<| Introduction

Forgetting momentarily about quadrupeds that can climb trees, etc, the best 4-legged climbers tend to be members of the goat and sheep families. These animals have relatively-lengthened "feet", as compared to other quadrupeds, and also possess hooves. They are members of a wider family called ungulates, and their foot design is termed unguligrade ["hoof-walking"] or digitigrade ["toe-walking"]. For more info on ungulates, see here: [1] [2] [3] [4] Examples of good climbers are big-horn sheep and mountain goats, and the latter seem to be especially nimble at scaling almost vertical cliffs in a manner that almost defies description, not to mention gravity [plus, of course, they always seem to be grinning]. Another sure-footed animal is the antelope. They are not really climbers, but have remarkable ability to run at high-speeds over broken and uneven ground. Pronghorn antelopes are the fastest animals in north america, and can hit top speeds over 50 mph [80 kph]. The two varieties of north american sheep are the big-horn and Dall [white] sheep. Deer, elk, caribou and moose are all members of the "deer" family. Mountain goats are in the same family [Bovidae] as antelopes, bison, buffalo, cattle, and sheep. For more info on western climbers, see: [1] If we're interested in building a robot to climb stairs, for instance, looking at sheep and goat families might be more helpful than looking at other quadrupeds that climb. For instance, cats and squirrels can also climb, largely on the basis of having highly-rotatable front paws, which allow them to be able to "grasp" a tree limb by positioning their paws on each side and pulling "inwards", as well as in having sharp claws for sticking into the bark. Monkeys and chimps are also good tree climbers, but this is probably on the basis of their having long arms which can reach overhead, plus dexterious hand designs with opposable thumbs [we'll have to check this]. For a walking quadruped robot, first we might want to get it to climb something "simple" like stairs, and maybe later worry about more complex situations like trees - [given our current state-of-the-art, a true tree-climbing robot is probably a "few" years down the road]. Climbing pictures: goats [1] [2] [3] [4] - a young goat [1] [2] (only 1-month old) understands where its center-of-gravity is.

<| Foot Design

Antelope Mule Deer Mountain Goat Big-Horn Sheep All ungulates would appear to have similar leg design as shown on the page about mammalian anatomy, including horses, mules, buffalo, wildebeest, etc, in addition to those mentioned above. Therefore, it would appear that successful climbing ability is due in large part to the specialized design of the feet rather than the legs, per se. Horses and a few other ungulates have a single hoof on each foot, but goats, deer, and sheep all have similar foot designs - with two split toes. Shown at the right are the track shapes of several of these animals. Antelopes are small (rarely over 110 pounds), deer, goats and sheep tend to be somewhat bigger (goats and sheep go 150-300 pounds), while moose are the monsters and can grow to over 7' tall (at the shoulder !!) and weigh up to 1800 pounds. Moose hooves weighted and splayed Moose The diagram at right shows how the toes tend to splay out sideways when the foot is weighted. For the moose, this helps keep it from sinking into boggy marsh bottoms. As shown below-left, the hooves of such animals are connected to the higher up leg bone [cannon bone] via separate phalanges, which give the toes somewhat independent action. For the animals which climb, the separate action of the 2 toes clearly will help the foot gain purchase on small ledges [1] and also compensate for uneven terrain when running. Note that, on these 3 animals, the cannon bone is much longer than on goats, as shown below. Also, on the backside of the legs and a little above the hoof on many ungulates are the "dew-claws", which dogs also have. The dew-claws apparently help some during down-climbing, but do not have the strength and structure of the main hooves. In summary, the animals discussed here have foot and bone structure very different from ungulates such as horses, zebras, burros, which have only a single hoof on each foot. Most other ungulates also have 2 toes per foot, while the hippo has 4, and the rhino 3. Animals with multiple toes run better on soft and uneven ground, but apparently are not as fast as those with single hooves on firm terrain. The antelope are the fastest by far over uneven terrain.

