1. IntroductionMechanical replication of a biological hand in general, and its thumb in particular, is one of the current challenges in the prosthetic and robotic fields, but it is far beyond the reach of today’s technologies. However, the presence of the thumb in the hand is highly required. Anatomists highlight that the hand, without a thumb, loses most of its capabilities, thus being “nothing but an animated spatula and, at best, a pair of forceps whose points do not meet properly” [1]. Theorising about the kinematic chain of the thumb is cumbersome. The classical mechanical models for the joints simplify their actual motion, which results from the flexibility and the complex sliding/rolling motion of the bone heads. Figure 1a shows the kinematic model of the thumb with 5 degrees of freedom (DOF) which best approximates the anatomical movements, where the joints with 2 DOF have non-orthogonal and non-intersecting axes [2]. The interphalangeal (IP) is the simplest joint and is considered a hinge joint (1 DOF). The carpometacarpal (CMC) joint, also known as trapeziometacarpal (TMC), is of saddle shape type (2 DOF, Figure 1b) and best approximated by a joint of hyperboloid geometry. The MCP joint has a condyloid type (2 DOF) with an important lateral and rotational (twist) DOF [3]. All 5 DOF of the human thumb are involved in achieving opposition: three DOF are necessary to make one point of the thumb’s fingertip meet the position of another point inside the reachable space of the thumb’s kinematic chain, and two additional DOF are necessary for the planes of the finger-pulps to match [4,5]. Beyond this kinematic configuration, the vastly sophisticated neuromuscular system of the hand gives the human brain an enormous ability for manipulation. The joints of the human thumb are actuated via muscles and tendons. The thumb muscles are nine skeletal muscles, five located within the hand (intrinsic) and four with muscle bellies in the forearm (extrinsic hand muscles). Muscles never work independently, and even the simplest motion comes from the coordinated and averaged action of several of them [6]. As stated before, the opposition motion represents the main functionality of the thumb and allows all configurations between the flat hand and the opposition for pinch and power grasps. The pure movements of the thumb’s metacarpal through the CMC joint are those of abduction/adduction (Ab/Ad) and flexion/extension (F/E) [4]; see Figure 1a and Figure 2. Specifically, combined F and Ab produce CMC opposition, and E and Ad produce CMC reposition [7].Nowadays, the popularisation of the FDM (fused deposition modelling) 3D-printing technology has enhanced non-profit initiatives [8,9] seeking to provide affordable prosthetic hands (normally, less than $500) for the 2.4 million upper-limb amputees living in low and medium-income countries (LMICs) [10,11]. Under the Do It Yourself premise [12,13], the altruistic designers feed Computer-Aided Design (CAD) repositories (such as www.instructables.com (accessed on 16 September 2021) and www.thingiverse.com (accessed on 16 September 2021)) from where anyone can freely download a ready-to-print prosthetic hand. From a mechatronics perspective, Controzzi et al. [14] identified six key issues to be considered in the design of such prosthetic hands, namely: (a) kinematic architecture, (b) actuation principle, (c) actuation transmission, (d) sensors, (e) materials, and (f) manufacturing method. The existence of a large number of affordable devices has prompted some reviews of the state of the art that can be contrasted with these key issues. Phillips et al. [10] examined 18 prostheses with a focused overview of the materials and actuation for each device and a discussion of their limitations. Ten Kate et al. [11] reviewed 46 current FDM upper limb prostheses, giving quantitative information about them. Burn et al. [15] and Tanaka et al. [16] looked over some of the most prevalent prostheses aimed at children. These studies make evident the predominance of underactuation (b) (i.e., having fewer degrees of control (DOC) than DOF [14]) using nylon threads running into sheaths (c) as tendons for the digits. These tendons link the motion of the joints at the digits in order to close the hand by pulling them. In the context of affordable designs, hands have no feedback from any sensor (d). The materials (e) normally used in FDM 3D-printers (f) are acrylonitrile butadiene styrene (ABS) or polylactic acid (PLA), also used in conventional