Posted by Wade

These experiments are a continuation of an earlier post on shock-absorbing feet, where I wasn't able to significantly smooth walker gaits without either:

1. robbing the walker of energy due to damping the legs' springs
2. exposing the walker to erratic and possibly destabilizing bouncing/vibration if the springs were not damped
3. reducing step-height when the legs' springs were at full extension, which tends to happen when the feet are lifted and returned to the front of the foot-path........right when you want the springs to be compressed and the feet to be as high as possible

Instead, in those experiments I tried adding padding to the feet, which only helped a little.
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This variation of shock-absorption via spring-loaded ankles avoids these problems, and is able to smooth Strider's gait while also increasing the percentage of foot-contact per crank rotation, which boosts stability and reduces the need for more legs.

The need for damping is reduced by using a spring which is weak enough to allow the heel to "bottom out" as the robot steps onto the ground, which mitigates bouncing. Yet, as can be seen in the second video below, the heels' springs still absorb much of the shock when the robot steps down to the ground hard and fast even if the heels are compressed completely.

Additionally, much of the energy absorbed by compressing the heel and stretching the spring is returned as the foot is lifted off the ground. Furthermore, the arc of the heel's rotation around the ankle joint tends to push the robot forward when the front foot lands, or the rear foot lifts, which helps to compensate for Strider's slightly slower foot-speed at that point in its foot-path.

There are a number of ways this idea could be implemented, such as via a compression spring that pushed the heel down, but I opted to use a simple rubber band to pull Strider's toes up, which rotates the foot at the ankle joint and pushes the heel down. 

​Strider's toes function as usual here, where they push down on the ground on the inner side of the foot-path. The toes are not involved in the heel's spring-based shock absorption - only the heels absorb shocks.

Below are tests of two variations of shock-absorbing heels. The first test uses longer heels like the GIF above:​

The second test below uses shorter heels, which don't always compress fully and look to be inferior to longer heels....but some load-bearing, top-speed, and high-speed vibration tests should be performed to confirm which heel length is indeed superior.

Conclusions? I recommend adding the longer version of shock-absorbing heels to 8 and 12 leg Strider robots, and as their weight increases use stronger rubber bands to handle the weight. However, I do not recommend building huge Striders in 8-leg versions regardless of adding shock-absorbing heels. Strider's high, boat-shaped footpath has a longer perimeter than walkers with triangular foot-paths like Jansen's Strandbeest or Klann's linkages, which reduces Strider's foot-contact with the ground to about 1/3rd of the crank's rotation.  Therefore, for large-scale Strider builds use at least 12 legs.

Good luck,
​Wade

Way back in 2016 we posted some ideas for how to make strong 120 degree cranks in LEGO here. We still get questions about 120 degree cranks, so here is another diagram to show how LEGO's Technic rotor part #44374 could be used to make cranks of length 2 LEGO holes to drive 3 legs 120 degrees out of phase. 

The purpose here is not to limit you to only using LEGO's rotors when making 120 degree cranks, but instead to use the rotors to illustrate the geometry of a 120 degree crank/axle system - hope it helps to clarify things.

​Good luck,
Wade

Notice that every crank connection is keyed such that every axle connected to them is forced to rotate along with the crank, which transfers the rotation to the adjacent crank.

Note: if you are building larger or heavier walkers you may want to support the axle between each leg with beams that connect the Center of Rotation to the robot's frame, as is done in the simple 180 degree crank/axle system below (of course, instead of using a single beam connection like below you should use two diagonals that connect the Center of Rotation to the front and back sides of the frame, creating a strong triangle that resists front/back forces) 

Posted by Oracid
(Editors note: you can see more of Oracid's inspiring creations here)

My goal is to explain simply how one can go from a usual 5 bars linkage to a 5 bars linkage with extension. The interest of this last mechanism is that it approaches the biological reality of a quadruped or a biped.

In Fig.1, I show the equivalence between a usual 5 bars and its diamond-shaped reduction.
The difference between these two linkages is located at the g bar which is fixed to the chassis. In the second linkage, the 5 bars turn into diamond with g = 0. Only the axis of rotation remains which fixes the 5 bars to the chassis.

​​In Fig.2, I show that the shape of the bar c1 does not matter, provided that its ends keep the same position.
For clarity, only the left side of the 5 bars is shown.

