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?

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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:

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:

Posted by Wade
If you are looking for ideas on how to create highly functional mechanical walkers, Professor Joseph Shigley's 1960 feasibility study for the army is a great resource. It combines engineering rigor and sound reasoning to illuminate many of the challenges, and potential capabilities of mechanical walkers.  

To meet the requirements of walking tanks, Shigley sought a mechanism that could:

• carry heavy loads efficiently
• traverse rugged terrain
• walk at the high speeds that tanks require

all while being mechanically reliable, which is a pretty rigorous set of requirements for a mechanical walker!

To meet the rugged terrain and speed requirements of tanks, much of Shigley's study focused on the foot-paths of mechanisms. Below is Shigley's diagram of foot-path types, with type E representing his ideal type for rugged terrain and fast speeds.

When Creating New Mechanisms, Start By Investigating 4-Bar Linkages
In general, the fewer bars in a linkage, the better (lower costs and build-times, less mechanical complication and friction, etc.). So, searching for a mechanical solution based on a 4-bar linkage is usually a wise first step. Shigley advised searching thru Hrones-Nelson's atlas of hundreds of 4-bar linkage coupler curves as a "good first approach to such a problem", which must have been a vital resource for mechanical engineers in the days before personal computers. Below is one of the better 4-bar linkage configurations Professor Shigley found in Hrones-Nelson's atlas, but it doesn't step high enough for rugged terrain.

​Shigley described how the step-height could be increased​ by allowing a joint to slide along a cam groove, but we wanted a mechanism that could be prototyped in LEGO. So, instead we experimented with pairing two 4-bar linkages into a combined 10-bar linkage with front and back legs, such that the rear leg lifted the front foot and vice versa. This allowed us to increase the step-height significantly. 

​We found that the boat-shape of Strider's foot-path mitigates this problem, since the foot's horizontal speed during the lift and lower phases is similar to the foot-speed of the drive phase. This can be seen in the above GIF of Strider walking across the screen. Notice how the bottom halves of its lift and lower phases are nearly vertical, which means that when a foot steps on an obstacle halfway down its lower phase it will be less likely to skid or cause the robot's forward motion to stop while stepping up onto the obstacle. 

The impact of the boat-shape can be exaggerated by reducing the number of legs from 12 to 8, causing the feet to contact the ground well above the bottom drive phase of a 12 leg Strider:

​You can see this in action in the below video of an 8-legged Strider walking on rocky terrain, where  Strider's feet often contact the rocks well above the bottom drive phase, yet the robot's speed remains fairly consistent as it walks across the rocks:

Triangular Foot-Paths​​           
​​How robot speed varies as ground height changes can also be gauged by simulating the front legs while keeping the mechanism horizontal, which results in fairly consistent speed for mechanisms with rounded foot-paths like Striders, and also serves to cushion the impact of hitting obstacles somewhat like a spring-based suspension:

​In contrast, the feet of robots with triangular foot-paths will be going the wrong way when stepping on/off obstacles, or when the terrain's slope changes abruptly. If the feet can't skid, then the change in the terrain's elevation can push the robot backward, as happens to Klann's Mechanical Spider below. If the rear legs aren't stepping on a similar obstacle at the same moment, then they'll be pushing the robot forward as usual, fighting the front legs and potentially jamming the mechanism.

Here's a test of how Strider and Klann linkage robots handle elevation changes, using a slope change to make the test scale-independent:

Foot-Path Symmetry
​The front-to-back symmetry of Strider's foot-path results in fairly consistent horizontal speed when the terrain's elevation changes on either side of its foot-path - e.g. when either ascending or descending the stilts in these simulations. In contrast, TrotBot's foot-path is somewhat teardrop-shaped. This causes TrotBot's horizontal speed to drop when encountering large elevation changes on the shorter, inner side of its foot-path, which can be seen in the below simulation when TrotBot steps down to a lower stilt:.

​Tank-Scale Functionality on Rugged Terrain?
Strider's high-stepping, boat-shaped foot-path allows it to meet Shigley's rugged terrain requirements fairly well at LEGO-scale. However, tank-scale functionality on rugged terrain is another matter, which would require the robot to be strengthened dramatically due to the lower strength-to-weight-ratios of larger scales. Furthermore, increasing strength typically involves adding structure and motor power, which further increases weight, which requires even more structure, which adds even more weight and costs, etc. 

The legs in particular would need to be strengthened, since walking along the side of a hill, or turning the walker tank-style while on rugged terrain would put a tremendous amount of sideways forces on the long legs - if it were even feasible at such large scales. However, adding too much structure and weight to fast-moving legs would create other problems. Instead, perhaps the lower half of the legs could be supported laterally by rails connected to the frame? Rails that created channels that the leg's path should follow? Positioned below the legs' knee and "hamstring" joints to reduce sideways forces on these weak points? Eh......for rugged terrain I think I'll stick to smaller-scale walkers, which also benefit from Shigley's insights.

