of these components of the resisting or facilitating loads for the actuation must be taken into account has to be decided for each new application separately, in particular considering the typical position held by the target patient while the actuator is functioning, whether the patient will be prone to uncontrollable movements (jerks, dystonia, convulsions, etc.), or, on the contrary, whether some physiological movements will be typically impeded or

The forces and strokes generated by the actuator must be suitably transmitted to the patient's limb, so connective or fastening elements have to be carefully considered in relation to local anatomical constraints, such as the size of the limbs or body parts and the available surrounding space. In particular, when designing a wearable device, additional dimensional and weight constraints must be taken into account. Generally, the device should be attached to the limb segments that articulate at the target joint, in order to promote their reciprocal movement. Designing such connections should take into account the dimensions of limb segments (that strongly depend on age, sex and pathology) and the available space (determined primarily by joint position and orientation relative to the rest of the body, sex and malformation, etc.). For example, a device to move the shoulder should be designed taking into account the sex of the patient, especially if a frontal strap is required; in the case of a knee device, on the other hand, the lateral aspect of the joint could provide more free space for attachment than the medial one, so that interference with the other leg can be avoided. Another important factor linked to the transmission of forces and movement is the device-skin interface. This must be carefully designed so that no excessive pressure, friction or relative motion occurs during activation of the actuator. Some of these problem can arise due to misalignment of the actuator rotation axis with respect to the corresponding anatomic joint axis. In case of wearable applications, also the weight and Safety is a mandatory constraint when designing medical devices in general. For the particular case of rehabilitation actuators based on SMA, most risks could arise from electric, mechanical or thermal hazards. IEC 60601-1 is a widely accepted standard for medical electric equipment, and many countries tend to require compliance with IEC 60601-1 before commercialization of an electrical medical device is permitted [55]. Even if the medical device is intended for use only in the scientific laboratory, reference to this set of prescriptions may suggest precautions and guide designers and engineers in the development of safe devices. In connection with this latter standard, international standard ISO 14971 specifies a process for identifying the hazards associated with the use of medical devices and carrying out a suitable risk analysis [56]. Consequently, good practice requires to try and minimise all the identified risks. Moreover, when the medical device is approaching clinical validation, another norm to be considered is ISO 14155, which addresses the issues of designing, conducting, recording and reporting of clinical investigations carried out on human subjects [57]. All of these guidelines are valid also for SMA-based devices and may help consider further implications of new designs for the human body.

Dealing with patients, there are still other questions to be considered. Even if the device is functional and efficient and the actuator fulfils all the technical requirements, they will not be employed in the clinical setting if they are not acceptable to the patient. At the basis of *acceptability* there is a set of physical and psychological factors. Of course, the medical device should not produce nuisance or pain during short or prolonged use. Those problems, in the particular case of rehabilitation appliances and actuators, may depend on badly-designed interfaces with the skin or on movements imparted too fast. In fact, as already stated, contracted and spastic muscles are very responsive to stretch, especially when it is applied rapidly. During mobilisation, the increased muscle tone due to spastic reflexes may result in much discomfort for the patient. The use of SMA actuators in general has the advantage of providing low movement rates; however, severe spasticity may be hard to treat even with slow active devices. Other acceptability issues are often connected to psychological aspects. In particular, wearable devices should not embarrass the patient with noisy, bulky or cumbersome structures. For children, shape and colour can also be important features. SMA actuators are likely to be silent and miniaturised, and thus suitable in this respect, but all other components may not (i.e. power supply). Other impediments for patients employing rehabilitation devices actively or for assistive therapies may arise from their possible coexisting cognitive impairment: this consideration supports the use of very clear instructions and user interfaces, especially using non-verbal pictorial communication, lights, vibrations or sounds.

### **2.2. Actuator design**

#### *2.2.1. Strokes and loads*

Rehabilitation devices in most cases are intended to generate a mutual rotation of limb segments around an anatomical joint. By employing rotary actuators, it is possible to provide directly angular strokes and torques. On the other hand, linear actuators can be coupled with suitable lever arms and achieve the same results indirectly. The first step in designing an SMA-based rehabilitation actuator is to define, by careful analysis of the biomechanical constraints and clinical requirements, the appropriate neutral position, range of motion and resisting loads. The neutral position and range of motion will help determine a correct linear or angular stroke for the actuator; the resisting loads will set the linear force (and lever arm) or torque requisites. Of course, the two quantities will influence each other, for example different choices of lever arm may affect the linear stroke.

