1. IntroductionTaking inspiration from millions of years of natural evolution, bio-inspired design is thought to have the potential to improve products [1,2]. Overall, two main approaches are taken to bio-inspired design. One of these approaches is to identify a natural solution and use it to inspire a new or improved product; whereas the other is to solve a design problem with inspiration from nature [1,2,3]. It can often be unclear how the biological innovation example itself is selected and there is little evidence in the literature to suggest that comprehensive and systematic biological example selection always occurs. Indeed, sometimes only one natural example is given, with limited justification as to why that one is chosen specifically.The rapid uptake sporting goods sector makes an ideal test arena for new technologies and processes [4], such as bio-inspired design. Examples of sport and exercise products where bio-inspired design concepts have already been applied include swimsuits [5], watersports boards [6], backpacks [2], knee protectors [3] and other protective equipment [7,8,9]. There is certainly opportunity to continue to take inspiration from nature to bring improvements to other sporting goods.Improvements in sporting goods are often gradual and incremental, with occasional step changes and innovations, which improves performance in the sport [10,11,12,13,14,15,16,17,18,19,20,21]. These equipment developments can be driven by various factors, including user preferences and trends, new materials and manufacturing processes, and innovative design techniques [10,13,21]. For example, rock climbing footwear has developed from adapted hiking boots to specialist tight-fitting shoes with stiff “grippy” rubber soles. Despite these developments, the few scientific publications on climbing shoes have focused on how an overly tight fit can impact comfort and cause foot injuries [22,23,24], rather than how design influences performance. With many diverse examples of climbing animals, the climbing shoe is particularly well-suited for showcasing a comprehensive and systematic process for selecting natural examples for bio-inspired design. Following such a process should lead to a rich variety of bio-inspired design concepts and could lead to further developments of the climbing shoe.Indeed, climbing is a prevalent locomotion type across animals and has led to various morphological adaptations of the foot. Overall, these adaptations can be split into two methods. One of these methods interlocks the foot with a surface, such as by having deformable pads, gripping paws or claws; whereas the other one develops bonds between the foot and surface, such as by applying adhesion or suction [25]. These natural adaptations to aid climbing have already inspired engineering designs, including robots that climb (e.g., gecko [26,27]) and walk (e.g., goat [28]), and adhesive nanoparticle innovations (e.g., climbing plants [29]).Animals that use adhesive pads for climbing vary in size from small mites to large geckos [30], but there are challenges with this approach as animals get even larger. For example, larger mammal and human feet attach less well to surfaces, due to their smaller surface-to-volume ratio, and because it becomes increasingly difficult to distribute load uniformly across large contact areas [30]. Therefore, interlocking mechanisms, like those observed in larger animals, especially mammals, might be better aligned to inspire a biomimetic human climbing shoe, rather than adhesive mechanisms, like those seen in smaller animals, such as mites and geckos [30]. There are certainly many foot shapes and structures in mammals, which are associated with climbing adaptations. For example, climbing primates and rodents both have long, moveable digits for grasping tree branches [25,31]. Climbing primates and marsupials both have reduced claws that do not impede grip, while, conversely, sloths have long claws for hanging from tree branches [32]. Rodents and small primates have many, textured, deformable foot pads [31,32]. The convex shape, compliant nature and texture of these foot pads increase surface contact area and improves grip during climbing [31]. These small pads also enable precise paw movements during climbing, as well as during object manipulation [32]. Conversely, larger primates tend to have fewer and larger foot pads, which helps to provide a uniform contact area for tree climbing [25].While studies have described foot adaptations in detail in primates, and in some depth in rodents, and marsupials [31,33,34], there has been no formal, systematic description of climbing adaptations across more diverse mammalian groups. Furthermore, studies have tended to focus on arboreality (tree climbing) [25,35], due to the first mammals being arboreal [36], and most extant climbing mammals still being arboreal, rather than rock climbers [25]. However, rock climbing is present across mammalian species (including in species of goat, sheep, deer, pika, and tenrec, among others), despite it being relatively understudied. Abad et al. [28] briefly described the morphology of goat hooves, which contain a shell of hard keratin and a compliant, textured pad to increase friction and stability on uneven ground, although they only investigated one species (the Ecuadorian mountain goat). As such, there is scope to explore and describe foot adaptations in a range of mammals, and especially with a focus on adaptations to rock climbing [35]. The aim of this study, therefore, is to describe the foot morphology of mammals and explore its association with Locomotion type (arboreal, rock climbing, terrestrial, digging and semiaquatic) and relatedness (i.e., Order). We predict that foot morphology will differ with Locomotion type in mammals. We will discuss our findings and their implications for a bio-inspired climbing shoe design. In particular, we showcase here a method to systematically survey biological solutions to gather a range of ideas prior to generating bio-inspired design concepts. 