One of the most frequent topics on the "legged-robots@yahoogroups.com" discussion group is leg design. This isn't very surprising , inasmuch as even mechanical engineers typically don't have much call to design legs. I thought it might be helpful to those starting out on legged robot projects to go over some of the technical problems encountered in the course of making my robots. For my purposes it is sufficient to consider some design categories that work reasonably well and speculate about how they might be improved.
Most of the walking robots that I've seen are inspired, at least in part, by biological models. So, I've couched this discussion in some quasi-biological lingo. There are lots of different leg types among living things, but the most common models for robot designs have been the arthropod (i.e.: crabs, insects) type and the higher tetrapod type (mammals principally). Figure A and figure B illustrate these types in highly schematic form.
Figure A shows the higher tetrapod type in a side view. In these animals (think dog,cat ) the legs are usually disposed below a relatively long, narrow body. Most of the movement is in the longitudinal plane, and the leg resembles a pendulum. The side view is used because lateral movement in this type of animal is fairly restricted. Ordinarily, vertical movement (leg raising) would be accomplished either by flexing of a "knee", or by a camming action which raises and lowers the pivot point. These are not shown here.
The main difficulty encountered with this type of leg is the "rolling" action produced by elevation changes in the pivot point if the leg is basically a rigid member. Figure A shows the leg at three positions in a forward stride. At the start of the stride (1) the pivot point would be lower than in mid stride (2), and again at the end of the stride (3). This is not the case in the illustration because I have shown a spring section which compensates for the variation in the compression component of the forces acting on the leg. Thus the pivot point, representing the attachment point of the leg to the body, stays at a fairly constant elevation as the compression component increases and then decreases again during the course of the stride. Instead of elevation changes in the pivot point, and hence the body, the leg length changes throughout the stride. An example of this leg type in a robot is the walking robot in the first edition of Gordon McComb's Robot Builder's Bonanza, and there are others as well, so the design can be used successfully even without the compression spring refinement.
The Arthropod type is probably the most commonly used leg design in walking robots (figure B). This leg type extends laterally out from the body, usually with a pronounced "knee."
into a downward extending lower member. However, the leg could extend downward at an angle as a single member, so Figure B shows the leg type in its simplest form. The principle difficulty encountered in using this leg design arises from the oar-like lateral extension. As the leg moves through a stride from forward to back (1-3) the contact patch of the leg on the ground increases and then decreases in distance from the body. Since the legs on one side of the body have counter-rotating counterparts on the contralateral side, the side forces generated during the stride tend to move the body, resulting in loss of traction on some of the legs. Figure C shows this in a more
direct way. Assuming the pivot point is rigidly connected to the body, the side forces generated by the lateral displacement of the contact patch as the leg swings through its arc result in a loss of traction at the foot pad.
To reduce this effect it is necessary to introduce some compliance into the leg so the foot pad can stay in one spot as the body of the robot moves forward. Figure D shows one way to accomplish this. In robots like Fuzzknuckles, the Lynxmotion Hexapod II and Quadraped,
and others which incorporate a parallel link to keep the distal segment vertical, the rigid link can be replaced with a spring. This will allow the link to extend as the leg moves back, and contract again as it rotates past the midpoint of the stride. Another possibility would be to make the proximal leg segment compliant rather than the parallel link, but I think this would be more difficult to construct. As in the higher tetrapod leg type, the arthropod type functions pretty well even without the compliant link. But under conditions where traction is critical, such as climbing a slope, or on certain types of carpet, I think the compliant link would really result in superior performance. The biggest obstacle to implementing it is finding a spring with the right characteristics for a robot of a given size and power.
Another way of mitigating the tendency of the feet to lose traction is to restrict the angular movement of the stride, thus reducing the size of the side forces. This requires an increase in the cyclical stepping rate if the same walking speed is to be maintained. I don't like this approach for a couple of reasons. First, there are situations, like turning in place, where it is advantageous to have an angular leg movement of 90deg. or more. A software solution could easily be written for that situation, but lots of other specialized situations are likely to arise and things could get messy in a hurry. Second, increasing the cyclical stepping rate reduces the maximum leg lift unless software is written so as to change the duty cycles of the lift and stride phases. Again, it would be easier not to get into these kinds of manipulations if they can be avoided. Nevertheless, that's the route I've taken with Fuzzknuckles 5 because I've yet to find the elusive spring that's just right for the mechanical solution, and it's so tedious making physical modifications to the 'bot.
John Zeissig
6/24/01