Once the required stroke and load have been determined, the geometrical parameters of SMA element can be worked out. Different types of actuators need different formulas for determining the parameters: for example, wire actuators have only two parameters, length and cross-section that directly depend on stroke and load respectively, while springs (helical, torsion or flat) parameters comprise coil dimensions, wire diameter and number of turns, which all depend on both stroke and load. Moreover material properties influence actuator parameters, especially in springs where anisotropy may play an important role [34]. Attention should be paid in particular to the critical stresses needed to detwin martensite both in the heated (above *Af*) and cooled (below *Mf*) states. This consideration can guide the choices about material composition and thermomechanical treatment, because those factor have great impact on the height of the plateaux and the mechanical hysteresis. In most actuation applications, in fact, it must be guaranteed that the load to be displaced is low enough that stress in the material is lower than the critical stress for the heated state; on the other hand, sufficient loading should be provided to detwin martensite and ensure actuator deformation and position reset during cooling for most cyclic applications. Whatever the SMA geometry, it can be stated in general terms that cross-section depends mainly on the maximum desired work output, through the mean level of stress acting on it. The question of choosing the level of stress is quite complex, and also involves the expected fatigue life of the actuator and the strains recovered upon activation. For example, it is reported that commercial NiTi-wire actuators can remain stable for more than 105 cycles at 200MPa and 4% of strain in traction [58], but other optimal compromises can be found, provided that stress does not exceeds 400MPa and strains 5%. The use of parallel actuators can help reduce required work from each actuator, i.e. given a stress level, cross-section can be reduced. Dimensioning crosssection should also take into account cooling rates, as will be discussed in the next section.

#### *2.2.2. Power*

Heating and cooling are key points concerning SMA actuation. The general equation that drives these processes is

$$P\_{ln}(t) = c\_p m \frac{d\tau}{dt} + m\Delta H \left| \frac{d\xi(\tau)}{dt} \right| + \frac{dW(\theta(t), t)}{dt} + P\_{d\text{loss}}(t). \tag{1}$$

Considering the heating (actuation) phase, *Pin(t)* is the heating power, ��� �� �� is the power needed to increase SMA element temperature (*cp* is the constant-pressure specific heat and *m*

is the mass), ��� ������ �� � is the power involved in phase transformation (� is the fraction of austenite and increases in time as transformation goes on, �� is the transformation enthalpy), *W(θ(t),t)* is the mechanical output (useful work, inertia and frictional losses) which varies along the movement trajectory *θ(t),* and *Pdiss(t)* is the power dissipated by thermal convection, thermal conduction and (less important in this case) thermal irradiation. Considering the cooling phase, and imagining that a bias force acts to restore the starting actuator configuration (by deforming the SMA element), *Pin(t)* is again a heating power that could be used to help control the cooling rate, ��� �� �� is the power to be dissipated in order to decrease SMA element temperature, ��� ������ �� � is the power involved in phase transformation (enthalpy in this case is negative), *W(θ(t),t)* accounts for the mechanical energy stored in detwinned martensite plus inertial and loss terms, and *Pdiss(t)* is the power dissipated. The contribution of *Pdiss(t)* is present both during the heating and cooling phases of an actuation cycle, but it may differ significantly if any active cooling system is included. Equation 1 gives a simplified description of the process, but permits to focus on some key points. First, SMA mass is an important factor when designing power consumption. Second, as all the diverse forms of dispersed energy depend on the amount of exposed surface, surface/mass ratio is the driving contribution to determine cooling time. Therefore, thin actuators (maximising the surface/mass ratio) should be preferred to bulky ones if cyclic, especially high-frequency actuation is desired. Having in mind which use is intended for the device provides a guidance for the choice of heating source and consequently gives some hints for the actuator design. The best strategy for providing controllable, cyclic actuation is heating by Joule's effect, but, especially for non-cyclic and one-shot activation, also direct thermal transfer may be suitable. Focusing on Joule's effect, the energy provided depends on the injected current and the electric resistance of the SMA element according to Equation 2:

$$P\_{\rm in}(\mathbf{t}) = P\_{\rm Ooule}(\mathbf{t}) = I(\mathbf{t})^2 \cdot R\_{\rm SMA}(\mathbf{f}) \tag{2}$$

where the electric resistance ������� can be expressed as

96 Smart Actuation and Sensing Systems – Recent Advances and Future Challenges

for example different choices of lever arm may affect the linear stroke.

