3.1. Anthropometric analysis measures

The U.S. Army ANSUR II Database was adopted in this work. It is titled “Anthropometric Survey of U.S. Army Personnel” and offers detailed information on the anthropometric measurements of the target population. The 2012 public update encompasses a thorough collection of publicly accessible data regarding body size and shape, featuring 93 measurements from over 6,000 U.S. military adults, comprising 4,082 men and 1,986 women. The dimensions in question are contingent upon the ethnicity of the subjects under analysis: the predominant group consists of Caucasians, with ethnic subgroups represented in accordance with their respective distribution [Reference Kang, Jeon, Kim, Kim, Jung and Lee32].

Anthropometric dimensions exhibit a Gaussian distribution within the reference population, with the reported data characterized by mean values and standard deviations, thereby facilitating reference and size assumptions. The limited, albeit extensive, variety of multiethnicity is not the sole factor contributing to variability: focusing exclusively on military subjects suggests that the data collected pertains solely to adults in good physical condition. This indicates that the dimensions of the designed exoskeleton are likely to be incompatible with children and individuals with obesity or general shape deformities. Considering these limitations and in relation to the reported upper limb model, the parameter sizes for the upper limb may be established as equivalent to the length of the radial styloid and the acromio-radial length, respectively.

3.2. Exoskeleton design

3.2.1. Distal mechanism

A kinematic diagram of the proposed system is shown in Figure 1, where the purple joints represent the human joints, and the gray joints represent the exoskeleton joints. The exoskeleton is moved by the human subject through the movements indicated by the red arrows during the approach to the interaction and the return to the resting zone. Once the interaction plane is defined, the exoskeleton acts mechanically with the movements indicated by the blue arrows in the interaction plane. The motorized rotary hinges D and A of the exoskeleton are made with ball joints to allow some movements of the human subject, e.g., forearm pronosupination, and to compensate for some mounting errors. In addition, the motion of the motorized hinges is transferred to the human subject through two connecting-rod-crank mechanisms with a carriage axis shown in green that allows the transfer of mechanical actions perpendicular to the body segment on which it is mounted while avoiding shear actions that would cross the joints.

Figure 1.

Kinematic diagram of the distal part of the proposed exoskeleton.

In the following, for the sake of simplicity, we will consider that the interaction movement (the lifting) acts in a plane parallel to the sagittal plane (a vertical plane), as shown in Figure 2, which reports a single connecting-rod-crank mechanism with two possible configurations that acts on the forearm, and it will be thoroughly studied, while the analysis of the analogous mechanism that acts on the arm will be omitted for the similarity of the two mechanisms.

Figure 2.

Scheme of a single connecting-rod-crank mechanism in two acceptable configurations.

Consider the planar mechanism in Figure 2, modeled as a multibody system of rigid bodies connected by ideal joints. In Q₁, there is a prismatic joint in the plane on a straight guide in the direction ξ₁, assumed ideal in the absence of friction. Q₁ allows for single relative mobility, translation along the guide, and prevents both translation normal to the guide and relative rotation between the two constrained elements.

Starting from the equation of motion of the system with holonomic constraints in Lagrangian formulation with multipliers (1), it is possible to isolate the contribution of the slider by introducing the constraints in Q₁ through a local basis of the guide represented by the unit vectors t and n, which represent, respectively, the tangential and normal actions to the direction of sliding. In particular, the constraints imposed by Q₁ (2) entail belonging to the linear guide and the absence of relative rotation.

(1) \begin{equation}\mathbf{M}(\mathbf{q})\,\ddot{\mathbf{q}}+\mathbf{h}(\mathbf{q},\dot{\mathbf{q}})=\mathbf{Q}(\mathbf{q},\dot{\mathbf{q}},t)+\mathbf{J}_{c}(\mathbf{q})^{T}\,\boldsymbol{\lambda }\end{equation}

(2) \begin{equation}\boldsymbol{\phi }_{{Q_{1}}}(\mathbf{q})=\left[\begin{array}{c} \mathbf{n}^{T}\left(\mathbf{r}_{{Q_{1}}}(\mathbf{q})-\mathbf{r}_{P}\right)\\ \theta _{rel,{Q_{1}}}(\mathbf{q}) \end{array}\right]=\mathbf{0}\end{equation}

The constraints impose the belonging of point Q₁ to the guide (zero normal component) and the absence of relative rotation (2). The constraint reactions of the slider enter the generalized equations as in (3), where λ_Q1 is the vector of multipliers and the subscripts n and m indicate, respectively, the normal and rotational constraints.

(3) \begin{equation}\mathbf{Q}_{{Q_{1}}}(\mathbf{q})=\mathbf{J}_{{Q_{1}}}(\mathbf{q})^{T}\,\boldsymbol{\lambda }_{{Q_{1}}},\quad \quad \mathbf{J}_{{Q_{1}}}(\mathbf{q})=\frac{\partial \boldsymbol{\phi }_{{Q_{1}}}}{\partial \mathbf{q}},\quad \quad \boldsymbol{\lambda }_{{Q_{1}}}=\left[\begin{array}{c} \lambda _{n}\\ \lambda _{m} \end{array}\right]\end{equation}

The virtual work is zero in ideal constraints, so the only admissible relative virtual motion in Q₁ is a translation along t, as expressed by the virtual twist in (4). The reaction of the slider is described by the planar wrench w_Q1, which for ideal constraints must satisfy (5) for every admitted virtual motion. Substituting (4) into (5), the moment term does not contribute, i.e., δθ_rel is equal to zero, and the condition ${\boldsymbol{F}}_{\boldsymbol{Q}_{\mathbf{1}}}^{\boldsymbol{T}}\boldsymbol{t}=\mathbf{0}$ is obtained, meaning the constraint force is orthogonal to the guide.

(4) \begin{equation}\delta \mathbf{V}_{rel,{Q_{1}}}=\left[\begin{array}{c} \delta \mathbf{r}_{rel,{Q_{1}}}\\ \delta \theta _{rel,{Q_{1}}} \end{array}\right]=\left[\begin{array}{c} \mathbf{t}\,\delta \xi _{1}\\ 0 \end{array}\right]\end{equation}

(5) \begin{equation}\delta W_{{Q_{1}}}={\mathbf{w}}_{Q_{1}}^{T}\,\delta \mathbf{V}_{rel,{Q_{1}}}=0,\quad \quad \mathbf{w}_{{Q_{1}}}=\left[\begin{array}{c} \mathbf{F}_{{Q_{1}}}\\ M_{{Q_{1}}} \end{array}\right]\end{equation}

Equivalently, the structure of the wrenches transmissible by the constraint Q₁ is expressed by (6): the slider can generate only a normal force and a constraint moment but no tangential force. The component parallel to the guide (responsible for tension/compression along the slider) is therefore the projection $\boldsymbol{F}_{\parallel }$ , which is identically zero as shown in (7). Therefore, in the absence of friction or actuation along the guide, no parallel force action to ξ₁ can be transmitted at Q₁.

