*2.4.2. General concept of the device*

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

martensite detwinning.

2. Choosing a reduced range for the device, biased towards dorsiflexion, has the advantage that the calf muscles are kept under a relative stretch (physiological neutral angle is around -25°); furthermore it is appropriate to avoid forcing the joint excessively towards the extreme dorsiflexion position (conservative approach to limit insurgence of spastic reflexes). A target ROM for mobilisation was therefore was chosen as -5°/+10°. Of course, the actual working range will depend on the passive characteristic of the

3. For a target population represented by this type of subjects it is reasonable to assume that passive resisting torque does not exceed 400Ncm in the range of interest.

Considering the general conditions of the patients in the first weeks after a stroke, it would be wise to design a device that can be employed in the bed. However, the knee joint should be sustained in a flexed position, so that the bi-articular *gastrocnemius* muscle is not prestretched and full ankle range of motion is available. As a way of compromise, an angle of 10° for the leg rest can be assumed, with the foot positioned lower than the knee. It should be taken into account that, in such a configuration, the contribution of foot weight to the resisting force is limited. Figure 3 shows the total resisting torque, comprising different foot weights, and the same viscoelastic resistance from a typical patient. The expected maximal resisting torque can be approximately calculated in 400Ncm. As the curve hysteresis is not large for this joint (cf. Figure 2), the same values used for dorsiflexion can be also utilised when considering the movement towards plantarflexion and the loading level associated to

**Figure 3.** Influence of foot weight on the total resisting torque at the ankle. Differences in foot weight (proportional to the body weight) account for little change due to the lying position of the limb.

specific ankle, but is not expected to be much different from the target one.

Figure 4 shows a simple embodiment of the concept. Two thermoplastic shells lined with soft foam are modelled on a prototype human lower limb of average size. These shells are hinged together and strapped by Velcro® bands respectively on the frontal aspect of the shin and the foot, in such a manner that the ankle and the hinge are perfectly aligned along the same axis (this minimises unwanted friction and sliding between the orthosis and the skin). The choice of planar hinges was also made to control (fixate) ad/abduction and in/eversion, although this solution makes the device unsuitable for patients that have already developed severe malformations out of the sagittal plane (unusual in the acute phase). With this structural configuration, two linear actuators are fixed on the front of the leg shell and transfer actuation pull to the foot shell through inextensible threads.

**Figure 4.** Implementation of an exerciser for the ankle joint with linear SMA actuators. The device is designed to provide cyclic joint flexion in the rehabilitation of neurological patients in the acute phase. On the left, schematic representation of the main design dimensions to calculate the lever arm.

The linear stroke and force output required of the SMA actuators depend, through the lever arm, on the fixation points for the actuators (on the shin), and the distal ends of the inextensible threads (foot shell). Actuators produce dorsiflexion, while plantarflexion and actuators position reset is left to gravity and viscoelastic resistances.

Power supply is to be provided by a dc-generator, which is not on board the wearable device, as the intended use is not for walking. This choice helps limiting weight and keep the device stable on the patient's leg during use.

An open-loop control strategy is adopted for the use as passive exercise device, whereas a simple closed-loop control for assistive rehabilitation employs the electromyographic activity from *tibialis anterior* as control signal, picked up by surface electrodes. As for the power supply, it was decided that all the components needed for control are not mounted on board the wearable device, even though integration would be possible by developing *adhoc* electronics.

### *2.4.3. Actuator design and characterisation*

With the selected set of geometrical parameters (Figure 4: *a*=16cm, *b*=8.5cm, *c*=15cm), a linear stroke of 2.5cm is required to produce an angular movement across the range -5°/+10°. Considering a linear deformation of 3%, the required amount of wire for linear actuation would be 83cm. However, in our case it would be impractical to have a free-standing wire of such a length as a linear actuator. For this reason, the NiTi wire should be confined into a more compact actuator. In dimensioning the length of wire now we must take into account also the local deformations that inevitably will be imposed on the SMA wire when coiling it. The actuator was designed as an insulated cartridge wherein the necessary reference length of NiTi wire is led back-and-forth between two arrays of ten pulleys. An end of the wire is connected to an inextensible thread that transmits the force to the foot, while the other one is fixed to the housing. A pseudoelastic spring is connected to the moving end of the NiTi wire in order to keep it just taut, and its pull is negligible during actuation.

Considering the force requirement, each actuator should bear half of the resisting torque *Tr* showed in Figure 3, and the amount of force varies at varying ankle angles *θ* (defined between the foot direction and the horizontal, Figure 4):

$$F(\theta) = \frac{\tau\_r(\theta)}{c \cdot \sin \varphi} \tag{5}$$

where ϕ is the angle between the inextensible thread and the foot and depends on *θ* according to:

$$\varphi(\theta) = \frac{\pi}{2} - \theta - \arccos\left[\frac{c\sin\theta + a}{\sqrt{(c\cos\theta - b)^2 + (c\sin\theta + a)^2}}\right] \tag{6}$$

With a maximum torque of 200Ncm, Equations 5 and 6 give a maximum load of 13N on each actuator. By selecting a 250μm-diameter commercial NiTi wire, stabilised for actuation, the maximum stress on the wire cross-section is 266MPa. In order to complete plantarflexion, full martensite detwinning should be achieved. It is certainly possible to find stabilised wires for which martensite detwinning occurs with less than 100MPa, corresponding to around 5N pulling on a 250μm-diameter wire. With the expected resisting torque in Figure 3 and the geometrical parameters, force requirement for martensite detwinning is always satisfied in the range -5°/+10° and thus cyclic actuation will take place in that range. Considering a diameter of the pulleys of 12mm, the maximum amount of localised strain is 2%. In order to respect the 3% limit for the maximal deformation, only 1% of strain is available for actuation and can be employed for calculating the length of wire to be coiled within each actuator, that is to say, 250cm.

