*2.7. Testing Procedures*

Two types of tests were performed: static and dynamic. In both tests, angular zero was defined as the position in which the arms were pointing downward, in agreement with the anatomical reference position. Angles increased as the arms were raised, corresponding to an increase in shoulder flexion up to a maximum of 180◦. Angles decreased in the direction of shoulder extension up to −20◦. At these extreme values, there was no exoskeleton actuation. Beam load cell zero was taken at the starting position of 180◦, at which there was no actuation of the exoskeleton under analysis. The final position was set at −20◦. Figure 7 shows a kinematic diagram of the test bench with the exoskeleton.

**Figure 7.** Kinematic diagram of the test bench with the exoskeleton.

In the static tests, a set of 10 consecutive measurements were taken from 180◦ up to −20◦, in steps of 8◦. At every step, the machine remained still for 500 ms for mechanical stabilization. To allow for compensation of the position and masses of the test bench, three tests without exoskeleton were carried out to measure the background forces. The background force at a certain angle was the average of these 30 measurements, after outlier removal. This value was subtracted from the actual measurements.

In the exoskeleton MATE (v1.0, Comau, Turin, Italy) used in this study, similar to most of the commercially available exoskeletons, it is possible to select different values of spring stiffness that provide different supporting torques. For the exoskeleton measurements, three runs were performed for each one of the seven spring levels available in MATE. The torque adjustment in MATE was performed with a mechanical switch with seven positions that indicate the level of strength. Level 1 is the weakest (lowest stiffness), and Level 7 is the strongest (highest stiffness). The value of the point of interest was the average of these 30 measurements, after removing the outliers.

In dynamic tests, three cycles of consecutive measurements were taken from 180◦ up to −20◦, in steps of 2◦. The velocity of movement was 18◦/s, to avoid vibration due to both step transitions at lower speeds and resonance at higher speeds. A single measurement was taken from each angle during a single run.

Background measurement was taken as a set of three runs without any exoskeleton attached to the test bench. The value of the point of interest was the average of the three measurements, after outlier removal.

Three runs were carried out for each level of the spring. The value of the point of interest was the average of the three measurements, after outlier removal.

### **3. Results**

In the next sections, static and dynamic results are presented.

### *3.1. Static Tests*

The torques obtained in the static measurements for each spring level are presented in Figure 8.

**Figure 8.** Computed static torques with the testbench configuration (at one extreme of the shoulder translation joint) for each of the seven spring levels in MATE. Level 7 is the strongest one, and level 1 is the weakest.

All spring levels started at zero in position 180◦. Actuation increased up to a maximum of around 45◦, and then, they decreased again until position 0◦. From 0◦ to −20◦, the torque remained constant between −2 Nm and −3 Nm. This behavior between 0◦ and −20◦ did not correspond to the expected traction forces, which is discussed in the next section. The maximum torque in position 45◦ was 5.6 Nm.

#### *3.2. Dynamic Tests*

The torques obtained during the dynamic tests are shown in Figure 9.

**Figure 9.** Computed dynamic torques with the testbench configuration (at one extreme of the shoulder translation joint) for each of the seven spring levels in MATE. Level 7 is the strongest one, and level 1 is the weakest.

All spring levels started at zero in position 180◦. Actuation increased up to a maximum between 20◦ and 30◦, decreasing until position −20◦. The behavior between 0◦ and −20◦ did not correspond to the expected traction forces and, as in the case of the static measurements, it is discussed in the next section.