(6) \begin{equation}\mathbf{w}_{{Q_{1}}}={\mathbf{A}}_{Q_{1}}^{T}\,\boldsymbol{\lambda }_{{Q_{1}}},\quad \quad \mathbf{A}_{{Q_{1}}}=\left[\begin{array}{c@{\quad}c} \mathbf{n}^{T} & 0\\ 0\,0 & 1 \end{array}\right]\,\Rightarrow \,\mathbf{F}_{{Q_{1}}}=\lambda _{n}\,\mathbf{n},\,\,M_{{Q_{1}}}=\lambda _{m}\end{equation}

(7) \begin{equation}F_{\parallel }=\mathbf{t}^{T}\mathbf{F}_{{Q_{1}}}=\mathbf{t}^{T}(\lambda _{n}\mathbf{n})=\lambda _{n}\,(\mathbf{t}^{T}\mathbf{n})=0\end{equation}

With reference to Figure 2: G is the position of the elbow; A is the position of the exoskeletal fixed revolute joint; B is the position of the exoskeletal mobile joint; Q is the position of the prismatic joint between the exoskeleton and the forearm; a is the length of the forearm GP; l is the length of the exoskeleton connecting rod BQ; m is the length of the exoskeleton crank AB; $\xi$ is the distance of Q with respect to the wrist P; $\beta$ is the counterclockwise rotation angle of m with respect to the vertical direction; $\varphi$ is the counterclockwise rotation angle of l with respect to the forearm’s direction; $\gamma$ is the counterclockwise rotation angle of a with respect to the horizontal direction (−90° in the resting configuration along the y direction and + 45° in the configuration of maximum flexo-extension). The misalignment between the elbow hinge G and the exoskeleton hinge A is described by the scalar terms dx and dy.

Figure 3.

Four possible configurations of the selected mechanism.

With the allowed preselected region of misalignment, the rotary crank mechanism is theoretically available in four generally different configurations depending on the initial value of $\varphi$ and of $\beta$ (and/or of $\alpha$ ), as shown in Figure 3; thus, a conventional constraint was initially imposed on the initial value of $\varphi$ associated with $\gamma$ equal to −90°, as shown in (8), to reduce encumbrance of the exoskeleton in the interacting area.

(8) \begin{equation}0\lt \varphi \lt 90^{\circ}\end{equation}

With reference to Figure 2, the closure equation of the system can be described by (9), which leads to the scalar expression (10) that represents a relation between the forearm and the exoskeleton kinematics.

(9) \begin{equation}(B-A)+(Q-B)=(G-A)+(Q-G)\end{equation}

(10) \begin{gather} [sin\gamma (dx-l\cdot cos\varphi )+cos\gamma (l\cdot sin\varphi -m-dy)]\cdot t^{2}+2m\cdot sin\gamma \cdot t\nonumber\\ +\, sin\gamma (dx-l\cdot cos\varphi )+cos\gamma (l\cdot sin\varphi +m-dy)=0 \\ t=\beta /2 \nonumber\end{gather}

To characterize the system’s appropriate behavior, it is beneficial to establish certain constraint conditions that can be classified into four distinct categories: obstruction conditions, working area conditions, anthropometric conditions, and kinematic conditions.

Obstruction conditions are designed to minimize the invasiveness of the exoskeleton. In this instance, the maximum allowable misalignment between A and G was established at 10 cm in both the x and y axes within the designated spatial area “above” and “behind” the elbow (dx > 0, dy < 0) (11).

(11) \begin{align} dx = 0\div 10\,\mathrm{cm}; \qquad dy = -10\div 0\,\mathrm{cm}; \end{align}

Working area conditions are devoted to respect the natural ROM of human joints and to realize the functional action (lifting in this case study). The crank mechanism solution permits four distinct configurations based on the fixed value of $\varphi$ throughout the flexo-extension range and the initial values of $\alpha$ and/or $\beta$ . The limitations on the range of $\varphi$ result in the examined crank mechanism having only two specific configurations: one with acute values and another with obtuse values of the initial angle $\beta$ ₀, as just mentioned. At this juncture, the total circumferences delineated by the end effector of the crank mechanism for the two examined sub-configurations must consistently encompass point G, indicating that the exoskeleton’s components must possess adequate length to consistently reach the limb’s interface, regardless of the degree of misalignment. Analytically, imposing this condition equates to asserting that the combined length of the crank and connecting rod exceeds the permissible maximum misalignment (12).

(12) \begin{equation}m+l\gt d_{max}=(\sqrt{dx^{2}+dy^{2}})_{max}=\sqrt{200}\ \mathrm{cm}\end{equation}

Furthermore, the constraint on the run distance accessible to the slider of the prismatic joint (point Q) was set as in (13), ensuring that Q remains in contact with the forearm without surpassing the wrist limit during the whole lifting action described by the angle γ.

(13) \begin{align} 0\leq \xi \leq a; \qquad \forall \gamma \in [-\pi /2,\pi /4]\end{align}

Utilizing the auxiliary relative frame of reference x^′y^′ with the origin at the elbow point G, y^′ aligned with the forearm link, and x^′ perpendicular to it in the sagittal plane towards the exoskeleton mechanism, the $\xi$ parameter can be expressed as in (14), where $y'_B$ denotes the y^′ coordinate of point B relative to the x^′y^′ frame.

(14) \begin{equation}\xi =a+y\mathrm{'}_{B}-l\cdot cos\varphi\end{equation}

To dimension the overall system and meet the target population’s needs with a singular physical solution, the aforementioned inequality for the slider’s run can be resolved by assessing the $\xi$ parameter under the most critical circumstances, leading to the application of the dimensioning conditions (15) to the two resultant sub-configurations of the crank mechanism.

(15) \begin{align} \left\{\begin{array}{ll} l\cdot cos\varphi \leq a_{min}+\left(y'_{B1,2}\right)_{min}\\[5pt]l\cdot cos\varphi \geq \left(y'_{B1,2}\right)_{max} \end{array}\right. &\quad \forall \gamma \in \left[-\frac{\pi }{2};\frac{\pi }{4}\right] \end{align}

The function $y'_B$ exhibits a quadratic characteristic and is contingent upon the trigonometric functions sin( $\gamma$ − $\delta$ ) and cos( $\gamma$ − $\delta$ ). Consequently, the mathematical system in (15) can be resolved by analyzing the maxima and minima associated with the stationary points of the $y'_B$ function and determining when these lie within the $\gamma$ range; if not, the extreme points must be examined. The stationary points are determined by utilizing condition (16).

