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4-Legged Creatures page.
A Simple Biomorphic Leg
|> Forward Strokes
|> Return Strokes
|> Increased Leg Complexity
|> Summary

The dog and horse legs we looked at on previous pages have multiple segments and joints, and highly complicated bending sequences in the various strides. The case we looked at of the front leg of the dog is especially complex, as that leg has both elbow and knee, and the shoulder also comes into dynamic play.

  • For our purposes, however, we wish to devise something less complicated, and are first going to consider simplified 2-segment legs having movements and bending similar to biological organisms, to see how useful such an implementation might be.
  • The intent is to develop designs better suited to simplified mechanical implementation and microprocessor control, but also having the advantages of 200,000,000 years of natural selection.

    <| Forward Strokes
    Leg movements are obviously periodic, but upper and lower leg segments have very different actions. The figure below shows joint bending for a simplified 2-segment leg for 30- and 45-degree strides, where the COG of the animal is purposely maintained at the same height above ground. The 2nd joint can be considered as either knee or elbow, depending upon the direction of travel.

    +/-30 degree stride +/-45 degree stride
    knee <===[ direction of travel ]===> elbow

    45 degrees is considered to be the largest usable stride in dogs, as described previously. It is seen in running and trotting dogs. It may be too large for a robot, but serves as a useful reference point. A 30 degree stride would be a fast walk in most animals. Note that, for the 30 degree stride, the animal's COG is held about 20% higher than for the 45 degree case.

    In this case, we specifically wished to examine the situation where the animal's COG is kept at the same height during all points in the stride. This leads to the smoothest forward movement, but also the most extreme leg bending. The arcs in the figure show how much the COG would move if the legs were held straight throughout the entire stride. For 30 degrees, the bounce would be about 1:6, or 16%. For 45 degrees, it would be about 2:5, or 40%. Later in our analysis, we can reduce this criteria, and allow the COG to move up and down by some amount, so the leg bending becomes less extreme.

    !! Gakk !! A major advantage of simple 2-segment legs is that the same bending movements come into play whether the 2nd joint is considered as knee or elbow. The only difference is the direction of travel, and the sequence of angles over time is reversed. It is conceivable that a robot could be designed that could walk equally well in either direction - kind of like Dr. Doolittle's Push Me - Pull You (but minus the internal conflicts).

    Bending Analysis. Observations on the figures:

  • the bends are quite extreme for the 45 degree case, and the elbow-knee sweeps very close to the ground - the extreme angle of the lower leg might lead to loss of traction, so this might be a good candidate for relaxing the level-COG requirement.
  • interestingly, in both "elbow" cases (movement to right), the upper leg moves through about 50% of its travel in only the first 1/8 of stride range - this might be fine for quickly absorbing the force of impact (but also when the potential traction problems just mentioned would be most severe).
  • also for the elbow cases, the upper leg segments overshoot the -30 & -45 degree angle points towards the end of the stride.
  • for the 2nd joint considered as "knee" (travel to left), the knee is seen to immediately bounce upwards, followed by a power stroke and maximal angle of the lower leg - the power strokes look good for transferring force to the ground, except again for the 45 degree case where the angle is so extreme that the foot would likely lose traction.
  • regarding the power strokes, large lower leg angles, and traction hazards, clearly a well-designed active foot would help here - alternatively, relaxing the requirement for level-COG will lessen the extreme angles and improve this situation, albeit adding some bounce to the body.
  • <| Return Strokes
    After the forward stroke, the leg resides at its furthest rear position, and must then return to the furthest forward position for the next step. One way to do this is to simply retrace the forward stroke in reverse. A little additional bend could be put into the lower leg segment, else the leg will simply drag along the ground and might catch on something. This should work fine for a leg with a knee, because of the acute angle of the lower leg with respect to the ground.

    Kneebow. For a leg with an elbow, however, we also have the option of bending the elbow into a knee for the return stroke. Animals cannot do this but a robot could, and this might actually be advantageous in the case of very uneven ground, else the normal "elbow-ish" return stroke might cause the leg to catch on something and trip the animal. On the other hand, if the robot is working slowly and exploring its environment, it should help to use an elbow-ish return stroke, where the robot's foot can feel ahead to sense things, such as uneven terrain, tilting terrain, and obstacles. A foot sensor in an elbow-front leg could sense all 3 conditions, whereas a knee-front leg would need both foot and knee sensors.

    As mentioned previously, animals such as dogs, cats, and horses have a complex front leg geometry with both elbow and knee [analog to human wrist]. This does allow them better probing capability than if the front leg had knee alone.

    <| Increased Leg Complexity
    [humans have knees] [birds have elbows] Humans. Everyone will note that humans do not walk as just described. Their legs do not flex nearly as much, and there is always a significant bounce to the body. The knee is normally straightened shortly after ground impact, and the ankle flexes to lift the body just enough that the other leg clears the ground in its forward stroke. And as we can see on the right, birds walk this way too, in the sense of having fairly straight legs and lifting off the rear "heel". Shadow.org shows an animated human skeleton walking [1] [2], but real people walk with slightly straighter legs, and lift the grounded heel earlier in the stride, as shown by the Rubberbug simulation, which lifts the body in time for ground clearance by the other leg. Both show the COG bounce.

    Birds. Interestingly, bird legs appear to have "elbows" rather than knees, but as the picture shows, they still walk similar to humans. Hmmm, I wonder why? Ha, this is really an illusion, as the bird actually has a true knee hidden under its feathers. The femur [thigh bone], however is relatively short. So birds actually have both true knee and a lower joint that bends like an elbow [similar to the hock joint in horses and dogs, and the heel in humans]. However, the particular bird shown here has such a finely specialized foot and leg that its hock joint looks more like an elbow than a heel.

    Heel Lift. The main difference between the straight-legged strides shown here and the 2-segment leg above is the presence of the foot. Just a couple inches of ankle lift in humans is all the difference between deep knee bending as above and relatively straight up striding. However, a little knee bend helps absorb the shock of foot impact, and interestingly, a lot of hikers with knee problems walk downhill with straight legs - a result of weak thigh muscles and inadequate compliance.

    It might be possible to greatly mitigate bending of the 2-segment biomorphic leg by adding a bit of extra complexity. Horses and dogs [and birds] have the extra joint, eg elbow plus knee in front leg, and humans have the foot and ankle.

    [spring loaded prosthesis feet]

  • one possibility is to change the ratio of upper-to-lower leg lengths; a relatively shorter upper segment will reduce the angular excursions of the lower - but might adversely impact the mechanical advantage of the leg.
  • another possibiity might be an active, retractable foot, which could retract linearly on impact, and extend during the stroke to raise the leg like a flexing ankle in a human - for simplicity, the retraction mechanism might work off a cam mechanism, graded to the angle of knee bend.
  • the foot might also contain a spring to arrest shocks - such as the passive, spring-loaded prosthetic feet used by double-amputee and paralympics athlete Aimee Mullins [1] [2] [3], or other prosthetic feet.

    The new Z-Coil shoes make use of coil-spring shock absorbers.

  • <| Summary

  • A simplified robotic leg consisting of 2 segments, looks eminently workable, given the limitations just discussed. These can be dealt with in various ways, however, and are not insurmountable at first appearance.
    ---- A simple 2-jointed leg undergoes somewhat extreme bending for large stride angles, eg 45 degrees. However, this can be reduced by allowing the COG of the frame to rise and fall somewhat during the stride.
    ---- If a compliance mechanism, such as a linear shock absorber, were built into the leg which would shorten it during ground impacts, this would help reduce the extreme bending problem.
    ---- In addition, different ratios between upper leg to lower leg lengths will change the relative bending amounts.

    [click for info on AMEE]

  • It might even be advantageous to have a convertible front leg, where the 2nd joint could function like a knee for running, but like an elbow for slow exploration of the environment.

  • Furthermore, such a robot could have a "morphable" front foot, which could act like a foot for running, but like a hand with an opposable thumb for fine work. Red Planet's AMEE and Tomb Raider's S.I.M.O.N [1] [2] both have multi-jointed legs and multi-functional hand-feet, but of course this is easier to achieve on film than in real life. On a related page, we present preliminary ideas for a Morphable Robotic Foot-Hand.

  • A priori, without some experimentation, it is difficult to know which front-back leg configuration will work the best: both as knees such as Kimura's Collie uses, both as elbows such as Kimura's Tekken uses, or a mirror-image arrangement such as Sony's Aibo uses. Of all the quadruped designs we have run across, only one has a complete leg arrangement such as dogs use, complete with shoulder and 35 DOFs total. This is Iida's Robot Dog, but it has not yet been implemented.

  • Since doing this, we discovered some simulations of a mirror-image legged quadruped by SANS. In this case, the walker stands very low due to holding its legs in highly-bent positions, and takes rather smallish steps mainly through bending of its lower leg joints. The upper leg segments move through no more than about 60 degrees, and there is considerable bounce in its COG, but it also quite facile and reminiscent of a cat walking.

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    © Oricom Technologies, Nov 2001, updated Nov 2004