The overall objective of this study is to design a passive upper-limb exoskeleton to assist the worker during an overhead task. The shoulder torque generated by the arm weight depends on both the subject anthropometry and the rotations at the elbow and shoulder joints. The shoulder torque reaches its maximum value when the shoulder elevation angle θ1 and the elbow flexion–extension angle θ2 are, respectively, 90 and 0∘. The pattern of the gravitational torque due to the weight of the upper limb alone, shown in Fig. 1, is calculated thanks to the inertial parameters identified by Zatsiorsky (de Leva, 1996) and listed in Table 1 for a subject of 1.74 m height and body mass equal to 73 kg.

To define the size of the pneumatic muscle and the architecture of the transmission system, the heaviest exoskeleton working condition is considered. Therefore, the system behavior is studied by changing the shoulder elevation angle (θ1∈ [90∘, 120∘]) while maintaining the elbow extended (θ2=0∘).

The tension force Fmu produced by a PAM is a function of many parameters, such as supply pressure p, diameter, and percentage of muscle contraction k. Therefore, two different sizes of the commercial McKibben artificial muscles (DMSP series, nominal length l0=0.21 m, FESTO, Germany) have been considered and tested for this application. The static characteristics of the PAMs tension force, shown in Fig. 2, are provided by the manufacturer and can be approximated by the modified Hill's muscle model proposed by Pitei and Tóthová (2016) and described by Eq. (1). The coefficients of the latter are obtained by interpolation and listed in Table 2. 1Fmu=a1p+a2ea3k+a4kp+a5p+a6

The choice of the PAM is mainly driven by the maximum force required by the application as well as the desired shape of the force–contraction characteristic, which also depends on the size and the bulkiness of the actuator. However, PAMs generally have limited stroke; therefore, they require appropriate transmission systems to achieve a wide workspace. Moreover, the transmission system has a critical impact on the general performance of the device. Indeed, to perform in the desired way, the exoskeleton should exert a supporting torque as close as possible to the torque due to the gravitational load. This result cannot be achieved by the PAM itself; therefore, a transmission system able to adapt the characteristics of the McKibben muscle to the external load is necessary. To fulfill this requirement, two designs of the transmission system are evaluated, aiming at reducing the mismatch between the torque provided by the PAM and the gravitational torque throughout the range considered. In both cases, the pneumatic muscles are placed behind the back of the user, and the traction force is transmitted by the sliding of a tendon cable on a pulley (first case, Fig. 3a) or on a fixed cam centered at the glenohumeral joint (second case, Fig. 3b).

In the first case (named pulley-based design), a transmission based on cable and pulley (or a fixed passing point) is hypothesized to transmit the PAM tension force to the bracelet, located on the user's upper arm (Lo Piccolo et al., 2022). Concerning Fig. 3a, a, c0, α, and β are constant and define the size of the exoskeleton. The cable length b and the lever arm r of the tension force, instead, depended on the shoulder elevation angle θ1 and were calculated by the geometry through Eqs. (2) and (3) (Magnetti Gisolo et al., 2021; Lo Piccolo et al., 2022). 2c=c0/cos⁡β,b=a2+c2+2accos⁡θ1+β-α;3S=a+b+c/2,A=SS-aS-bS-cr=2A/b. In the equations, A is the area of the triangle (a, b, c), while S is the semi-perimeter of the same triangle.

The variation of length b corresponds to the contraction of the pneumatic muscle. This allows for the evaluation, through Eq. (1), of the tensile force exerted by the PAM at different supply pressures. Finally, the torque provided by the exoskeleton is obtained.

A second architecture using a cam-based transmission system is also studied. To avoid the onset of forces that can cause discomfort or undesired movements of the limb, the cam center must coincide with the ideal center of the glenohumeral joint (Dehez and Sapin, 2011; Gull et al., 2020). In addition, the cam should not obstruct the user's view. To optimize the functionality of the overall architecture, a solution based on a cam radius increasing with the shoulder elevation angle is proposed. The tension force produced by the PAM and, consequently, the shoulder torque provided by the exoskeleton decrease with the contraction of the PAM. Therefore, the increase in the cam radius should partially balance the reduction of the maximum tensile force and extend the workspace of the exoskeleton. The cam design has been performed by the graphical approach described in detail by Magnetti Gisolo et al. (2021), briefly summarized in the following and shown in Fig. 4.