(16) \begin{align} \frac{dy'_{B1,2}}{d\omega } & \omega =\gamma -\delta \end{align}

In addressing anthropometric conditions and aiming to transform exoskeletons into a mass-consumption product, we calibrated parameter a, which denotes forearm length and, by extension, the roller’s maximum stroke, to accommodate the broadest possible demographic. We assessed the extreme cases pertaining to the female 10th and male 90th percentiles, utilizing the anthropometric tables from the ANSUR II database (17).

(17) \begin{align} 22.3\ \mathrm{cm}\leq a\leq 28.8 & a_{\textit{avarage}}=25.6 \end{align}

Examining the instantaneous center of rotation (ICR) of the connecting rod BQ reveals that the rotational orientation of the forearm alters when the ICR intersects the vertical line passing through B. This behavior is suboptimal from a functional perspective. We can separate the possible locations of the ICRs due to the constraints downstream of BQ, identifiable by a line r_G passing through G, from the possible locations of the ICRs due to the constraints upstream of BQ, identifiable by a line r_B passing through B. In some situations, these two lines intersect at infinity; that is, they are parallel, and the transmission of mechanical actions is limited because there is no action component perpendicular to the forearm. Even if this condition is acceptable for an accelerated motion excluding the initial configuration of the motion, it is still preferable to avoid it in general during slow motions, as it may cause discomfort. These conditions can be expressed in geometric and mathematical terms, assessing the system’s configuration using an auxiliary reference frame x^′y^′ positioned at the elbow and moving in synchrony with the forearm. In this reference frame, the preceding requirements indicate that the y^′ _B coordinate must be either positive or negative, but never zero.

The location of point B can be determined by assessing the intersection of the circular path traced by the crank link around point A, with a radius of m, and the straight line rB that extends through point B and is parallel to the forearm link. The equation that describes the first geometric function for the auxiliary frame x^′y^′ is expressed through the coordinates of the center, specifically point A, as shown in (18). Here, δ stands for the constant angle formed by the vector connecting point G to point A (distance d) with respect to the absolute frame’s horizontal line (19).

(18) \begin{align} x'_{A}=d\cdot sin(\gamma +\delta ), &\quad y'_{A}=d\cdot cos(\gamma +\delta ) \end{align}

(19) \begin{align} sin(\delta)=dy/d, \quad cos(\delta)=dx/d, \quad \delta =atan\left(\frac{dy}{dx}\right) \end{align}

Therefore, the sign of $\delta$ acquires the geometrical constraints shown in Figure 4.

Figure 4.

Geometrical representation of the allowed A-G misalignment region.

Referring to Figure 4, the allowed region for the misalignment shows how the $\delta$ angle will always be taken with its acute non-positive values according to the obstruction constraints (20).

(20) \begin{equation}-\frac{\pi }{2}\leq \delta \leq 0\end{equation}

The path of B describes a circumference C ^′ _m around the point A as shown in (21), where $x'_B$ and $y'_B$ are the general coordinates describing the circumference with radius m and center ( $x'_A$ , $y'_A$ ) with reference to the rotating relative frame Gx^′y^′ . After some geometrical stages, we can also affirm that B must lie on the line r ^′ _B (21).

(21) \begin{align}\left\{\begin{array}{ll} C'_{m}\colon & \left(x'_{B}-x'_{A}\right)^{2}+\left(y'_{B}-y'_{A}\right)^{2}=m^{2}\\[5pt] r'_{B}\colon & x'_{B}=-l\cdot sin\varphi \end{array}\right.\end{align}

After some mathematical computations, we can obtain the two solutions of expression (21), as shown in (22), where B and Δ are mathematical functions of various parameters.

(22) \begin{align}\begin{cases} y'_{B1}=\dfrac{-B+\sqrt{{\unicode[Arial]{x0394}} }}{2}; & -\dfrac{\pi }{2}\leq \beta _{0}\leq \dfrac{\pi }{2}\\[4pt] y'_{B1}=\dfrac{-B+\sqrt{{\unicode[Arial]{x0394}} }}{2}; & \dfrac{\pi }{2}\leq \beta _{0}\leq 3\dfrac{\pi }{2} \end{cases}\end{align}

After different computations, expression (22) drives to the dimensioning condition of the crank in two sub-configurations (23), which must be considered in the most critical condition in the correct range of the angle γ, considering the variable misalignment dx and dy.

(23) \begin{align} m\gt \sqrt{l\cdot sin\varphi \left[l\cdot sin\varphi +2(dx\cdot sin\gamma -dy\cdot cos\gamma )+d^{2}\right]} &\quad for\ y'_{B1}\nonumber\\ \left\{\begin{array}{c} m\gt \sqrt{l\cdot sin\varphi \left[l\cdot sin\varphi +2(dx\cdot sin\gamma -dy\cdot cos\gamma )+d^{2}\right]}\\[4pt] m\gt \dfrac{dy}{cos\beta _{0}} \end{array}\right. &\quad for\ y'_{B2} \end{align}

We establish a constrained range for $x'_B$ between 3 cm and 7 cm to prevent interference with joint movement and the irregularities of attire linked to shorter lengths, as well as to mitigate environmental interference or discomfort resulting from excessive lengths. This range ensures that the length of $x'_B$ is practical for users, allowing for comfortable movement while also maintaining a neat appearance and enhancing usability. After different computations, we can generate Table II, which indicates the limits of different parameters, specifically the minimum values of m to avoid jamming or motion inversion in both configurations for different values of $x'_B$ . We selected the second configuration because, as can be seen in Figure 2, it minimizes the encumbrance of the exoskeleton. As can be computed and as also will be verified experimentally in the result sections, it allows the slider to remain between the rail borders also along the shortest female forearm of the target anthropometric population.

Table II.

Selected values of geometrical parameters of the exoskeleton

This means that any errors made during donning, in accordance with the experimental anthropometric measurements indicated in the ANSUR II database, the exoskeleton is always compatible with the subject’s anthropometric structure. Donning can lead to any kind of error. In this sense, it can be stated that the device is one-size-fits-all and does not require manual or automatic calibration during donning or during working.

3.2.2. Proximal mechanism

This framework’s upper limb exoskeleton project was designed to be used in upper body equipment with motors integrated with a Variable Speed Transmission (VST) for action distribution and a transmission system to transfer actions to the upper limb end effectors. To allow portability of the whole system, the heaviest part, the motor, should be worn (it is not necessary in general). In portable exoskeletons, it is crucial that the motor design does not raise the center of gravity of the user, as this can affect balance and stability. By relocating the motor and actuation components away from the limbs, such as using a backpack system, the center of gravity can be maintained [Reference Nycz, Butzer, Lambercy, Arata, Fischer and Gassert33]. After establishing the position of the motors, we adopted a transmission system for the upper limb, which consists of a VST and a combination of gearboxes and flexible transmission beams. This system is capable of transferring the lifting torque from the motor to the articulated mechanisms applied to the upper limb. We chose flexible beams over rigid ones to limit the user’s mobility constraints when wearing the exoskeleton and to adapt the equipment to all target percentages of the reference anthropometric population. The employment of joints with multiple degrees of freedom and the decoupling of the overall exoskeletal harness, which relatively isolates the forearm, arm, upper body, and pelvis, also helped accomplish this task (Figure 5).

