Posted by Wade Vagle
Like how we appreciate Nike's when running on concrete, large-scale walkers benefit from shock-absorbing feet. By increasing the spring's travel, shock-absorbing feet may also be able to smooth the gaits of high-stepping walkers like TrotBot and Strider. And of course this would create new problems to be solved! 

First, here's the Mondo Spider's feet in action, which provide some shock absorption, and they also slide on the smooth concrete, which helps with turning and with smoothing Klann's speed:

It walks amazingly fluidly considering how Klann's foot-path comes to a stop at each end, and the springs probably smooth the transition between feet somewhat:

Watching the video raises some questions, like:

• how much power is consumed by friction when the feet slide? 
• is there a way for the feet to slide (or roll) when turning on rough terrain?

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Implementing Klann's linkage without shock-absorbing feet that slide results in a more halting gait, as can be seen in this version of the Walking Beast:

​​Next, here are some shock-absorbing feet ideas from Mechanical Walker pioneer, Professor Joseph Shigley:

​Feet with such springs extend the feet toward the ground. So, in addition to absorbing shocks, the springs also increase the percentage of ground contact of each leg per crank rotation. 

Taken to an extreme, feet with very long springs could theoretically increase an 8-legged Strider's  ground-contact of the legs to the point that it always had one foot on the ground at each corner of robot, and do so without causing the robot's height to drop when the feet touching the ground switch. This is because both of the feet will be near the ground at the foot transition, meaning two springs will be pushing the robot up, reducing how far the robot falls at foot transitions. 

However, a few of the (probably numerous) issues of long-spring feet are:

• if the energy used to compress the foot's spring isn't returned to the mechanism when the foot lifts, then the power requirements to walk would skyrocket, similar to how post-holing when walking in deep snow is exhausting, and the motors would quickly stall.

• on the other hand, if the springs weren't damped in order to save energy, then the walker would be less stable, and vibration at a resonance frequency could be disastrous - can you imagine how much more violent this Klann's shaking could be if it had long, un-damped springs for feet?

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• if the horizontal foot-speed at the curled up ends of the foot-path are slower, the feet will skid, or the robot will lurch unless the speed variability is managed in other ways (like the Mondo Spider did with it's sliding feet)
• if the force required to compress the springs is too low or too high, the gait won't be as smooth
• the springs will be fully extended when foot is lifted and returned to the front of its foot-path, so long springs will lower step-heights

So, springs long enough to convert a large-scale Strider to an 8-legged walker wouldn't be feasible, but we'll try to put together an experiment to check if shock-absorbing feet can smooth a 12-legged Strider's gait efficiently by testing it (or TrotBot) with a heavy load. For now, here are simulations of adding shock-absorbing feet to 12-leg versions of TrotBot and Strider (assuming perfectly elastic springs without damping that comply with Hook's Law, and ignoring inertia and spring oscillation):

Maybe the smoothest solution for larger scale Striders would be to add shock-absorbing pads to the bottom of Strider's feet with toes, like the toes simulated below? Pads with a smooth, hard surface to facilitate sliding while turning like the Mondo Spider's feet? Note: the more refined dimensions of this non-LEGO version of Strider's linkage can be found here.

Strider's linkage variation 7 may also be smoothed by shock-absorbing foot pads, since the bump in it's gait occurs at the foot transition, and this should be easier to test since variation 7 can be built in LEGO.

Posted by Ben and Wade Vagle
​As you can see in the following images, Klann's foot-speed slows down significantly at each corner of its foot-path:

​This causes robots using the Klann linkage to have a halting gait, which can be a problem on higher-friction terrain at higher speeds. One solution is to add feet that passively rotate as Klann's speed varies, like Strandbeest uses. 
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​As you can in the following video, rotating feet also reduce how much the feet drag during turns, since the inner and outer feet can rotate at different speeds and function somewhat like a differential. 

In case you were wondering, Klann's violent shaking on the carpeting did cause it to flip over a few times, but at least it didn't do this: 

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Rotating feet also improve performance on rugged terrain, since the feet are less likely to catch on obstacles. Prior to adding wheels to the feet, the Klann below couldn't take one step on those air filters without the feet catching and jamming the linkage, and if LEGO's XL motors had been used, jamming the linkage could have broken the gears.  