orthotics [15,17]. Additionally, the use of elastic cords or thermoplastic elastomers (such as Ninjaflex®) in the joints may avoid the need for a digit extension system [18,19]. Regarding the underactuation (b), slightly more than half of all the prostheses in these studies were body-powered (BP), i.e., these tendons are pulled remotely by moving another part of the body as the only DOC, with all fingers bending together. Some models may include DC motors located in the palm or the forearm in order to achieve more precise grasping postures by having more DOC. All in all, prostheses designed for LMICs exhibit simplified designs. Both assembly and maintenance are very easy in these kinds of hands pulled by tendons. In the scope of these affordable designs, one key factor in succeeding in finding the proper distribution of the digits on the palm and especially of the thumb, i.e., kinematic architecture (a). In fact, the primitive orientation of the thumb in the hand has aroused little discussion amongst designers, yet it has crucial importance for the opposition of the thumb [2]. In affordable designs, the two DOF of the CMC joint are usually simplified to the unique DOF of a hinge joint with a permanent orientation or even suppressed (see Figure 1c). This leaves the thumbs in these affordable hands with three or two DOF, respectively. Regarding the range of motion (ROM) of these movements, designers are committed to the idea of getting a natural motion between the values documented in medical sciences (46°/−14° in F/E, and 25/−8° in Ab/Ad) [20]. They assume that the natural disparities in the ROM of the thumb among individuals do not impair manipulation skills as long as the stability of the thumb is maintained [21]. In this sense, the designer’s main aim has been to provide a sufficient opening angle for common objects [22]. Only a few authors exposed some guidelines for the design of the thumb but in the context of robotic hands, which are much more technologically complex than those in the scope of this research [21,22,23,24,25].The difficulty in putting together and maintaining small integrated mechanisms, such as those used in robotics or more expensive electric hands [26,27], explains why the designers often use simplified conceptions of the thumb for affordable hands [19]. Nevertheless, this conception attends to the designers’ intuition. None of the aforementioned studies evaluated the performance of the hand. Therefore, in order to regain the ultimate goal of providing solutions from the designer’s point of view, evaluation of the performance must condensate the two concepts of function and actual behaviour. Function and behaviour are usually taken as synonyms. However, there is a subtle difference (see Figure 3) [28]: on the one side, the function is the desired outcome from a device that may even be yet to be designed; on the other side, if the device exists, its behaviour can be ascertained. In the context at stake, behaviour is the actual response of the prosthetic hand to the control inputs, aiming to serve a specific task (at this point, desired performance). Thus, the behaviour can be measured by registering and scoring the actual response, whereas any implemented function is only a means. Lately, numerous high-technological hand prostheses have been confronted with the SHAP [29] with diverse outcomes [30,31,32]. It has also raised some criticisms about the applicability of the SHAP [33,34,35], which prompted a proposal for a reduced version of the procedure [35]. This research assessed the performance and the functionality of four 3D-printed hand prostheses by confronting them to this reduced SHAP and the AHAP [36], respectively. As the focus is on the influence of the thumb, two of the hands are different versions of the same model, only varying the orientation that the thumb has after fusing the CMC joint within the palm body. The other two hands incorporate one DOF at the CMC joint of the thumb. One of these last two hands has been developed by our group based on the other models studied here, but considering two DOC for the thumb instead of one. These assessments are intended to address the importance of the orientation and the minimum DOF of the thumb in affordable prosthetic hands and how its control should be managed in order to maximise the user experience. After presenting the four hands and the test protocols, the results will be presented for discussion. Finally, conclusions on DOF and DOC in these hands will be drawn. 4. Discussion