High Speed Walking
As Shigley described, an ideal walking mechanism for a tank should have the constant horizontal speed of a wheel, while also being able to step over obstacles that block wheels. Strider has relatively constant foot-speed, as indicated by how little the feet skid in the following video. Since the feet aren't constantly accelerating/de-accelerating the robot this improves the gait's efficiency, and Strider is the only mechanism that we've tested which can walk with a 1:1 gear ratio without the LEGO motors stalling: 

High Speed Vibration
Shigley also described how the vertical and horizontal inertia forces of leg mechanisms should be balanced for a tank to walk fast without vibrating itself to death. Such vibration isn't much of a problem at LEGO-scales, but it gets exponentially worse as scale increases. If you've ever driven a vehicle where the steering wheel shakes due to its wheels being out of balance, and seen how it's corrected by attaching small metal weights to the wheels, then you can probably imagine how much worse the vibration problems could be for a vehicle with large mechanical legs running at high RPMs.  

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Strider's mechanism would need to be modified in order for a large-scale version to walk at high RPMs with limited vibration. If curious, Shigley's study below shows how to mathematically analyze inertia forces by calculating the horizontal and vertical accelerations of the legs' masses, and gives some suggestions for balancing them. 

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Load Bearing and the Linkage's Bar Count
​​The more bars a linkage has, the more joints it needs. Each joint adds friction. Furthermore, the joints will always have some play, which can cause long legs with many joints to bend sideways under loads, especially when turning them tank-style. Like Klann's sturdy 6-bar linkage, Strider's linkage has relatively few bars per leg with 10 bars per leg pair, versus TrotBot's and Strandbeest's 8 bars per leg. If implemented well, this implies that Strider's linkage has the potential to be relatively energy efficient and should be able to handle loads relatively well.   
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Below tests linkage variation #6 with a 25 pound load. The plastic parts bend and shift somewhat under the load, increasing the difficulty of carrying the load, but the LEGO motors didn't stall. Also, we were planning on uploading a video with Strider self-destructing at the end by attempting to turn it while carrying 25 pounds. Some of our other walkers self-destructed while carrying much less weight, so we were a bit surprised that Strider survived with its legs intact. Strider's low bar count per leg does appear to result in a stronger linkage.

Notice how adding the weight causes Strider v6 to have a stammering gait, which is partially due to Variation 6 having less consistent foot-speed than does Variation 7 featured in the slow motion video above.

Before performing this test the plastic LEGO axles were replaced with steel axles to handle the torque. Other than that, and the 2 steel support rods, all of the parts are plastic LEGO parts connected by LEGO pins (no glue). ​

Strider's linkage dimensions can be found here, and other configurations of Strider can be found here where you can also create your own customized Strider linkage with an interactive simulator.
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​Below is Prof Shigley's feasibility study, a 1960 Popular Science article discussing it, and the Hrones Nelson  Atlas of four bar linkage coupler curves.

Michael Frey, an enthusiast who makes technical animations of mechanisms, has created some wonderful animations of TrotBot's Linkage.

Some of his work is shown below: 

You can see more of Michael's creations here, like his animations of engines - so cool!

TrotBots with 8 legs balance by having 4 feet in contact with the ground, one at each corner of the robot.  If one of these feet were removed, then TrotBot would tip, similar to what would happen if you took one wheel off of a car.

For a tripod gait to be balanced, the feet need to be arranged like an equilateral triangle, so we removed the two outer pairs of legs, and added a pair of legs to the center of TrotBot, inside the frame:

Also, we needed to adjust the timing of TrotBot's front and rear feet.   As shown in the image below, hexapod robots with tripod gaits transition from one tripod to another as they walk, which requires TrotBot's front and rear feet to be 180 degrees out of phase: 

​However, orienting TrotBot's front and rear cranks 180 degrees out of phase won't put the feet 180 degrees out of phase, because the location of the two leg's upper frame connections relative to the cranks is in the opposite direction.  Looking from the side of the robot, the left leg's upper frame connection is 49.4 degrees to the left, and the right leg's is 49.4 degrees to the right.  Here's a diagram of the left leg's frame connection relative to the crank:

So, in order to have the left and right feet touching the ground at the same time the right crank would need to be rotated clockwise by  49.4 degrees x 2, or 98.8 degrees.  For the foot contact to be 180 degrees out of phase, the right crank would need to be rotated a further 180 degrees, or 278.8 degrees in total, as shown in the image below. 

​Here's a simulation of TrotBot's legs with this 278.8 degree phase shift of the right crank:

​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.