Previous work (Magnetti Gisolo et al., 2021) showed a preliminary design of the cam profile, with an initial cam radius ri equal to 23.5 mm. This solution exhibited good performance; however, it can be considered only the result of a theoretical optimization approach. For the actual realization and integration of the cam within the final exoskeleton design, the initial cam radius should be greater than 34.5 mm, which represents the longitudinal distance between the acromion (highest point of the human shoulder complex) and the center of the shoulder joint (de Leva, 1996). For this reason, the theoretical result is compared to a more feasible solution that considered an initial cam radius set equal to 37 mm. By design specification, this value corresponds to the initial lever arm ri (θ1=90∘) of the muscle force. Starting from this initial condition, the two parameters do not coincide for any of the higher elevation angles. The initial contraction of the PAM ki is defined by considering the force–contraction characteristics for a nominal supply pressure (DMSP-10-100N: 4 bar; DMSP-20-200N: 2 bar), to balance the gravitational torque calculated at the initial condition. The behavior of the system is studied for elevation angles comprised between 90 and 120∘. For values higher than 120∘, the PAM reaches the end of its stroke. The muscle force lever arm at the maximum elevation angle (rf), instead, is tuned between 40 and 70 mm to achieve the best performance that can be reached by the PAM selected, given the characteristics shown in Fig. 2. Its value is selected also by considering that a large rf corresponds to a large cam radius, likely resulting in a solution hard to implement in the final structure. The cam profile has been obtained graphically by circular arc interpolation, ensuring the tangency between the profile itself and the cable trajectory for the initial and final elevation angles selected. The iterative process is repeated for two more intermediate positions (θ1=100 and θ1=110∘) that are arbitrarily selected. Finally, discrete data from the CAD files are imported into MATLAB; then, through a fourth-degree-polynomial interpolation function, the muscle force lever arm r, the free cable length b, and hence the percentage contraction k are calculated for each elevation angle within the working range. Finally, the muscle tension force and the muscle torque are evaluated, given in Eq. (1), and the analysis of the static equilibrium condition of the system is performed.

A preliminary assembly of the complete exoskeleton is shown in Fig. 5.

The PAM (1) is on the user's back. Its upper end is connected to the structure while the lower end is connected to a cable (2) that is wrapped around the shoulder pad (3) and connected to the bracelet (4) that supports the user's upper arm. This bracelet must be rigidly coupled to the structure of the exoskeleton to prevent sliding along the longitudinal direction of the arm due to large shear force. Moreover, the position of the bracelet with respect to the structure of the exoskeleton also depends on the anthropometry of the user; therefore, a telescopic linear guide (5) could be used to adjust the longitudinal position of the bracelet along the arm.

The human shoulder joint complex can be modeled as a 5 DoF joint: 3 rotations (flexion–extension; abduction–adduction; internal–external rotation) and 2 translations (elevation–depression and retraction–protraction). However, the first 2 rotational DoF, with larger ranges of motion, can be considered the most significant to comfortably carry out most of the work activities. For this reason, the exoskeleton architecture proposed integrates a universal joint (6) that replicates flexion–extension and abduction–adduction of the shoulder. To achieve the correct functionality, the two rotation axes of the mechanical joint shall be aligned with the glenohumeral joint axes, and their intersection shall coincide with the ideal center of such a joint, as shown in Fig. 6. The first arch of the universal joint is fixed to the frame, while the second one can rotate with respect to the first one, thanks to a bearing. This relative motion allows for the shoulder abduction–adduction. Then, a strut connects the bracelet to the moving arch, and its rotation with respect to the moving arch matches the flexion–extension of the shoulder joint. The shoulder pad is rigidly connected to the movable arch of the universal joint so that it can follow the user's limb during the arm abduction–adduction movement and limit friction between the cable and the cam profile.

Finally, some adjustable systems are proposed to make the exoskeleton adaptable to different subjects' physical characteristics:

A telescopic rod (7) is proposed, positioned at the back of the subject, to adjust the vertical position of the shoulder pad;

Simulations were performed to analyze the two different commercial PAMs and the two transmission systems presented. The exoskeleton structure was based on the following geometrical parameters and conditions: c0=0.2 m, β=14, and θ2=0∘ (see Fig. 3a, b).

For the pulley-based design simulations, the constants a and α (shown in Fig. 3a) were set equal to 0.15 m and 80∘, respectively. As far as the cam-based design is concerned, the behavior of the device was tested for both the theoretical optimal value (ri=23.5 mm) and the actual feasible value selected (ri=37 mm) for the initial cam radius. The performance of the general system has been evaluated in different conditions of external load and supply pressure, for several combinations of shoulder elevation and elbow flexion–extension angles representative of the theoretical workspace of an exoskeleton for such applications. In particular, an unloaded condition, considering only the weight of the arm, and a loaded condition, with an additional 1 kg weight in the hand, were considered. All the simulations have been performed in the MATLAB environment.

In the previous study (Magnetti Gisolo et al., 2021), the DMSP-20-200N pneumatic muscle had been tested in the pulley-based design and by employing the theoretical optimal value of cam initial radius (ri=23.5 mm). Figure 7 shows the torque values due to gravity in the unloaded and loaded conditions, along with the torque values exerted by the PAM at different supply pressures, for both solutions. The limited mismatch between the gravitational torque and that provided by the exoskeleton suggested that the cam-based solution can be more effective than the pulley-based design. In the cam-based solution (Fig. 7b), the exoskeleton provided most of the muscle work needed to raise the arms and hold the position. The remaining part, instead, can be easily provided by the user.