<| Some Feet

Besides the 2-toed shape, plus splaying and semi-independent action of the toes, the hooves of these animals have special designs for traction. There is a hard and strong outer wall (W) made of keratin, plus softer inner sections of sole (S) and pad (P), as shown on the right for moose and elk. The dew claws (D) can also be seen. The arrangement of sole and pad varies between animals. In addition, the soles of goat feet are slightly convex and extend beyond the rim of the outer hoof wall, and provide excellent traction on rock surfaces. Some comments indicate they act like "suction cups" - [hard to imagine, considering how rough most rock surface is ???]. The picture at left shows the soles of the mountain goat. The uppermost picture at the top-right on this page shows how a mountain goat uses its feet to provide a friction grip on the rock surface during down-climbing. The picture to the left shows a close-up of how mountain goat hooves differ from the moose above (a grazing goat is seen in the background). The goat toes are taller and thinner, and the sole pads raise the outer rims slightly above the ground. Note the large separation of the toes in front. The triangular shape of the goat hoof probably makes it stronger than the flatter moose hoof, and the narrowness allows it to be inserted into thin cracks in the rock. For more info, see: goat hooves [1] [2] [3] [4] [5] [6] [7]. As long-time hikers, we can attest to the "extreme" importance of a well-designed boot sole to providing good traction on wet rock surfaces. Some soles slip right off - very bad news in the backcountry. Original Vibram compound soles seem to be the best on wet rock. Nike has adapted the idea of the goat hoof design as a commercial "selling point" in their Nike Air Terra shoe. Rock-climbing and mountain sport shoes have special high-grip soles: [1] [2] [3] [4] [5]. Hiking boot soles might make a good foot surface for a climbing robot.

<| Stocky Bodies

Of some interest is that the two premiere climbers mentioned above, namely the mountain goat and big-horn sheep, both have somewhat "low-slung" and stocky bodies. Both animals live at high elevations in the mountain west, but only the goats inhabit the highest most crags. The stockiness clearly relates to the muscle power necessarily to climb steep slopes at high elevations - and muscle power relates to the ability to "jump" from ledge to ledge, and also to "pull" oneself up onto a higher ledge. Mountain goats have very powerful shoulder muscles. Regards height, adults of both varieties tend to be only 36-42 inches [90-105 cm] at the shoulders. The ratio of leg-length relative to body-length is typically somewhat less than that of other native american ungulate species, such as antelope, deer, and moose - meaning the center-of-gravity is relatively low in goats and sheep. Deer and moose are taller with longer legs, while antelope are similar to goats and sheep in height, but only about 1/3 the weight and with much thinner legs. The cannon bone averages 8" in deer, 12" in horses, but only 4" in mountain goats. The short cannon length can be seen in the goat hoof picture (left, just-above). This is the area between the goat's "knee" and "ankle", which actually corresponds to the hand area from the wrist to the knuckles in humans. The goat is built more like the dog than the horse in terms of lower leg length, but there is a reduction in the number of lower leg bones, compared to the 5 metacarpals and 4 toes of the dog. This means less flexibility, but probably more strength. By having relatively foreshortened lower leg segments compared to other ungulates, the goat gains an advantage in maneuvering and placing its feet during climbing. Anyone who has ever seen a horse trying to get up from a sitting or prone position knows that the long leg bones (adapted as they are for speed) represent a serious handicap - the horse literally must leverage itself up against those long "torque arms". [note - we had a similar problem when using long tibias on our walking robots - it's easy to overpower drive servos when the torque arms are too long]. Regards running, it was already noted that the horse has long thin legs [especially the lower segments] with the majority of heavy muscle mass located close to the body. This aids the animal in that low leg mass means faster movements with less energy expenditure. On the other hand, lions have relatively shorter legs with much heavier bone structure and more muscle mass towards the extremity. This difference gives lions the strength advantage, but horses the speed advantage. Likewise, compared to the antelope and deer which are adapted for running, the goat and sheep body and leg arrangement must be better adapted for climbing, which requires more strength relative to speed.