Figure 5.

Schematic design for the overall upper limb exoskeleton equipment.

The presence of a VST enables the use of a constant-speed motor to move individual working parts. The advantage of this solution is that the user only needs to provide control input to the VST, which usually entails adjusting the gear ratio within a transmission. This last operation can be performed manually or with the use of another motor that only drives the VST and is thus much lighter than the driving motor.

For this solution to meet all functional requirements, the VST mechanism must be capable of performing the following tasks:

• • Connecting the arm and disconnecting the forearm;

• • Disconnecting the arm and connecting the forearm;

• • Connecting both arms and forearms;

• • When both arms and forearms are connected, adjust the gear ratio between them.

By doing so, the VST/motor combination would be equivalent to two lifting motors, potentially resulting in a lighter overall weight. Similarly, in order to reduce the number of possible driving motors that can be connected to the VST, all of the above-mentioned functions should be performed using a small number of degrees of freedom. Furthermore, in order to mimic the natural anatomical movements of the arm and forearm and achieve a solution as close as possible to the standard one involving the two lifting motors, the gear ratio tuning should not be discontinuous at all. Typically, this task entails increasing the number of gear wheels, resulting in a large and complex mechanism. We designed the VST for the intended exoskeleton prototype using all of the discussed conditions and objectives. It consists of a variable-diameter transmission beam connected to two gear wheels (one for the arm, one for the forearm). These gear wheels can slide across the beam’s surface, adjusting the corresponding gear ratio (Figure 6).

Figure 6.

Mechanical functioning system intended for the arm-connected shoulder transmission.

A spherical joint connects the VST (Figure 7) to the motor. The inner sphere of the joint receives motion from the rotor, while the outer casing of the joint mechanically couples with the stator and, consequently, with the pelvis of the subject wearing the exoskeleton.

Figure 7.

Assembly of the VST mechanism.

This mechanism enables the user’s back, connected to the transmission system, to move freely without restriction from the exoskeleton’s mechanical components in three primary degrees of freedom: flexion–extension (in the sagittal plane), lateral flexion (in the frontal plane), and rotation (around the spine), as illustrated in Figure 8.

Figure 8.

Allowed VST mobility.

A fixture link applies the rotary driving motor to a nut, converting the provided torque into a linear action through a nut/screw mechanism. A prismatic extremity, rigidly fixed to the inner part of the beam’s bearing joint, acts as a “linear guide” to prevent the screw from rotating around its axis, thereby transmitting the provided torque as a linear force against the rotating beam. Finally, a "mechanical stop" establishes the positions of the linear motion’s "start run" and "end run." The collaboration between this system and the rotary motor results in the linear driving motor intended for the VST.

The rotary crank mechanism on the arm and forearm must receive the tuned speeds and torques from the gear arches of the sliding wheels. To transfer the motor torque from the VST on the user’s pelvis to the transmission boxes at the shoulder level, directly connected to the crank mechanisms on the upper limb, we employed a flexible transmission beam.

The shoulder transmission serves as an intermediary phase between the VST and the terminal effectors of the upper limb. To make sure that the actions sent by flexible beams work properly in parts of the body that move differently than the spine and to accommodate differences in the user’s body shape, they need to be carefully controlled. To achieve this goal, we separated the transmission system for the crank mechanisms into two distinct components: one that directly connects to the arm’s crank mechanism and controls the forearm’s end effector, and another that sits on the user’s shoulder and controls the arm’s end effector. The shoulder transmission component linking to the forearm’s effector is minimally influenced by the relative mobility of the interfacing body parts. On the other hand, the transmission to the arm’s effector needs to take into account the user’s shoulder, which has a significantly wider range of motion. The resolution for the arm-related shoulder transmission entailed a gear mechanism capable of receiving torque from the flexible beam at an optimal angle and position, along with a spherical sliding gear joint that could convey flexo-extension movements to the end effector while permitting a degree of mobility in all other spatial dimensions. A transmission beam possessing a linear degree of freedom interlinks the two gear mechanisms. Figure 9 shows how the shoulder transmission is supposed to move the arm effector and the arm itself along the x-axis (for horizontal adduction and abduction), rotate slightly around the y-axis (for internal and external rotation), and rotate slightly around the z-axis (for vertical adduction and abduction), all while transferring torque around the z-axis (for flexion–extension motion).

Figure 9.

Allowed shoulder transmission mobility.

The transmission system to the forearm is composed of a gear mechanism connected with a spherical gear joint by means of a belt transmission, which is inserted within the arm’s crank mechanism. This second shoulder transmission loses one degree of freedom due to the reduced relative mobility between the arm and forearm compared to the arm and shoulder: a fixed beam replaces the sliding beam, as there is no relative translation at the elbow.

3.3. Exoskeleton prototype

A single mechanism, encompassing the prototype for the upper limb exoskeleton, underwent design, printing, and assembly.

All structural components printed using Fused Deposition Modeling (FDM) were conservatively sized taking into account the typical mechanical properties of the adopted materials, PET-G and PLA, the intrinsic anisotropy of the FDM process, and the cyclic nature of the loads in an exoskeleton [Reference Martins, Branco, Martins, Macek, Marciniak, Silva, Trindade, Moura, Franco and Malça34, Reference Bembenek, Kowalski and Koson-Schab35].

Tensile tests were performed on parallelepiped and dumbbell specimens by creating specimens with side walls 1.2 mm thick (3 loops of filament), parallel to the print bed with a thickness of 0.8 mm and a triangular structure filling at 50%, practically just one layer of 0.2 mm, the rest is solid (Figure 10).

Figure 10.

Stress–strain diagram of a dumbbell-shaped PET-G specimen obtained from a tensile test performed on an Instron 3,366 testing machine and repeated three times.

Figure 11.

Static FEM analysis of a crank.

For PET-G FDM in a favorable orientation, typical values of ultimate tensile strength (UTS) are observed to be around 41–49 MPa and up to 55 MPa with optimal parameters; the Young’s modulus is estimated to be between 1.5 and 2.2 GPa, and ductility is approximately 6–14%, while the observed flexural strength is in the range of 60–70 MPa [Reference Dolzyk and Jung36]. However, as also observed in the literature, the strength is highly dependent on the printing and loading orientation, resulting in a reduction of up to 50% due to inter-layer adhesion [Reference Bembenek, Kowalski and Koson-Schab35].

For the fatigue durability of FDM PET-G, literature data indicate a load ratio of 10% and a stress level of approximately 60% UTS (around 29 MPa) to allow for more than 10⁵ cycles [Reference Dolzyk and Jung36]. Moreover, the presence of notches and stress concentrations is critical: stress concentrators can reduce fatigue strength/life by up to 30%, and defects/porosity (void fraction 2–8%) can reduce performance by up to 25%, making generous fillets and the minimization of geometric discontinuities in stressed areas necessary [Reference Wiklo, Byczuk and Skrzek37].

In light of such evidence, PET-G was prioritized for the load-bearing parts, and a Von Misees verification criterion based on equivalent stress (Figure 11), with an allowable lower-bound stress that incorporates a knockdown for anisotropy, a conservative environmental margin, and a Safety Factor (SF) consistent with the literature: SF ≥2 for static conditions and SF ≥3 for cyclic/fatigue-critical conditions [Reference Martins, Branco, Martins, Macek, Marciniak, Silva, Trindade, Moura, Franco and Malça34].

Operationally, adopting a conservative value of 40 MPa for PET-G, applying a knockdown normal to the printing plate (×0.5), and SF = 2 (static), an allowable value on the order of 10 MPa is obtained; for cyclic conditions with SF = 3, the allowable limit is reduced to 6–7 MPa (further conservative values in the presence of notches or slender geometries). In parallel, as a fatigue verification, using a reference of 29 MPa at 10⁵ cycles for PET-G in favorable conditions and incorporating anisotropy (×0.5) and SF = 3, a cyclic allowable load of the order of 5 MPa was used as a constraint in areas subjected to repeated loads [Reference Wiklo, Byczuk and Skrzek37].

Finally, to reduce the risk of sudden failures typical of FDM components, the connection areas were designed with fittings and curvature radii to limit stress concentrators, print orientations that avoid predominant tension along the print axis in critical areas, and load distribution through multiple wall geometries and high local density (high infill).

We adjusted the VST function by incorporating specialized belt tensioners into the overall physical assembly. These elements enhance the belt’s tension, thereby augmenting its adhesion to the gear arches of the sliding wheels. The belt tensions exert a pulling force on the belt via a belt wheel, while the recoil of a spring or elastic string enhances this tension augmentation. We additionally fabricated the belt tensioners using PLA material, effectively enhancing the tensile strength by selecting properly the printing orientation. We designed the belt tensioners using a bar-like structure perforated with holes, connecting the belt wheel through a pivot joint and adjusting its position to ensure the belt engages with only one arch at any given moment. Subsequently, we assembled the belt tensioners with the belt wheels and affixed them to the VST.

Ultimately, we successfully linked the VST to both shoulder transmission elements. We chose a 300 mm flexible beam for the forearm-connected shoulder transmission and a 400 mm variant for the arm-connected shoulder transmission, informed by the shoulder-pelvis distances within the 10th to 90th percentile of the target anthropometric population. Male-male hexagonal connectors joined the female ends of the two flexible beams to the hexagonal cavities of the side wheel beams. In contrast, the male extremities formed connections with the small gearboxes of the shoulder transmission apparatus.

To integrate the shoulder transmission and the crank mechanism into a unified system, the arm’s rail was contoured for attachment to the two gear joints and to facilitate the passage of the double belt. Subsequently, we affix the belt to the corresponding rollers, which serve as tensioners and facilitate the straightforward replacement with cylinders of varying thicknesses according to the necessary tension. We engineered the form and measurements of the two cavities to accommodate the variability in the rollers’ diameters. Moreover, the cylinders containing the four rollers function as connection points for the two gear joints within the shoulder transmission assembly. Figures 12 and 13 subsequently present the comprehensive upper limb apparatus.

Figure 12.

3D design of the exoskeleton (left), 3D printed arm crank mechanism (center), and overall system (right).

Figure 13.

Scheme of a motor circuit, where (a) is the Arduino platform, (b) is the driver, (c) is an eventual joystick modulator, and (d) is the actuator.

In order to streamline the experimental activity, we adopted DC motors for both the power source and the driver motor of the VST and correlated the arm and forearm motions in our prototype.

3.4. Control system

The exoskeleton joint dynamics are described by Eq. (24), where M, C, and g represent, respectively, the inertial, Coriolis, and gravitational components; τ _f , τ _ext , and τ are, respectively, the friction effects, the interaction torques due to the user and variable loads reduced to the joint, and the actuator actions; finally, q, $\dot{\mathbf{q}}$ , and $\ddot{\mathbf{q}}$ denote the joint variables and their time derivatives.

(24) \begin{equation}\mathbf{M}(\mathbf{q})\ddot{\mathbf{q}}+\mathbf{C}(\mathbf{q},\dot{\mathbf{q}})\dot{\mathbf{q}}+\mathbf{g}(\mathbf{q})+\boldsymbol{\tau }_{\mathbf{f}}(\mathbf{q},\dot{\mathbf{q}})+\boldsymbol{\tau }_{\mathbf{ext}}(\mathrm{t})=\boldsymbol{\tau }\end{equation}

Given a desired time reference q _d belonging to ℜ², and measuring the joint coordinates q belonging to ℜ², the task is to generate appropriate actuation pairs to contain the measurement error, which is given by the difference between q _d and q.

τ _f and τ _ext are difficult to identify accurately because, as the task and anthropometry vary, although the exoskeleton is capable of adapting kinematically to donning conditions (being one-size-fits-all), the dynamics of load transfer to the joints are highly dependent on the user’s donning method and external conditions. For this reason, it is even more important than in other exoskeletons to provide a closed-loop control system. Different studies focused the attention on the control problem of this class of devices [Reference Brahim, Saad, Ochoa-Luna, Archambault and Rahman38–Reference Wang, Zhang, Kong, Su, Yuan and Zhao41]; i.e., in the work proposed in [Reference Nguyen, Truong, Tran, Yoon and Tran42], it is demonstrated how important it is to consider the time delay of the control action relative to a baseline PD controller, achieving significantly relevant performance. For this reason, this work implements a modified PD controller by including a time delay estimation (TDE).

To proceed with the definition of the PD-TDE control law, we start from the classical PD control indicated in (25), where kp and kd are positive definite control parameter matrices.

(25) \begin{equation}\boldsymbol{\tau }_{\mathrm{PD}}(\mathrm{t})=\mathbf{K}_{\mathrm{p}}\mathbf{e}(\mathrm{t})+\mathbf{K}_{\mathrm{d}}\dot{\mathbf{e}}(\mathrm{t}),{\quad}{\quad}\mathbf{e}(\mathrm{t})=\mathbf{q}_{\mathrm{d}}(\mathrm{t})-\mathbf{q}(\mathrm{t})\end{equation}

To proceed with this modification, we add and subtract the expression (26) from (24), where $\mathbf{M}'$ is a suitably determined constant matrix, thus obtaining (27).