In Fig.3, I show that we can move part of the line c1, provided that the parts are connected by an articulated bar forming part of a parallelogram.
For clarity, only the left side of the 5 bars is shown.
Here is how to go from the assembly in Fig.3-1 to the assembly in Fig.3-2 by translating part of the line c1 and the line a1. Notice that point P remains at the same position.

​​In Fig.4, I show that whatever the angle of c1 with the horizontal in Fig.4-1 and Fig.4-3, there is respectively equivalence of the position of point P in Fig.4-2 and Fig.4-4.
It is as if the two parts of c1 are one. This is because a1 and c2 (not shown, here) form a parallelogram which keeps the two parts of c1 at the same angle.
For clarity, only the left side of the 5 bars is shown.

In Fig.5, we can see a summary of the translations of the bars c1 and a1.
The bar a1 is positioned at the end of the remaining part of the bar c1, while the “ghost” of the second part of c1 is translated and merged with a2.

Fig.6 shows the result of the transformation and the equivalence of the two mechanisms.

Also, check out Oracid's single DOF linkages, like this:

Posted by Wade
​As we learned during our attempt to scale up TrotBot, not all robot's legs will walk by pushing or pulling the robot. When we pushed TrotBot Ver 0 with its more rectangular-shaped footpath, the cranks would initially rotate, and then the linkage would freeze and the feet would skid on the pavement. Instead, we had to manually rotate TrotBot's cranks to make it walk:

The same thing happened when we tried to push our LEGO Klann walkers with the motors disengaged - the feet would skid and the cranks would not rotate. In both cases, this was due to the linkage being at a sort of reverse Dead-Point.

This behavior can be predicted from the image of Klann's linkage below.  Notice that when the crank is in such a horizontal position, all four feet are at the bottom corners of Klann's triangular foot-path.  Also notice that the feet slow to a virtual stop at these corners, as indicated by how bunched together the red dots are at the bottom corners of the foot-path.  In other words, rotating the crank +/- 10 degrees from this horizontal position would barely cause the feet to move. This also means that pushing the robot (and hence the feet) would not cause the feet to move nor the crank to rotate. Instead, it would only cause the legs to bend and the feet to skid, as happens with our prototypes.

This behavior is also indicated by linked bars being parallel - notice in the image above that the legs' connections to the crank are parallel with the crank, a tell-tale sign of a Dead-Point.

Below the crank has been rotated past this dead point where crank rotation causes foot movement and vice versa:

If another pair of legs were added to each side of Klann, as done in the simulation of Strider below, then maybe its legs could be driven by pushing the robot (although one of Klann's feet would still skid at the corner of the foot-path, so it may not work so well - maybe adding feet that could slide or rotate a little would help?)

Here's a test to see how easily this linkage variation #6 of Strider's mechanism can be driven by an external force - gravity in this case:

​Notice how the robot wavers slightly to the left and right as it descends, due to the foot-speed varying a little.  Linkage variation 7 below has more consistent foot speed, and waivers less

​Passive walking can also be tested by pulling the robot with a rope:

Strider's legs can also be driven by pushing the robot when built in an 8-leg version, although not nearly as efficiently as 12-leg versions, and the ramp's slope had to be increased to get an 8-legged Strider to walk below:

​Dead-Points part 1 is here.

Posted by Wade
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?

​
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:

Our LEGO Klann walkers could also benefit from shock-absorbing feet when walking on hard surfaces like wood floors:

​​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 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 shock-absorbing feet can still help to reduce the force of impacts of feet with the ground.  To illustrate, below 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):

Notice how adding springs to TrotBot's feet causes the rear feet to skid somewhat as its feet are lifted off the ground (because its foot-speed slows at that point in its foot-path). Strider's linkage simulated below has more consistent foot-speed, so its rear feet do not skid when springs are added

As an alternative to springs, foam padding can be added to the feet which also provide some damping. This idea is tested below which explores how much an 8-legged Strider's gait can be smoothed by adding thick foam pads to its feet:

Below tests foam "boots" on snow and ice:

And thinner, foam weather stripping for doors was used in this feasibility test of a jumping robot:

On a related note, our LEGO walkers' gaits are somewhat smoothed by the flexing of the metal support rods, although such shock-absorption isn't consistent since it varies depending on how far the legs are from the inner frame.  You can see this in action in the following video, where the outer frames bounce more than the center frame: