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|> Impact and Compliance
|> Note Added in 2004
|> Robot Legs
<| Impact and Compliance
The first two figures show the arc of travel of the front (at left) and rear (at right)
legs of a dog under light impact conditions. The 3 positions are ground impact, bend
during weighting and force absorption, and push off to the next step.
Note how the shortening and lengthening, in conjunction with the angular movement,
tends to keep the top of the legs at the same height above the ground. This helps
to keep the animal's COG on an even plane during stepping.
Heel & Toe.
For every gait from walk to run, the heel of the extended foot hits the ground first,
and so must take up the shock of impact, while the toes are the last to leave the
ground at the start of each suspension, and so should add some extension and spring to
the step for maximum effect.
For these reasons, the feet of dogs and cats and humans have padded heels for softening
impacts, and all animals have a series of tendons and leverages in the feet and lower legs
for pushing off.
In addition, animals like horses don't have much in the way of padded feet, and additional
mechanisms of compliance are built into the system.
The figure on the left shows how straight the horse's legs are held during walking, with
compliance mainly in the ankle joint.
The bent overlays are the legs returning to the front for the start of the next step.
As the various pictures show, however, the rear legs of dogs and horses have a decided
crook which comes down at an angle during hard striding, and in conjunction with the
knee joint, the rear legs scissor and absorb the shock of impact.
This can be seen on the running dog page, especially in
positions 14 and 15 for the Gallop.
On the other hand, one can only imagine the serious forces that the front legs of a horse
must experience when going over a jump. As the horse's knees do not bend in this case,
the forces must be absorbed mainly by compliance of the tendon arrangement connected
around point  in the horse figure.
For the running dog, compliance in the lower front leg is
evident in Gallop positions 6 and 11.
The scissoring of the rear leg helps absorb impact shock, but the front legs have a
more difficult time.
The front knee bends only backwards, so the front leg extended forward comes down
straight at impact.
We speculate that the front knee-elbow arrangement do not scissor at impact
like the back leg, since body inertia into it would probably cause the front leg to
collapse the dog into the ground. Therefore, the leg is held straight and ankle joints
(plus pads on the dog) register the major shock.
However, as the figure at the right shows, if the forward angle of the leg is correct,
given the stride, then the force of impact will be lessened.
If the leg comes down too soon at too steep an angle, then the foot "pounds" into the
ground, increasing the force of impact. And if the leg comes down at too shallow an
angle, the dog will loose grip and skid.
We have all observed humans who are pounding walkers. Their heels crash into the floor
at every step. They are usually wearing shoes with elevated heels, and the analysis
here shows that this amounts to a shortened stride and increased impact forces.
This has some bearing on how far forward and backward a robot's leg might be
set to move, and at which angle it comes down.
There will be an optimum angle, given the speed and the stride and the nature of
the ground surface.
Furthermore, with the design of a robot, it might be possible to design flexing
(eg, scissoring) into the front legs to help absorb impact shocks. We might be
able to go nature one better.
<| Note Added in 2004
2 1/2 years after starting research on legged locomotion, we think we may be starting
to get a handle on the issue - regards adapting quadruped structures and movements to
simple walking robots.
As noted elsewhere, our robot designs have simple legs, largely because of the complexity
involved in building legs anywhere near as complex as what animals have. Therefore, we
have been going for simple 2-jointed legs so far, and have been trying to take advantage of
other features of quadruped locomotion, such as specific sequences of leg movements,
as well as looking at issues of impact energy absorption, leg compliance, energy storage, etc.
Our original robot, Nico,
walked with front legs carried in a manner similar to those shown at top-left.
In fact, we used this exact diagram as a model to calculate joint bending angles at various
positions in the gait.
Note that, in the diagram, the humerus (upper leg bone) is shown to swing "almost"
symmetrically around vertical, and very little bending is seen in the elbow joint at the
extreme front and back positions.
However, we came to discover a serious ground clearance problem when using this degree of
symmetry, and have been working on solutions since.
Some "short-legged" dogs walk as shown, but many field observations of larger dogs
show much more bending in the elbow at the extreme positions.
The degree of elbow bending and difference between walks of short-legged and long-legged dogs
is discussed more on our Walking Gaits page (see
Note Added in 2004)
and also on our Dog's Elbow page.
Rear Leg. The various pictures show bending of the rear legs in the horse
and dog. During lighter movements like standing and walking, there is an easy
bending and extension of the legs which keeps the haunches and COG of the body
of the animal at the same relative level during the stride. A major portion of
impact force is taken by compliance in the ankle (horse), plus some light flexing
in the other joints (dog).
For more intense movements like running and jumping, the rear legs undergo a
scissoring movement of all major joints for shock absorption.