(26) \begin{equation}\mathbf{M}'\ddot{\mathbf{q}}=\mathbf{0}\end{equation}

(27) \begin{equation}\mathbf{M}'\ddot{\mathbf{q}}-\mathbf{M}'\ddot{\mathbf{q}}+\mathbf{M}(\mathbf{q})\ddot{\mathbf{q}}+\mathbf{g}(\mathbf{q})+\boldsymbol{\tau }_{\mathbf{f}}(\mathbf{q},\dot{\mathbf{q}})+\boldsymbol{\tau }_{\mathbf{ext}}(\mathrm{t})=\boldsymbol{\tau }\end{equation}

Then the matrix N is defined, as indicated in (28), to obtain the new expression for the system dynamics highlighted by (29).

(28) \begin{equation}\mathbf{N}(\mathbf{q},\dot{\mathbf{q}},\ddot{\mathbf{q}})\equiv\; \mathbf{M}(\mathbf{q})\ddot{\mathbf{q}}-\mathbf{M'}(\mathbf{q})\ddot{\mathbf{q}}+\mathbf{g}(\mathbf{q})+\boldsymbol{\tau }_{\mathbf{f}}(\mathbf{q},\dot{\mathbf{q}})+\boldsymbol{\tau }_{\mathbf{ext}}(\mathrm{t})\end{equation}

(29) \begin{equation}\mathbf{M'}\ddot{\mathbf{q}}+\mathbf{N}(\mathbf{q},\dot{\mathbf{q}},\ddot{\mathbf{q}})=\boldsymbol{\tau }\end{equation}

If N varies slowly over a short time interval L, which in our case could be the sampling time or a time value of the same order of magnitude, then expression (29) can be differentiated with respect to finite differences to obtain expression (30).

(30) \begin{equation}\mathbf{M'}\ddot{\mathbf{q}}(t-L)-\mathbf{M'}\ddot{\mathbf{q}}(t)+\mathbf{N}(t-L)-\mathbf{N}(t)=\boldsymbol{\tau }(t-L)-\boldsymbol{\tau }(t)\end{equation}

So, recalling expression (27) and substituting it into (30), we obtain (31), highlighting that the time transients are negligible within that variable change interval.

(31) \begin{equation}\mathbf{N}(t)=\boldsymbol{\tau }(t-L)-\mathbf{M'}\ddot{\mathbf{q}}(t-L)\end{equation}

Expression (31) represents the TDE needed for estimating N. By imposing, as a design choice, the error dynamics perfectly controlled by a PD controller, as indicated in (32), and taking the temporal derivative of the error definition twice (33), the desired dynamics for the joint variables (34) are obtained.

(32) \begin{equation}\ddot{\mathbf{e}}+\mathbf{K}_{\mathrm{d}}\dot{\mathbf{e}}(\mathrm{t})+\mathbf{K}_{\mathrm{p}}\mathbf{e}(\mathrm{t})=\mathbf{0}\end{equation}

(33) \begin{align} \mathbf{e}(\mathrm{t})\equiv \mathbf{q}_{\mathrm{d}}(\mathrm{t})-\mathbf{q}(\mathrm{t}),\, & \ddot{\mathbf{e}}(\mathrm{t})=\ddot{\mathbf{q}}_{\mathrm{d}}(\mathrm{t})-\ddot{\mathbf{q}}(\mathrm{t}) \end{align}

(34) \begin{equation}\ddot{\mathbf{q}}(\mathrm{t})=\ddot{\mathbf{q}}_{\mathrm{d}}(\mathrm{t})+\mathbf{K}_{\mathrm{d}}\dot{\mathbf{e}}(\mathrm{t})+\mathbf{K}_{\mathrm{p}}\mathbf{e}(\mathrm{t})\end{equation}

Rewriting the actual dynamics (29) as in (35) and substituting them into (34), the torque control law indicated in (36) is obtained.

(35) \begin{equation}\ddot{\mathbf{q}}=(\mathbf{M'})^{-\mathbf{1}}(\boldsymbol{\tau }-\mathbf{N})\end{equation}

(36) \begin{equation}\boldsymbol{\tau }=\mathbf{M'}(\ddot{\mathbf{q}}_{\mathrm{d}}+\mathbf{K}_{\mathrm{d}}\dot{\mathbf{e}}+\mathbf{K}_{\mathrm{p}}\mathbf{e})+\mathbf{N}\end{equation}

Finally, using the TDE (31) for the estimation of N, the complete control law (37) is obtained.

(37) \begin{align}\begin{cases} \mathbf{N}(t)=\boldsymbol{\tau }(t-L)-\mathbf{M'}\ddot{\mathbf{q}}(t-L)\\ \boldsymbol{\tau }(t)=\mathbf{M'}(\ddot{\mathbf{q}}_{\mathrm{d}}+\mathbf{K}_{\mathrm{d}}\dot{\mathbf{e}}+\mathbf{K}_{\mathrm{p}}\mathbf{e})+\mathbf{N}(t) \end{cases}\end{align}

The controller identified by (37) was implemented in discrete time with a sampling frequency of 1 kHz and with a hypothesized delay L equal to the sampling time, so the accelerations of a single joint are calculated using finite differences according to (38), where k is the sequence index, and appropriately filtered in accordance with (39), where the subindex f indicates the filtered value and α is the smoothing factor equal to 0.85.

(38) \begin{equation}\ddot{\mathbf{q}}\left[\mathbf{k}\right]\approx \frac{\mathbf{q}\left[\mathbf{k}\right]-\mathbf{2}\mathbf{q}\left[\mathbf{k}-\mathbf{1}\right]+\mathbf{2}\mathbf{q}\left[\mathbf{k}-\mathbf{2}\right]}{\mathbf{L}^{\mathbf{2}}}\end{equation}

(39) \begin{equation}\ddot{\mathbf{q}}_{\mathbf{f}}[\mathbf{k}]\approx (1-\alpha )\ddot{\mathbf{q}}\left[\mathbf{k}\right]+\alpha \ddot{\mathbf{q}}_{\mathbf{f}}\left[\mathbf{k}-\mathbf{1}\right]\end{equation}

The controller is implemented on embedded hardware that generates PWM commands in a voltage range of 0÷5 V and with an 8-bit resolution. In accordance with the experiment indicated in [Reference Nguyen, Truong, Tran, Yoon and Tran42], a command (40) was identified for each joint i to test the technical solution on slow cyclic movements, ensuring non-zero speeds and accelerations to evaluate the behavior of TDE compensation. The controller parameters were iteratively tuned by monitoring tracking and command smoothness until the values indicated in (41) were achieved.