4. DiscussionThis study showcases the first step of a bio-inspired design process, to systematically survey biological solutions, in order to gather a range of ideas before generating design concepts. It is the first study to describe foot morphology over a diverse group of mammals. To do so, we developed a new approach to measure and categorise foot morphology in mammals, which was sensitive enough to reveal differences between certain groups of species. As predicted, Locomotion type affected aspects of mammalian foot morphology. Species relatedness (Order) also strongly affected foot morphology (i.e., all λ values > 0.75 and p values Rock Climbing and Rock Climbing & Terrestrial), compared to tree climbing species in our sample (including Arboreal, and Arboreal & Terrestrial). Specifically, this suggests that the rock climbing species had fewer digits and larger anterior pad areas. Indeed, the rock climbing species often had hooved feet and if they had pads, they tend to be smooth-ish (Figure 2).The presence of many, small foot pads (especially in the anterior region), indicated by large PC2 and PC4 values (Figure 1), were present in arboreal mammals (including Arboreal, and Arboreal & Terrestrial) within our sample. The presence of many, small foot pads has been documented before in small primates [25] and rodents [31]. The presence of long, deformable digits is also associated with arboreality, particularly for grasping during tree climbing in primates and rodents [25,31]. Rock climbing species in our sample had fewer digits and larger anterior pads than tree climbing species (Table 2 and Table 3), which highlights the importance of focusing on rock climbing animals during a survey of this nature, rather than simply looking generally at animals that climb. The fewer digits in rock climbing species might reflect the typically large, inclined surfaces of rocks, which are dissimilar to the smaller branches that can be grasped during tree climbing. Having larger, fewer pads (or fused pads), has only been observed before in larger and heavier arboreal animals (i.e., in large primates and humans [25,42]). Large pads are thought to provide a uniform traction surface for tree climbing [30,42], and are likely to also provide a similar function in these rock climbing animals.Labonte and Federle [30] state that larger animals can compensate for their weight during climbing by having larger pads, as well as increasing attachment efficiency (i.e., friction per unit contact area). We notice that the rock climbing animals in our sample, overall, had smooth-ish pads or hooves (Figure 4). However, even though the foot surfaces may appear largely smooth, there were differences in surface texture (see Figure S2 (SupplementaryMethods.pdf)). These differences were hard to categorise further, as texture varied upon a continuum. Even small changes in surface texture can increase friction. For example, even the small ridges on primate and human volar skin (i.e., the fingertip ridges) may increase friction during climbing (see Figure S2b (SupplementaryMethods.pdf)) [25]. And even hooves (e.g., Figure 2b,c,e), which appear to be smooth, have a textured surface, which is thought to increase friction with smooth surfaces and also absorb shocks [28]. Therefore, surface area, texture, compliance, and friction are all likely to aid climbing.Although, on the whole, rock climbing species had few digits, and large smooth-ish pads or hoof-like feet, there was still some variation, especially in pad shape and position (Figure 2). Much of this variation is likely to be dependent on the relatedness of species, with those that are more related having more similar feet, irrespective of their Locomotion type. This would explain why our phylogenetically-corrected ANOVA had no significant effect of Locomotion type on PC values 1–4, whereas our classic ANOVA revealed significant effects in PC1 and PC2 (Table 3). Indeed, Order had a significant effect on PC1–4, with the orders Primates, Artiodactyla and Rodentia often differing from the others (Table 3). Within each of the orders, Locomotion types varied. For example, rock climbing (including Rock Climbing & Terrestrial) species were present in the orders Carnivora (e.g., foxes), Artiodactyla (e.g., bovids and goats), Rodentia (e.g., gundis or comb rats), Afrosoricida (e.g., tenrecs) and Lagomorpha (e.g., pika) (see examples in Figure 2). Therefore, perhaps it would be beneficial to consider innovations from each Order, when considering rock climbing feet adaptations for bio-inspired footwear design, since between-Order effects were large in our sample.