However, as discussed in Sect. 2.3, the cam with initial radius ri equal to 23.5 mm cannot be easily mounted over the user's shoulder. For this reason, the cam profile has been recalculated by increasing the initial radius. By considering the renewed, feasible cam profile obtained based on ri=37 mm, the trend of the torque values exerted by the exoskeleton is quite different with respect to the gravitational load (Fig. 8), causing higher efforts on the shoulder complex muscles to be balanced by the user. Therefore, the DMSP-20-200N McKibben muscle is not suitable for this application for any of the transmission systems tested (see Figs. 7a and 8). The cam-based mechanism (Fig. 8) partially reduces the mismatch, but the optimal performance could not be achieved due to the cam size.

The adoption of a different PAM (FESTO DMSP-10-100N) highlights a significant increase in the performance of both transmission systems (Fig. 9). In the unloaded condition, the exoskeleton can balance at least 58 % of the gravitational torque with the pulley-based design (Fig. 9a), while the cam-based system provides at least 74 % of the gravitational torque (Fig. 9b). With respect to the results shown in Fig. 8, the torque values exerted by the more compact PAM (Fig. 9b) enable a significant reduction of the efforts required by the user to keep the upper limb lifted in the working position and allow them to obtain the best results among the tested configurations. As signaled by the curves presented in Fig. 9, through appropriate regulation of the supply pressure, the device action can be adapted to the weight of the user's arms and different operating conditions. On the other hand, the maximum force exerted by the PAM strongly depends on its size, and even at its maximum operating pressure (8 bar), the FESTO DMSP-10-100N PAM is not able to fully balance the gravitational torque with more than 2 kg of additional payload. However, since the proposed exoskeleton aims to support the user during repetitive lightweight overhead tasks, the more compact PAM can be considered appropriate for the intended application.

Finally, compared to the FESTO DMSP-20-200N (Fig. 8), higher pressure values (5 to 6 bar) are required to provide the required traction force and the corresponding supporting torque at the shoulder when a more compact PAM is chosen.

In this section, the torque provided by the cam-based mechanism, employing the FESTO DMSP-10-100N actuator, is evaluated by varying both the elevation angle of the upper arm (θ1) and the elbow flexion–extension angle (θ2). The ranges selected are θ1∈ [90∘, 120∘], as considered in Sect. 3.1, and θ2∈ [0∘, 90∘], since larger elbow flexion angles are unlikely maintained during overhead tasks.

The absolute difference between the two torque values is calculated for each position inside the theoretical workspace, providing the residual torque that the shoulder complex muscles must provide to lift or to lower the upper limb from each equilibrium position. The results of the analysis for the unloaded condition are shown in Fig. 10 when the DMSP-10-100N pneumatic muscle is pressurized at 5 bar (Fig. 10a) or 6 bar (Fig. 10b). Those values are selected given the results of the simulations discussed in Sect. 3.1 (Fig. 9b). The surface ΔTorque, obtained as the absolute difference between the gravitational torque and the one generated by the PAM, was projected in a “horizontal” plane π: ΔTorque = 0. In Fig. 10a, the black line represents the configuration within the theoretical workspace that corresponds to the static equilibrium condition, in which there is no effort on the user's shoulder muscles since the two torque values are equal. When a supply pressure equal to 6 bar is selected (Fig. 10b), no static equilibrium condition is achieved throughout the workspace, yet no black line is shown. The same result is highlighted in Fig. 9b, where no intersection between the gravitational torque and the torque provided by the device is observed for the θ2=0 condition. This result confirms the necessity for an appropriate selection of the supply pressure when a stable equilibrium position is required. However, due to the limited magnitude of the residual torque shown for most of the positions inside the workspace (Fig. 10), the worker is expected to provide such a difference during operation by their muscle strength.

Figure 11 reports the effort required from the user in loaded condition by pressurizing the DMSP-10-100N muscle at higher supply pressures (7 bar, Fig. 11a, and 8 bar, Fig. 11b). Higher pressures, with respect to the ones selected in the unloaded condition (see Fig. 10), are required to provide the balancing torque due to the participation of the additional external load. In both Figs. 10 and 11, the area surrounding each black line corresponds to low values of residual torque that are requested from the user to move the arm away from the equilibrium condition. Especially in the unloaded condition (Fig. 10), the area corresponding to low values of residual torque (up to 2.5–3 Nm) is large enough to cover the theoretical workspace for the most part. In this condition, we can assume that the real workspace of the exoskeleton is rather comparable to the theoretical one. In the loaded condition (Fig. 11), the workspace seems to be narrower. At such high supply pressures, even small variations of the PAM tensile force generate large variations in its length and consequently in the free cable length. Although the exoskeleton is no longer able to guarantee the desired arm elevation angle value with the same level of performance obtained in the unloaded condition, it is still allowed to reach high elevation angles and elbow flexion–extension angles up to 50∘, which might be appropriate for most of the applications considered.