Global AHAP and SHAP scores (GAS and LIFLAO, respectively) are consistent, as they show IMMA and Lb-0 as the best options from a global point of view. Furthermore, the AHAP protocol allows us to discern the proficiency of these hands into two additional interpretations: Grasping and Maintaining (in a sort of function and behaviour, as exposed in the introduction). The IMMA hand got the best score at Grasping by far. Grasping scores for the rest of the hands were similar, with Lb-45 four points ahead of the Dextrus and Lb-0. However, Lb-0 scored slightly better than the rest of the hands at Maintaining. Dextrus was last at both Grasping and Maintaining scorings. IMMA and Dextrus, with 3 DOF at the thumb, ranked first and last at GAS, respectively. IMMA also led the LIFLAO from the SHAP. The LIFLAO of the Dextrus was closer to the bottom of that ranking, between both Lb-0 and Lb-45 models. It may demonstrate the utility of having one specific DOC for one DOF of Ab/Ad at the CMC joint of the thumb, decoupled from the other DOC that actuates the thumb F/E. The only drawback is that it makes the control more cumbersome because of the additional DOC, yet the findings suggest it is worthwhile.

Leaving aside the fact that LIFLAO and AHAP’s GAS offered like-minded global results, it is interesting to observe and interpret the evaluation for each of these GTs. For clarity, both denominations of the six GTs that SHAP and AHAP contemplate are shown in Figure 10. It is important to note that the opposition of the thumb has a great influence on all these GTs. It can be appreciated how IMMA (which reached stage 4 in the Kapandji opposition test) and Lb-0 (which reached stage 2 more convincingly than the other two hands) have two of the widest outlines.As stated earlier, SHAP has been submitted to some debate [35,56] and, afterwards, the linear scoring system and the use of the LAO set seem to provide a clearer insight into the capabilities of any prosthetic hand for the most basic performance expected. Hands confronted with basic shapes representative of most common handling situations in ADL result in more obvious interpretations. Such is the case of the spherical and power grasps: all hands performed quite well in front of these two objects, which are the biggest of the LAO set. Extension and tip grasps are two other basic grasps to aim at, and the scores dropped for all hands as the tiny plates used are more challenging. Together with the poor results obtained with the tripod grasp, it confirms that the use of these assistive devices is more suitable for bigger objects. Finally, the inherent difficulty in grasping the lateral object of the LAO set gives rise to a debate. Troubles come from its mass distribution and, again, one can ponder on the need for this grasp in the context of assistive devices where the solution towards performance also comes with the use of adapted objects [33]. That said, it should be noted that the current linear scoring system observes the reference values given for the healthy hand at [54], that is, the mean time and time limit shown in Table 2. It should be noted that we want to evaluate assistive devices, and not the rehabilitation of human hands, as originally the SHAP was intended for. In the context of prosthetic hands, it may make the evaluation too sharp: mean and limit times should be reviewed to tune the comparative in terms of avoiding null scores and thus being able to better compare the hands amongst themselves. In this regard, Figure 11 shows the same comparison with the mean and limit times from Table 2 doubled.Again, not only by observing Figure 10-right but also now Figure 11, it is clear the importance of having two independent DOCs at the thumb, one for F/E and one at the CMC for thumb Ab/Ad, as the IMMA hand plot almost encircles the rest of the plots in this comparison. On the other side, although the Lb-45 performed averagely in some grasps, its plot tends to cover the smallest area in both studies, pointing out the inconvenience of such a fixed degree of palmar abduction. Finally, Figure 11 shows that having a coupled DOF at the CMC, like in the Dextrus, is not necessarily better than removing this joint with an appropriate fixed orientation because the plot of Lb-0 encircles that of the Dextrus. That said, it is interesting to note the great differences observed between the two Limbitless hands in the two protocols regarding the tripod and lateral grasps. The greater disparity observed with the SHAP (see Figure 11) may be due to the specificity of the tripod and lateral objects used. Both objects are quite difficult to grasp from the table, while they are offered to the hand and taken properly in the AHAP protocol (see Figure 10-right). That said, the Kapandji test already showed that Lb-0 had a better opposition aiming for these tasks, as the contact of the thumb with the index finger at Lb-45 was feeble (see Figure 6).Some discussion may arise for the whole set of hands by observing Figure 10-right. The pGAS scoring is more analytical than the SHAP in evaluating the grasp taxonomies, as it observes the proper execution of the GT at first (i.e., function) and then the ability to hold the object against gravity (behaviour). Such a precise observation is not requested within the SHAP, being the shape of the object that hints at performing a GT. Forcing a hand to grasp an object in a precise specified manner, the object being offered by the operator, could appear to be counterproductive for knowing the actual final performance, that is, for self-achieving a task as observed with the SHAP. Nevertheless, in the context of the present research, this distinction is very interesting to get insight into the pros and cons of the different orientations of the thumb, namely:

SG (spherical): Although all hands performed SHAP quite well, a fixed palmar abduction of the thumb may cause instability in grasping the different sizes of the spherical objects used at the AHAP.