The figure on the right shows the changes that take place in the front leg of a dog
during a typical step. The direction of travel is to the left here.
Shown are the shoulder blade (uppermost), shoulder joint, upper leg, elbow, lower leg,
knee joint, and foot, which contains the heel, ankle, and toes.
Note that, like the horse, the dog "appears" to have an extra joint in its front leg,
due to the elongation of its lower leg - ie, it has "both" elbow and knee.
This diagram shows the front leg of a dog absorbing ground impact by bending and
shortening [positions 2-4] and pushing off into the next step by straightening
[positions 5-6]. The last 2 positions are the leg moving forward during the
first part of the next step.
Note how the shortening and lengthening, in conjunction with the angular movement,
tends to keep the top of the mechanism at the same height above the ground. This
helps to keep the animal's COG on an even plane during stepping.
Of interest here is the extra degree of freedom afforded by the shoulder joint.
The shoulder has more mobility that the pelvis at the rear, and moves through fully
45 degrees here. This in, conjunction with flexing at the elbow, takes up some
of the impact shock, by shortening the leg.
The shoulder joint also has another degree of freedom, which allows the front legs to
move laterally for turning.
So it seems that, compared to the rear leg dynamics shown above, the front leg
dynamics are much more complex.
Another complication, which adds even more degrees of freedom to animal movement,
is the flexing of the spine. For the less intense movements, this flexing is minimal.
For turns and running, however, the pictures all show significant spine curvature.
During running, flexing of the spine clearly allows the animal to increase its stride
and power, by recruiting every major muscle group in the body, and also to optimize
its footfall angles given its speed, stride, and variations in the underlying
Turning is another issue. Animals bend at the spine during turning, with the angle
dependent upon how tight the turn is. Added to this, are changes in shoulder and
haunch attitude, as well as compensatory head and tail movements.
All in all, very complex.
<| Robot Legs
When it comes to robot leg design, we can use any or all of the mechanisms shown
here - multiple joints with multiple ways of flexing, padding, scissoring,
joints working alone or in conjunction with others, and finally, trajectory angles.
Furthermore, we can employ methods not used by nature, since we are the
designers - for instance, wrong way flexing in joints, or completely different means
for impact absorption, such as linear piston shock absorbers.
The first question to ask is, do we really need 5 leg sections and 5 joints, or can
we do the whole thing in a much simpler manner and still get the same end result?
We are going to proceed on the assumption that legs are mainly big pendulums, and
subscribe more or less uniform front to back swinging movements, due to inertia
maintaining even flow of the animal's body absent of large accelerations.
This means roughly sinusoidal action in the legs.
Furthermore, the legs shorten and lengthen during the stride in such a way as to
reach ahead, absorb impact, and push off into the next step, all the while keeping
the COG of the animal at a relatively fixed height.
If we make these our major criteria, then we don't neccessarily need to implement
legs which are as complicated as say the dog's front leg, but can use the governing
principles instead - the same way that airplane wings substitute for bird wings
without having to flap.
Furthermore, for a first cut, we can simplify the design because
our robot doesn't need to gallop or curl up into a ball to sleep.
A simple mechanical leg might have as few as 2 joints, shoulder and knee (or elbow),
where both can rotate through much larger angles than in animals, as well as some
means to absorb impact shocks in lieu of complicated bending movements in the joints.
This might be a linear shock absorber of some kind, or maybe just a rubber ball.
The complexity of the shock absorbing mechanism will be directly related to the
types of stride the mechanical being engages in. If it isn't going to run and jump,
then the requirements are not as stringent.
In addition, having a knee that can bend like both knee and elbow,
ie a "knelbow",
would allow the robot to raise and lower itself by scissoring its legs inboard, and also
walk and run like animals. The major requirements are that the leg be fully extendable
to front and back at close to a 45 degree angle, shorten to about 70% of that length
during the impact phase of the step (based upon simple geometry), and lastly shorten
to less than 70% of its maximum length during the movement which takes the leg forward
to initiate the following step.
The 45 degree and 70% numbers are based upon the dog pictures shown above. On the
other hand, the horse above steps through a much smaller angle, about +/-30 degrees,
so the shortening amount is only about 86% there (ie, cosine of the angle).
The swing angle will obviously depend upon whether the animal is doing a simple walk,
a trot, or a run. +/-45 degrees from vertical will accommodate both walking and trotting;
more would be necessary for running.
The shortening amount will directly relate to the swing angle used for each specific stride.
We have only begun to think about making a 4-legged robot turn.
In the animal, the spine bends, the shoulders angle, and the legs move laterally in
and out. The front legs cross over, and the back legs cross under.
For straight ahead walking, all 4 legs move through the same swing angle,
but what happens during a turn?
Well, it's a start.
© Oricom Technologies, Nov 2001, updated June 2004