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