## 3 Results
### Actuation Characterization  
In order to characterize and validate the actuation system performances, we performed a series of test campaigns involving the most relevant upper-limb motions in a worst-case scenario. The exoskeleton was configured in the maximum percentile condition (95 th percentile male), namely extending all the adjustable links to their maximum positions. This represents the worst working operation condition for the actuation system, since all the actuators will perceive the maximum gravitational load. On top of this, we also added a load of 3.3 kg in correspondence to the arm brace. This weight corresponds to the 60% of a 99 th percentile male human arm weight (5.56 kg [16]). The choice of 60% comes from a preliminary experimental analysis of the distribution of the human arm weight between the subject and the exoskeleton. This additional load brings the test setup to the aforementioned worst-case scenario, namely the largest percentile patient (maximum gravitational load on the exoskeleton) with the exoskeleton carrying the highest possible load. In such a condition, the following exercises--in the Kinematic mode--have been performed:  
* Shoulder flex-extension 60\({}^{\circ}\) in 2 s (full-extended arm);
* Shoulder abduction 95\({}^{\circ}\) in 3 s (full-extended arm);
* Horizontal shoulder abduction 100\({}^{\circ}\) in 3 s (full-extended arm);
* Humerus internal rotation 55\({}^{\circ}\) in 2 s (elbow at 90\({}^{\circ}\));
* Humerus external rotation 50\({}^{\circ}\) in 2 s (elbow at 90\({}^{\circ}\)). All the exercises were performed at the maximum allowed speed. This does not represent the maximum reachable speed of the exoskeleton, but it represents the allowed speed during clinical utilization of the device. An additional test campaign was performed in the Repeat Trajectory mode, where the exoskeleton was first manually moved by an external user mimicking a complex motion involving all the five active joints of the device. For each test, the angular positions and the absorbed motor currents were measured for each joint. From the angular positions, by means of numerical derivation, the angular speed  
Figure 12: Float exoskeleton cloud point of the end-effector (elbow) from different angles (blue dots). Passive polyarticulated arm cloud point in red. The combination of the two cloud points results in a large workspace allowing 3D movements. (**A–D**) offer different view angles of the same cloud point. of the joints was computed. Additionally, form the motor currents, using a model-based relationship, the generated output torques were estimated using the following relationship:  
\[T_{j}=i_{j}K_{t_{j}}\tau_{j}\eta_{m_{j}}\eta_{t_{t_{j}}}\]  
where \(T_{j}\) represents the \(j\)-th output torque, \(i_{j}\) is the \(j\)-th joint motor current, \(K_{t_{j}}\) is the \(j\)-th motor torque gain, \(\tau_{j}\) is the \(j\)-th transmission ratio, \(\eta_{m_{j}}\) is the \(j\)-th motor efficiency and \(\eta_{t_{j}}\) is the \(j\)-th transmission efficiency. The experimental torque-speed profiles of the different performed exercises were then compared with the nominal torque-speed envelope of the gearmotor at each joint. The obtained results are presented in Figures 13 and 14. Figure 13 shows the cloud points of all the different Kinematic mode exercises. It can be observed that all the performed exercises cloud points lay within the nominal torque-speed envelope at each join. The only exception is observable on joint 4, where the shoulder abduction slightly overshoots the nominal torque. However, this does not represent a critical condition for the system, since the nominal torque can be exceeded for a limited period of time. Additional observations can be made with respect to the specific exercises. In fact, shoulder abduction and flexion, mainly involve J2 and J4, while horizontal abduction activates mostly J1, J3, and J4. The internal and external rotation are carried out mainly by J5.