IEEE Robotics & Automation Magazine - December 2010 - 82

to generate more force. Instead, the force exerted by an actuator
can be increased by combining multiple cells.

Active Force−Displacement: Five Actuators

2.5

Electrical Resistance Response
The response of the cell to different values of electrical current
was also tested. The response is shown in Figure 7, where we
can observe the resistance change at least 15% of its initial value
when the transition temperature is reached. The value of the
resistance correspond to 24 cells (d ¼ 1:2 mm) in series. The
intensity of the electrical current affects the time taken to reach
the transition temperature. In the case of 0.9 A, the transition
temperature was not reached in the time window considered
for the experiment.

Force (N)

1.5
1
d = 0.6 mm
d = 0.9 mm
d = 1.2 mm
d = 1.5 mm
d = 1.8 mm

0.5
0
−0.5

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8
Normalized Displacement

Composing Actuators

Figure 6. The active force-displacement response of the five
actuators shows that for d <¼ 1:2 mm; the peak and average
exerted force increases quickly with increasing d. For
d > 1:2 mm; the force begins to slowly drop off as d becomes
progressively larger. The active force is obtained by discounting
the passive force from the total force measured.

displacements less than 1.0, the force remains roughly constant.
For displacements greater than one, the forces reduce rapidly.
For system design purposes, we consider the unit cell an on/off
actuator, which operates in the expansion region, and whose
force depends on its maximum displacement.
Discounting the passive force, the active force generated at
normalized displacement xnorm ¼ 1 is 2:25 N. The maximum
normalized displacement achieved is xnorm ¼ 1:436.
In Figure 6, we can observe the active force response of
different sized actuators. As we increase the size of the cells,
the generated force increases. This behavior reaches a peak
around d ¼ 1:2 mm; and as the size of the cell increases further,
each generates less force. This can be attributed to the structural
effects as explained in Figure 2(b). This shows that continuing
to increase the amount of SMA in a unit cell does not continue

SMA Resistance (Ω)

SMA Resistance Versus Time Versus Driving Current
1.6
2.0 A
1.55
1.8 A
1.6 A
1.5
1.4 A
1.45
1.2 A
1.0 A
1.4
1.35
1.3
1.25
1.2
1.15

0.5

1.5

2 2.5
Time (s)

3.5

4.5

Figure 7. Current applied to the SMA was swept from 1.0 to
2.0 A to determine the response time of the SMA actuator as
indicated by a change in its resistance. Higher currents
produced quicker responses (less than 0.5 s).
82

IEEE Robotics & Automation Magazine

In general, actuation mechanisms that work effectively in small
dimensions but do not scale up well can be combined to
obtain larger forces or displacements. Consider human muscle
where the output force is generated by a combination of
contractile proteins (myofilaments) connected in parallel and
in series. We can do the same with the unit cells of our SMA
actuators. The force exerted by a single unit cell does not scale
up well, because the current required to heat thicker pieces of
SMA becomes prohibitive. As shown in the "The Unit Cell:
The Effect of Unit Cell Dimensions" section, increasing the
length of the SMA beyond a certain point does not continue
to produce larger forces either.
The alternative is to combine the output effects of multiple unit cells by mounting them in parallel and/or series to
obtain different expansions, trajectories, and forces. The
complexity of fabricating such actuators increases because
many unit cells need to be mounted and controlled, but this
additional complexity is more than offset by the flexibility
offered in return. In many cases, the control of the unit cells
can be simplified by separating them in groups. These groups
of cells can be placed in a common electrical circuit for
simultaneous activation.
Figure 8 shows different configurations of unit cells to create linear, rotational, and surface actuators. All the actuators in
this figure use 24 unit cells, electrically connected in series.
These unit cells are organized in 6 3 4 or 4 3 6 arrays that are
mounted in different support structures to produce the desired
trajectory. The array of unit cells was patterned with a laser on
an SMA sheet (0:05 mm thickness) whose default position is
flat. These actuators were built to operate in one direction.
Bidirectional actuators can be achieved by using two or more
actuators antagonistically.
Linear Actuator
Figure 9(b) shows the idea used to build a linear actuator. Six
cells are mounted on plastic hexagons that serve as support
structures. Figure 9(a) illustrates the working principle; the six
cells expand simultaneously on a linear trajectory. By mounting 24 unit cells on five hexagons (3-D printed), we build a
four-stage linear actuator that is shown in Figure 9(c). This linear actuator was operated with 1:5 A and 4 Vð6W. The maximum output force measured is 80 gf ¼ 0:784 N. The
DECEMBER 2010

Table of Contents for the Digital Edition of IEEE Robotics & Automation Magazine - December 2010