While we took care to proportionally sample from each Order, we have only captured a small selection (~3.5%) of mammalian species. Therefore, more adaptations in foot morphology may exist than what we have characterised here. However, we have represented many different mammalian Orders, and our results do suggest that between-Order effects are large, compared to within-Order effects (i.e., from our Phylogenetic statistics). Therefore, we may not expect to see many further extremely distinct examples of foot morphology if we were to sample from more species. Furthermore, this study represents the largest comparison of foot morphologies in mammals, and the largest biological comparison (to our knowledge) for bio-inspired design purposes.

Implications for Bio-Inspired Climbing Shoe DesignThere is some variation within the foot morphology of climbing mammals, however, most species we sampled had large, smooth-ish foot pads or hooves (Figure 4b). Indeed, the hooved feet of many rock climbing mammals look somewhat superficially like current climbing shoes (Figure 5a,b). Therefore, perhaps climbing shoe designs have convergently developed, or “evolved”, to be relatively similar to the feet of rock climbing mammals. However, while there are some similarities, we do believe that there is room for further innovations, taking inspiration from rock climbing mammals (Table 5). The presence of pads on some climbing species, suggests that having a compliant structure might be useful during rock climbing, especially a large anterior pad (i.e., Figure 5d).Compliant pads have also been documented in hooves (e.g., in goats). Although the edge of the hoof is made of stiff keratin, the central area is compliant for stabilization and to absorb shocks [28]. This palmar region is also slightly textured to increase friction with a surface [28]. Therefore, a compliant and textured sole surface might be a useful addition to climbing shoes (i.e., Figure 5c or d). However, texture, and shape needs to be better captured and described in our samples before fully developing these bio-inspired designs, perhaps by using three-dimensional imaging techniques, such as photogrammetry and structured light scanning. Indeed, future work could focus on characterizing these features on the feet of climbing animals in more detail, to aid the development of candidate shoe design concepts. Overall, incorporating surface textures and compliant pads into a climbing shoe may well improve grip and traction with the climbing surface, as well as improving stabilization and shock absorbance. The texture, compliance and position of these structures will need further characterization and testing before full candidate design concepts can be proposed. These concepts could then be tested experimentally, such as with tests of friction (e.g., [43]) and compliance, to better determine those which could be applied to improve climbing shoe designs. These tests should, ideally, be representative of the forces being applied to the shoe sole in the same way that they are applied to the mammalian foot during rock climbing. 5. Conclusions

We suggest that a systematic survey of biological examples, such as we have conducted here, will help to solve design problems using true inspiration from nature. While many bio-inspired studies appear to focus on only one biological solution, we show that there may be an array of biological solutions to a common problem, which in this case is rock climbing. This study showcases the first step in a bio-inspired design process, to systematically explore and describe biological examples. This step may include comparing specific biological solutions to those of other traits. For example, here we find the adaptations of rock climbing mammalian feet by comparing them with species that undertake other locomotion strategies. While comparisons are important to highlight adaptations, they also need to be specific and appropriate. For example, in our study, tree climbing and rock climbing animals had distinctly different foot morphologies, so it would be inappropriate to base a rock climbing shoe on an arboreal mammalian foot. The next step in the design process, would be to: (i) further quantify and test the functional properties of these adaptations (i.e., pad texture and compliance), and then (ii) develop and test candidate design concepts. We feel that such a systematic survey of biological examples will lead to a more stringent approach to bio-inspired design and generate more possible solutions to engineering problems.