<| Goats Climbing

Doug Chadwick [Chad83] spent 7 years, mostly around Glacier National Park, studying mountain goats [Oreamnos americanus]. His observations support several points made above: mountain goats are seen 75% of the time on slopes over 40 degrees in steepness, while mountain sheep are generally seen on less steep slopes. [in Colorado, mountain goats are mainly found near the tops of the highest peaks - above 13,000']. herds of animals follow one after another up and down seemingly impossible cliffs. goats use their ears and tails to signal stress and distress in a similar manner to other animals. goats are territorial, and billies will covet the nannies, and nannies are very protective of their young. animals built with low center-of-gravity body designs lower the COG even more during climbing - the picture at the right shows a goat down-climbing a steep slope, as seen from below. goats use a special friction stance during down-climbing very steep slopes (left). [down-climbing steep cliffs is especially problematical for humans; the safest way, short of rappelling, is to face "into" the cliff, down-climb feet first, and pick hand- and footholds very carefully]. goats will go down a steep chute by bounding from side to side, to catch small ledges and distribute some of the forces laterally - (not unlike a snow skier making back and forth turns on a steep slope, rather than going striaght down). goats will meticulously climb up a series of ledges, or bound up vertical areas which are too steep to climb, by leaping up and attaining footholds [or toeholds] in tiny crags. typically, goats will choose a slow and meticulous course, with frequent route checks and stops to test footing. the toes of the 2-toed goat hooves are used individually for support and to attain footholds in small and uneven places. the toes splay out sideways, especially during down-climbing, to distribute the animals weight, and to increase purchase on the slope by partially directing forces laterally. compared to humans who have many small bones in the back of their hands, and dogs with the 5 metacarpals, in the corresponding anatomy of the goat, the bones have fused into a single and strong "cannon" bone; below that, the phalanges are separate, which gives a certain amount of independent action to the 2 toes. while horse hooves are concave and the animal essentially walks on the "rims" of its toes, goat hooves have a protruding pad with rough surface texture that provides considerable friction, yet is pliant enough to conform to surface irregularities. the relatively short distance between front and rear feet in the natural stance aids goats in placing feet close together on small ledges. the mountain goat is relatively more muscular in the front than rear, which aids its climbing (pulling-up) ability. goats will turn around on tiny ledges by using their front feet to work along the rock surface above and in the backwards direction, while standing on their hind legs. they have also been observed to plant their front feet on a ledge and do the acrobatic equivalent of slowly "cartwheeling" the back legs over top, by "walking" them along the steep rock surface above. goats use a 3-point stance when climbing, lifting only 1 leg at a time - similar to what human rock climbers are taught to do. The blow-up to the right shows hoof placement by a mountain goat while up-climbing a steep ledge. Its lower body is almost vertical below, and its front end is bent sharply to get its COG close to the wall. It clearly helps to have a short and strong cannon bone. Imagine the difficulty in trying to get leverage if that cannon bone were 2X or 3X longer, like on a deer or horse. A younger goat patiently awaits its turn below.

<| Robots

In passing, we note that we have been exploring similar issues related to robot leg design. To some extent, we have tried both longer and shorter leg lengths relative to body length, on our quadruped and octopod robots. In general, the longer legs exhibit 2 disadvantages. First, it's more difficult to control balance during slow dynamic movements with longer legs. Secondly, it takes a lot more "torque" from the servos to move the body weight via longer legs [for obvious reasons]. For our octopod, Gimlee-U8, which is a little too heavy in general [having 16 servos + aluminum frame], it has been found to be too easy to overpower the servos when using long tibias. In the latest go around, the tibias were shortened by half. Another problem with long tibias on Gimlee was that ground clearance was a problem during certain phases of the step - mainly the recovery phase. Real animals with long tibias have the extra joint [ie, "wrist" front, and hock rear] - which Gimlee does not have - and which bends to increase ground clearance. This will be discussed more on the Gimlee page. Ultimately, we would like Gimlee, or a similar design, to be able to climb stairs. Another degree-of-freedom which Gimlee does not have is a flexible back [although we did design it with a jointed back]. As shown at the right, besides the ability to "pull-in" lower leg segments to increase ground clearance during locomotion, animals also are able to extend their backs during leaps, and compress during landings - to take up shock and recover kinetic energy (cf, leg dynamics page). See also similar back movements during dog (cf, positions 8 vs 13) and cheetah running.

<| Summary

Some characteristics of good natural 4-legged climbers are: muscular stocky bodies with relatively low center-of-gravity, and good balance. hooves with hard outer shells and high-traction soles. short cannon bones which allow better leverage during up-climbing. 2-pronged hooves with "independent" suspension between the toes. 2-toed hooves are better for running over uneven broken ground, while single hooves [eg, horses] are faster on smooth terrain. Other animals use different means for climbing, such as claws in cats and squirrels, and long arms with opposible thumbs and upright stance in primates, but these methods won't be considered here.