*2.2.2. Power* 

drives these processes is

���(�) � ���

��

Considering the heating (actuation) phase, *Pin(t)* is the heating power, ���

provide directly angular strokes and torques. On the other hand, linear actuators can be coupled with suitable lever arms and achieve the same results indirectly. The first step in designing an SMA-based rehabilitation actuator is to define, by careful analysis of the biomechanical constraints and clinical requirements, the appropriate neutral position, range of motion and resisting loads. The neutral position and range of motion will help determine a correct linear or angular stroke for the actuator; the resisting loads will set the linear force (and lever arm) or torque requisites. Of course, the two quantities will influence each other,

Once the required stroke and load have been determined, the geometrical parameters of SMA element can be worked out. Different types of actuators need different formulas for determining the parameters: for example, wire actuators have only two parameters, length and cross-section that directly depend on stroke and load respectively, while springs (helical, torsion or flat) parameters comprise coil dimensions, wire diameter and number of turns, which all depend on both stroke and load. Moreover material properties influence actuator parameters, especially in springs where anisotropy may play an important role [34]. Attention should be paid in particular to the critical stresses needed to detwin martensite both in the heated (above *Af*) and cooled (below *Mf*) states. This consideration can guide the choices about material composition and thermomechanical treatment, because those factor have great impact on the height of the plateaux and the mechanical hysteresis. In most actuation applications, in fact, it must be guaranteed that the load to be displaced is low enough that stress in the material is lower than the critical stress for the heated state; on the other hand, sufficient loading should be provided to detwin martensite and ensure actuator deformation and position reset during cooling for most cyclic applications. Whatever the SMA geometry, it can be stated in general terms that cross-section depends mainly on the maximum desired work output, through the mean level of stress acting on it. The question of choosing the level of stress is quite complex, and also involves the expected fatigue life of the actuator and the strains recovered upon activation. For example, it is reported that commercial NiTi-wire actuators can remain stable for more than 105 cycles at 200MPa and 4% of strain in traction [58], but other optimal compromises can be found, provided that stress does not exceeds 400MPa and strains 5%. The use of parallel actuators can help reduce required work from each actuator, i.e. given a stress level, cross-section can be reduced. Dimensioning crosssection should also take into account cooling rates, as will be discussed in the next section.

Heating and cooling are key points concerning SMA actuation. The general equation that

needed to increase SMA element temperature (*cp* is the constant-pressure specific heat and *m*

�� � � ��(�(�)��)

�� � �����(�). (1)

��

�� is the power

�� � ��� ���(�)

$$R\_{SMA}(\xi) = \rho(\xi) \cdot \frac{\iota(t)}{\mathcal{S}} \tag{3}$$

with ���� representing the SMA resistivity, *S* the cross-sectional area of the SMA element, *L*(t) the length over which the current flows, that obviously changes as actuation goes on. Given a length of SMA wire (which depends directly on the stroke required from the actuator), the thinner the wire, the higher is the electrical resistance. Moreover, massdependent contributions to Equation 1 are also minimised, and heating efficiency increased.

SMA actuators are subjected also to the Clausius-Clapeyron relation, that can be expressed as:

$$
\Theta^\* = \Theta + \frac{\sigma}{c} \tag{4}
$$

where � is one of the transformation temperatures, which is effectively increased to �\* when a stress � is applied to the material. This is a very important issue when purchasing shape memory materials or dimensioning SMA actuators powering: the transformation

temperatures as provided by DSC analysis will be shifted when the material is loaded. Typical values of *C* for NiTi range from 5 to 9 MPa/°C, i.e. an actuator designed to bear 200MPa would have transformation temperatures increased by as much as 40°C. However, actuation temperatures cannot be increased indefinitely: in fact, above a certain temperature (*Md*), part of the deformation cannot be recovered and material undergoes plastic slip.