Strandbeest's foot-speed also slows at each corner of its foot-path, but less so than Klann's:

This may be part of the reason that Theo added feet that passively rotate to Strandbeest? ( Jeez that thing is cool!)

Similar to Klann robots, adding rotating feet to LEGO Strandbeests smooths their speed:

As can be seen in the following simulation of one side of an 8-legged Strandbeest, the variation in Strandbeest's foot-speed is exaggerated when built with only 8 legs since the foot transition occurs when the feet are already lifted off the ground:

​In this test, 10 pounds were added to TrotBot with 3 versions of feet:
1. feet with heel and toe linkages
2. feet with only heel linkage
3. feet without heels or toes.  As can be seen in the video, TrotBots without heels and toes should be built in a 12 leg version to handle heavy loads.

Also, we added 10 pounds to a toe-less TrotBot that used LEGO's plastic axles, but its bumpier gait required more torque than the plastic axles could handle. Those axles twisted so much that TrotBot could barely walk, so we replaced them with steel axles before filming this test. We should have included a clip of the plastic axle version to better show how heavy walkers with bumpy gaits  may need LEGO's plastic axles replaced with steel axles to handle the torque.  

An alternative to adding heel/toe linkages to TrotBot is to build it in a 12-leg version, which results in a similar increase in foot-contact with the ground. However, it's a wider build, so the longer crank/axle system will twist more if LEGO's plastic axles are used. For this reason we usually replace at least the inner leg's plastic axles with steel axles when building 12-legged walkers.

I've been thinking about creating an EV3 Strider Ver 2, but to handle the increased weight and width Strider needs to be improved in a few ways, like by increasing the amount of foot-contact it has with the ground.

One way to increase foot-contact is to add four more legs. To check how this would smooth the gait I simulated one side of a 12-legged Strider (Ver 2), and if you watch the video below you'll see Strider bounce whenever the feet touching the ground switch. This bouncing shouldn't be much of a problem at LEGO scale, but it would be at large scale.
 
While a scaled-up Strider's linkage could be optimized for a smoother gait, it can also be smoothed by adding feet that are shaped to offset the gait's bumpiness. As an example, in the second half of the video I added small triangular feet to the front legs, which act like heels and toes. These feet reduce the gait's bumpiness by about 1/3rd.  However, the toes are more likely to catch on obstacles, which can cause the linkage to lock and gears to grind.  

UPDATE:  in 2018 we re-optimized Strider's linkage again, and published a half dozen new variations who's gaits can be smoothed by adding toes like those added to Strider Ver 3 below:

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Below is Strider Ver 3 in a LEGO prototype with the above simulated toes of length 2:

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And here's the same Strider linkage with 8 legs plus longer toes of length 3.  Longer toes were used to reduce how far the robot falls at foot transitions when built with only 8 legs:

Curved feet​​
Feet with curved bottoms that are shaped to offset the bumpiness of a particular linkage should be even more effective at smoothing gaits - at least when walking on smooth ground.  Below is a great example:​

And here's another example by Eko Widiatmoko:

​The first result of that effort was TrotBot's heel linkage.  As you can see in the diagram below, TrotBot's heel strikes before the main foot, taking the weight while pushing backward to continue driving the robot forward.  The resulting smoother gait reduces both torque and power requirements (for an analogy of why bumpy gaits require more power, think how much harder it is to do lunges than it is to simply walk).  

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Another benefit of TrotBot's heel is it steps higher on the backside of the foot-path, allowing TrotBot's rear legs to step about as high as the front legs to avoid getting stuck astride obstacles, as can be seen in this heel-path simulation:

​​​Without its heel, TrotBot's rear legs probably would have gotten stuck on some of these 2x4s:

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We've also played around with a few ideas for active toes that push down on the ground as the foot begins to lift:   

Using shaped feet to smooth gaits is explored next in Feet Part 2, and the impact of TrotBot's active toes are explored in Feet Part 3.