(40) \begin{align} q_{d,i}(t)=-\frac{\pi }{9}sin\left(\frac{\pi }{10}t\right), \quad i=1,2 \end{align}

(41) \begin{align} \mathbf{K}_{\mathbf{p}}=\left[\begin{array}{c@{\quad}c} 180 & 0\\ 0 & 140 \end{array}\right], \quad \mathbf{K}_{\mathbf{d}}=\left[\begin{array}{c@{\quad}c} 48 & 0\\ 0 & 100 \end{array}\right] \end{align}

The system thus obtained produced the results indicated in Figure 14, where the reference signal to the joints and the consequent response are shown. Furthermore, Figure 15 represents the experimental tracking error signal in which a sufficiently contained error is observed for the desired application. The compensatory term N of the controller is responsible for balancing the dominant macroscopic components of the phenomenon, while the PD component stabilizes the residual dynamics.

Figure 14.

Response (black) and reference (red) for the proximal (left) and distal (right) joints.

Figure 15.

Tracking error for the proximal (left) and distal (right) joints.

3.5. Joint effects

A biomechanical model of the upper limb can help to evaluate the effects of the exoskeleton on the subject’s joints to avoid eventual overstress. The focus is placed in the following solely on the elbow joint to contain the discussion. When a load is applied distally to the upper limb, the portion transmitted to the elbow is typically divided between the radiocapitellar and ulnotrochlear contacts in a ratio of approximately 54–67% and 33–46%, respectively [Reference Smithson, Smith, Hogue, Mannen and Ahmadi43], while contact forces during activities of daily living (ADL) often reach values on the order of 337–450 N [Reference Chadwick and Nicol44]. These high loads are mainly due to muscle contraction and cocontraction, as will be seen below, where a direct biomechanical model is presented in which, for simplicity, the elbow is flexed at a generic angle $\phi$ . A reference system is introduced, described by the local basis $(\hat{\mathbf{n}}(\phi ),\hat{\mathbf{t}}(\phi ))$ in the sagittal plane, centered at the elbow, with the $\hat{\mathbf{n}}$ -axis parallel to the forearm (compression) and the $\hat{\mathbf{t}}$ -axis normal to it (shear). Then, the vector of joint actions at the elbow $\mathbf{R}_{tot}(\phi )$ can be defined, described by the components $N_{tot}(\phi )$ and $V_{tot}(\phi )$ , as indicated in (42) as the sum of the contributions from the load $\mathbf{R}_{W}(\phi )$ , the muscles $\mathbf{R}_{mus}(\phi )$ , and the soft tissues $\mathbf{R}_{soft}(\phi )$ . In particular, $\mathbf{R}_{W}(\phi )$ is associated with the mass of the hand and the load $m_{L}$ , the mass of the forearm $m_{fh}$ , and the length L of the forearm, generating a moment around the elbow equal to $M_{W}(\phi )$ (43). The component $\mathbf{R}_{mus}(\phi )$ due to muscle tension derives from the actions $F_{bi}(\phi )$ , $F_{br}(\phi )$ , $F_{bra}(\phi )$ , and $F_{tri}(\phi )$ , respectively, produced by the biceps, brachialis, brachioradialis, and triceps muscles, as indicated in (44), where $r_{i}(\phi )$ are the respective lever arms relative to the elbow that satisfy the moment equilibrium by imposing a cocontraction of the triceps $M_{tri}(\phi )$ through the cocontraction coefficient $\kappa$ , as described in (45), where $M_{flex}(\phi )$ is the total flexor moment distributed among all flexors through the dimensionless weights $w_{i}$ (44). The muscular contribution $\mathbf{R}_{mus}(\phi )$ is decomposed in the elbow reference frame through the respective angle $\theta _{i}(\phi )$ between the muscle’s line of action and the unit vector $\hat{\mathbf{n}}(\phi )$ , as observed in (46), where $s_{i}$ is the positive sign function in the direction of the flexors. Finally, the contribution to the joint actions of the soft tissues $\mathbf{R}_{soft}(\phi )$ is indicated in (47), completing the calculation of the total action $\mathbf{R}_{tot}(\phi )$ and its components (48).

(42) \begin{gather}\mathbf{R}_{tot}(\phi )=\mathbf{R}_{W}(\phi)+\mathbf{R}_{mus}(\phi)+\mathbf{R}_{soft}(\phi)\nonumber \\ N_{tot}(\phi)=\mathbf{R}_{tot}(\phi)\cdot \hat{\mathbf{n}}(\phi),\quad V_{tot}(\phi)=\mathbf{R}_{tot}(\phi)\cdot \hat{\mathbf{t}}(\phi),\quad \mathbf{R}_{W}(\phi)=\left[\begin{array}{c} N_{W}(\phi)\\ V_{W}(\phi) \end{array}\right] \end{gather}

(43) \begin{gather} V_{W}(\phi)=(m_{L}+m_{fh})gcos(\alpha (\phi)),\quad M_{W}=\Big(m_{L}+\frac{m_{fh}}{2}\Big)gLcos(\alpha (\phi))\nonumber\\ N_{W}=(m_{L}+m_{fh})gsin(\alpha (\phi)) \end{gather}

(44) \begin{equation}F_{i}(\phi)=w_{i}\frac{M_{flex}(\phi)}{r_{i}(\phi)}\,(i\in \{bi,br,bra\}),\quad F_{tri}(\phi)=\frac{M_{tri}(\phi)}{r_{tri}(\phi)},\quad w_{bi}+w_{br}+w_{bra}=1\end{equation}

(45) \begin{equation}M_{tri}(\phi)=\kappa M_{W}(\phi),\quad M_{flex}(\phi)=M_{W}(\phi)+M_{tri}(\phi)=(1+\kappa )M_{W}(\phi)\end{equation}

(46) \begin{gather} N_{i}(\phi)=F_{i}(\phi)\cos (\theta _{i}(\phi)),\quad V_{i}(\phi)=s_{i}F_{i}(\phi)\sin (\theta _{i}(\phi))\nonumber \\ N_{mus}(\phi)=\sum _{i}N_{i}(\phi),\quad V_{mus}(\phi)=\sum _{i}V_{i}(\phi) \end{gather}

(47) \begin{equation}\mathbf{R}_{soft}(\phi)=\left[\begin{array}{c} N_{soft}(\phi)\\ V_{soft}(\phi) \end{array}\right],\quad N_{soft}(\phi)=\sum _{j}N_{j}(\phi),\quad V_{soft}(\phi)=\sum _{j}V_{j}(\phi)\end{equation}

(48) \begin{gather} N_{tot}(\phi)=N_{W}(\phi)+N_{mus}(\phi)+N_{soft}(\phi),\nonumber \\ V_{tot}(\phi)=V_{W}(\phi)+V_{mus}(\phi)+V_{soft}(\phi),\nonumber \\ \left| \mathbf{R}_{tot}(\phi)\right| =\sqrt{{N}_{tot}^{2}(\phi)+{V}_{tot}^{2}(\phi)} \end{gather}

The model thus obtained can be expressed inverted and in matrix form as indicated in (49). At this point, by applying the actions of the exoskeleton composed of a term in the direction of $\hat{\mathbf{t}}(\phi )$ and a bending moment both opposite to the load (neglecting response delays in this simplified model) and both applied at the slider and derivable from (24), $\mathbf{F}_{1}(\phi )$ (50) can be obtained, which is correlatable with the percentage of load alleviation implemented by the exoskeleton and can be used to recompute all internal actions. As already observed in (7), the exoskeleton produces only a $V_{e}(\phi )$ action, so it is possible to set, for example, the relief coefficient by appropriately setting $V_{e}(\phi )$ . This does not produce a direct joint action, but it affects the reduction of the load $\mathbf{F}_{0}(\phi )$ to be lifted and the consequent muscle contraction and cocontraction. Therefore, the exoskeleton can only produce a reduction in joint load.

