IEEE Robotics & Automation Magazine - September 2016 - 70

160

10

Cooling
Angular Velocity (°/s)

Angle (°)

100
70

Heating

40

P = 0.41 W
P = 0.37 W
P = 0.34 W

10
−20

Cooling

5

130

0

10

20

30
Time (s)

40

0
−5
−10

Heating

−20
0

50

P = 0.41 W
P = 0.37 W
P = 0.34 W

−15
10

20
30
Time (s)

(a)
Cooling
105
Angle (°)

Temperature (°C)

145

P = 0.41 W
P = 0.37 W
P = 0.34 W

60
50
40

65

Heating

25

30
20
0

10

50

(b)

80
70

40

20
30
Time (s)

40

−15

50

P = 0.41 W
P = 0.37 W
P = 0.34 W
40

30

50
60
Temperature (°C)

(c)

70

80

(d)

Figure 3. The experimental results for the load-free test. Three power levels are tested as input to the heater for a certain time until
the actuator reaches its closed configuration. Then power is switched off for cooling. (a) The angular displacement of the actuator
over time and (b) the corresponding angular velocity are the outputs of the (c) temperature behavior measured on the actuator.
(d) The temperature-to-angular displacement relation is plotted.

160

30
Torque (mN ⋅ m)

Angle (°)

130

35
Model
Experiment

100
70
40
10
−20
25

Model
Experiment

25
20
15
10
5

35

45
55
Temperature (°C)

65

75

(a)

0
30

40

50
60
70
Temperature (°C)

80

(b)

Figure 4. (a) The experimental angular deflection in a load-free test and the computed angular deflection using the model and (b) the
measured blocked torque at i = 90c and the calculated value based on the proposed model.

C 2 /C A x = C 2 /C M x = 0 , and T is taken as the actual
measured temperature of the actuator for P = 0.37 W .
As a result, the model complies relatively well with the
experimental results, with a maximum deviation of
11.3%. The A s , A f , M s , and M f values obtained from
the model fit are summarized in Table 2.
70

*

IEEE ROBOTICS & AUTOMATION MAGAZINE

*

September 2016

Blocked Torque Test for T 2 A f
The blocked torque test determines the maximum torque
x max generated by the actuator at T > A f . In this test, we performed blocked force measurements at different angles, and
then torques were calculated by multiplying by the length of
the moment arm. Initially, the actuator is mounted from both



Table of Contents for the Digital Edition of IEEE Robotics & Automation Magazine - September 2016

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