CG (power): again, high variability in the pGAS for the Limbitless models is observed due to the dependence between the abduction of the thumb and the various objects of the AHAP. It should be noted that Lb-0 got the best Ts with the SHAP for Cylinder L, but the object was instinctively grasped from the top. Again, it gives rise to a debate about getting a good performance while the functionality of the cylindrical grasp in this model was scarce.

TP (tripod): being one of the trickiest GT due to the need for coordination amongst the thumb, the index and medium fingers, all hands showed having this function (all have similar pGAS), with IMMA and Dextrus taking the best scores. Leaving aside the fact that the Lb-0 had the proper abduction of the thumb for this particular SHAP task, the comparison between the performances of the IMMA and Dextrus backs up the convenience of having two independent DOCs at the thumb for F/E and Ab/Ad.

LP (lateral), PP (tip), and EG (extension): these three grasps at the SHAP involve grasping a fine plate of balsa wood. The first observation is that Dextrus does not function properly for these GTs (see Figure 12). Accordingly, note that functionality was merely demonstrated in the Kapandji (see Figure 6) and the pGAS (Figure 10-right, using some thicker objects of the YCB set). That said, the performance is a dissimilar approach when assessing the hand with the SHAP. The rated performance results from instinctive alternatives of grasping, but all of them are highly unstable., such as pressing against the dorsum of the thumb, as mentioned in Section 3.1. Regarding the Limbitless models, while they both provide the function of LP (as seen with the Kapandji test), they swap their places in the ranking when it comes to the PP and EG (see Figure 10-right). It also may be due to what was pointed out with the Kapandji test, that is, how the force is exerted: Lb-0 may exert a greater closure force against the index alone for a sort of PP grip; Lb-45 has a loose contact with the radial side of the index finger but opposes better against the whole set of fingers for an EG.

The scope of the present research focused on affordable prosthetic devices, mainly devoted to amputees in low-resource sceneries. In the short term, the main goal of a designer should be to obtain functional prostheses that make life easier for users, with basic needs as the first to be covered. Their usefulness turns out to be subjective and multifactorial, i.e., it depends on various factors that may compensate for each other without it being clear their relevance in each particular situation. This poses the need to be pragmatic when considering the functionality intended vs the performance obtained by the user. The ultimate interest is to discern practical information for the designers regarding the design of the CMC joint in these kinds of affordable devices. SHAP only with LAO showed great sensitivity to the effects of the thumb design on their performance. At this point, it is important to note the coexistence of different assessment procedures that give complementary information: the tests for evaluating the performance should consider focusing on the success or failure of the tasks to be performed, while tests for evaluating the functionality do have to consider the GT adopted and its basic behaviour. AHAP showed to be a useful set for this second purpose.

5. Conclusions

It is clear that, nowadays, the design of a human-like prosthetic hand is utopian in the context of affordable designs. A trade-off between grasp capabilities and having as many DOF as the human thumb has to be found. This study confirms that the current mechanical designs of the CMC seem fortuitous in that context.

The comparison of affordable prostheses points out the shortcomings of some designs. As observed with the two versions of Limbitless, thumb placement was critical to performance as it influenced the manipulability with objects of different sizes. The lack of the CMC joint in the thumb prevented its circumduction rotation. In the human hand, it is the movement required to alternate between an LP (lateral), and a CG (power) or PP (tip) grasps. It can be thought that the addition of a CMC joint for thumb circumduction would guarantee a better polyvalence for different object sizes, yet results demonstrate that it should be supplemented with one additional DOC for this additional DOF.

In conclusion, the advantage of having two decoupled DOC at the thumb is not only evident in the functionality evaluated first with the Kapandji and then with the AHAP but also in the performance demonstrated in the SHAP tasks with LAO. The results of the IMMA hand assert this fact: one DOC moves the Ab/Ad at the CMC joint, and the other flexes the IP and MCP joint. The final design of the thumb is a tradeoff between desired versatility and control complexity, yet this additional DOC could be justified in this case. On the other side, if having an additional DOC is out of the debate, the results with both protocols reinforce the idea of avoiding underactuated F/E and Ab/Ad, like in the Dextrus, in favour of the thumb having a fixed palmar abduction. That said, excessive palmar abduction should be avoided, as justified by the better results of Lb-0 compared to Lb-45.