(49) \begin{gather} \mathbf{F}_{0}(\phi)=\left[\begin{array}{l} N_{W}(\phi)\\ V_{W}(\phi) \end{array}\right],\quad \mathbf{f}_{m}=\left[\begin{array}{l} F_{bi}(\phi\\ F_{br}(\phi)\\ F_{bra}(\phi)\\ F_{tri}(\phi) \end{array}\right],\quad \mathbf{R}_{mus}(\phi)=\left[\begin{array}{l} N_{mus}(\phi)\\ V_{mus}(\phi) \end{array}\right]\nonumber\\[6pt]\mathbf{f}_{m}(\phi)=\mathbf{B}_{m}(\phi)\mathbf{F}_{0}(\phi),\quad \mathbf{R}_{mus}(\phi)=\mathbf{U}_{m}(\phi)\mathbf{f}_{m}(\phi),\quad \mathbf{R}_{soft}(\phi)=\mathbf{K}_{soft}(\phi)\mathbf{F}_{0}(\phi)\nonumber\\ \mathbf{R}_{tot}(\phi)=\mathbf{A}(\phi)\mathbf{F}_{0}(\phi),\quad \mathbf{A}(\phi)=\mathbf{I}+\mathbf{U}_{m}(\phi)\mathbf{B}_{m}(\phi)+\mathbf{K}_{soft}(\phi) \end{gather}

(50) \begin{equation}\mathbf{F}_{1}(\phi)=\left[\begin{array}{c} N_{W}(\phi)\\ V_{W}(\phi) \end{array}\right]-\mathbf{V}_{e}(\phi)\end{equation}

3.6. In vivo experiments

To validate the safety and usability of the novel exoskeleton, in vivo experiments were conducted following a thorough assessment of mechanical risks. An elbow flexion–extension exercise is performed with a 1 kg weight in the laboratory, both without and with an exoskeleton for each subject analyzed, collecting an electromyographic (EMG) signal from the biceps brachii at a sampling frequency of 1,000 Hz [Reference Terlizzi, Tonelli, Ciccarelli, Papetti and Scoccia45]. During data processing, the DC offset component was removed, and the signal was filtered with a fourth-order Butterworth band-pass filter (20–450 Hz). A narrow 50 Hz notch filter was applied to eliminate the effects of the electrical supply. Therefore, the envelope of the signal was obtained with a Butterworth low-pass filter (6 Hz) of the fourth order. Then, the activation intervals were identified based on a baseline threshold if the duration of the activation is at least 100 ms with an additional padding of 30 ms. Finally, the EMG envelope was integrated over the segmented epochs. To compare the activation profiles independently of the epoch duration, amplitude normalization (within trial) and linear interpolation were performed, distinguishing the onset or offset phases. The differences in all signal characteristics were computed using the Mann–Whitney U test for methodological consistency, and the effect of the exoskeleton was evaluated using the Clifford and Hedges tests. The confidence intervals for the means, both time-normalized and non-normalized, were set to the 95% percentile.

Then, an in vivo study was conducted on 30 subjects in two phases, in accordance with ISO 9,241–11 standards in a realistic use environment to evaluate usability, with the primary outcome being the System Usability Scale (SUS), associated with two secondary outcomes: user satisfaction with the first 8 items of the Quebec User Evaluation of Satisfaction with Assistive Technology (QUEST) scale and psychological acceptability with the Psychosocial Impact of Assistive Devices Scale (PIADS). Prior to the experiment, informed consent was obtained, and the subjects participated free of charge. A pre-experimental interview addressed potential risks of the proposed exoskeleton, explicitly not designed for medical applications, such as skin pinching or discomfort due to tight clothing, ensuring participant awareness and voluntary participation. In the first phase in the laboratory, information was collected on the subject (age, sex, height, dominant limb, and length of body segments related to the limb); the subject was instructed on how to use the exoskeleton; the EMG signal on the biceps brachii was measured during lifting operations; and the subject was observed during simple activities to ensure that the use did not produce risky situations and to evaluate the system’s mechanical reliability [Reference Aggogeri, Borboni and Faglia46], control accuracy, and adaptability to user-generated commands. Then the exoskeleton was given to the subject to take home for a day, and they were asked to perform some Activities of Daily Living (ADL): reach and grasp an object on a shelf, bring a glass to the mouth, manipulate a small object, open/close a door or drawer, and bring the hand to the forehead. So, the subject was asked to fill out three questionnaires related to the three previously validated scales: SUS, QUEST, and PIADS.

Referring to standard terminology ASTM F3323-21 [Reference Massardi, Briem, Veneman, Torricelli and Moreno47], a standard operating procedure for the use of a powered upper limb exoskeleton can be subdivided into four macrophases: preparation, donning, verification, and removal (or doffing) [Reference Golabchi, Riahi, Fix, Miller, Rouhani and Tavakoli48]. In our solution, with proper preparation of the exoskeleton, there is not a need for an operator during these macrophases; thus, the standard operator can be coincident with the wearing subject. Although this simplification, the verification of the ability of the subject to wear the exoskeleton must be performed “off-line” to allow the safety of the operations. In fact, the subject must confirm the absence of open wounds, severe spasticity (modified Ashworth score greater than 3), or contraindicated implants. The subject must wear at least a tight-fitting, breathable vest without metal fastenings, have baseline vital signs that place them in a healthy condition in terms of resting heart rate, blood pressure, and perceived pain on the visual analog scale, and, of course, be able to maintain the position in which the exoskeleton is worn (standing or sitting) and, if necessary, be able to change posture without experiencing sudden changes in blood pressure or, in general, be able to avoid falling. The donning procedure differs significantly from that of a standard exoskeleton because, in our case, it is performed by the subject independently and no special adjustments are required.

The removal phase presents some critical issues that may be resolved in future work. Currently, the exoskeleton is expected to be placed back on a table while the subject unfastens all the straps. At times, during the removal procedure, we observed the exoskeleton becoming unstable on the table. An alternative solution, which should be tested, could be to hang the exoskeleton from a wall-mounted attachment and then proceed with its removal. In this case, since the exoskeleton is constrained at the top and subjected to a downward pull, it would be in a stable equilibrium position and therefore less likely to fall during disassembly.