Having limited strains to 3% and stress to 300MPa, a cycling life of 30k-100k cycles is expected [58].

#### *2.4.4. Power dimensioning*

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

actuators position reset is left to gravity and viscoelastic resistances.

in order to keep it just taut, and its pull is negligible during actuation.

between the foot direction and the horizontal, Figure 4):

�(�) <sup>=</sup> � �

the device stable on the patient's leg during use.

*2.4.3. Actuator design and characterisation* 

*hoc* electronics.

according to:

The linear stroke and force output required of the SMA actuators depend, through the lever arm, on the fixation points for the actuators (on the shin), and the distal ends of the inextensible threads (foot shell). Actuators produce dorsiflexion, while plantarflexion and

Power supply is to be provided by a dc-generator, which is not on board the wearable device, as the intended use is not for walking. This choice helps limiting weight and keep

An open-loop control strategy is adopted for the use as passive exercise device, whereas a simple closed-loop control for assistive rehabilitation employs the electromyographic activity from *tibialis anterior* as control signal, picked up by surface electrodes. As for the power supply, it was decided that all the components needed for control are not mounted on board the wearable device, even though integration would be possible by developing *ad-*

With the selected set of geometrical parameters (Figure 4: *a*=16cm, *b*=8.5cm, *c*=15cm), a linear stroke of 2.5cm is required to produce an angular movement across the range -5°/+10°. Considering a linear deformation of 3%, the required amount of wire for linear actuation would be 83cm. However, in our case it would be impractical to have a free-standing wire of such a length as a linear actuator. For this reason, the NiTi wire should be confined into a more compact actuator. In dimensioning the length of wire now we must take into account also the local deformations that inevitably will be imposed on the SMA wire when coiling it. The actuator was designed as an insulated cartridge wherein the necessary reference length of NiTi wire is led back-and-forth between two arrays of ten pulleys. An end of the wire is connected to an inextensible thread that transmits the force to the foot, while the other one is fixed to the housing. A pseudoelastic spring is connected to the moving end of the NiTi wire

Considering the force requirement, each actuator should bear half of the resisting torque *Tr* showed in Figure 3, and the amount of force varies at varying ankle angles *θ* (defined

�(�) <sup>=</sup> ��(�)

where ϕ is the angle between the inextensible thread and the foot and depends on *θ*

��� arccos � ��������

With a maximum torque of 200Ncm, Equations 5 and 6 give a maximum load of 13N on each actuator. By selecting a 250μm-diameter commercial NiTi wire, stabilised for actuation, the maximum stress on the wire cross-section is 266MPa. In order to complete

����� � (5)

�(��������)��(��������)�� (6)

In order to evaluate the parameters for Joule's effect heating, various experimental tests were carried out on samples of NiTi wire. First, the transformation temperatures were investigated by means of differential scanning calorimetry (on DSC 220 SSC/5200 - Seiko Instruments, Tokyo, Japan), showing *Af* = 351K and *Mf* = 274K. However, calorimetry gives information about the material with no loads applied, whereas Equation 4 suggests that transformation temperature depends on the load applied. For this reasons, tensile tests on the material at different temperatures were conducted using an MTS 2/M thermomechanical test machine (MTS Systems, Eden Prairie, MN, USA) equipped with a 2kN load cell. The material was deformed up to an engineering strain of 5%, at 365K, 380K, 390K and 400K. The pseudoelastic plateau values varied as a function of temperature with a ratio of 8.402 MPa/K, which is exactly the constant *C* in Equation 4. With the estimated stress level of 266MPa, full transformation and strain recovery can be achieved at 383K.

Activation tests on the wire were conducted injecting different currents (0.65A, 0.7A, 0.75A, 0.8A) in the wire at a constant strain of 3% for a set period of 13s, in order to evaluate what current value is most appropriate to provide the working load of 13N, minimizing current expenditure and heating time. As expected, the higher the current the faster is actuation. Patient safety considerations should be taken into account, as well. A compromise solution can be accepted with 0.7A, which allows for reaching 13N within 6s. With the selected current, voltage is limited to 35V, considering an average resistance of 49.5 Ω (45-54Ω during transformation from fully austenitic to fully martensitic). Notice that the rehabilitation device mounts two actuators, which need a 0.7A current each. The electrical configuration of the two actuators could be a series or a parallel circuit: in the first case, the dc-generator should be able to provide 0.7A at 70V, in the latter case 1.4A at 35V. According to IEC 60601-1 specifications, dc tension preferably does not exceed 60V, i.e. in our case the two linear actuators are better connected in parallel.

Heating parameters can be extracted by testing a free-standing NiTi wire, and by applying 35V to the ends of the cartridge actuator suspending a 13N weight. It was demonstrated that nominal linear stroke is reached in around 6s (mean dorsiflexion speed 2.5°/s). On the other hand, cooling times depend strictly on the geometrical arrangement of the wire in space. A

compact actuator may have a considerably slower cooling and position reset time, as tests on the actuator confirms. Basically, if the vertical free-standing wire cools down in approximately 10s, cooling and actuator position reset takes place in 30s. The full cycle thus lasts 36s, which makes it possible to deliver 100 cycles/hour to the patient's ankle, as required by the design specifications.
