Post by Wade Vagle
​As we learned from our TrotBot Scaleup attempt, not all robot's legs will walk by pushing or pulling the robot.  When we pushed TrotBot Ver 1's linkage the cranks would initially rotate, and then the linkage would freeze and the feet would skid on the pavement.  So, 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.  As you can see in the image of Klann's linkage below, pushing Klann's feet at this point in the crank's rotation would not cause the crank to rotate.  Instead, pushing the robot would only cause the legs to bend and the feet to skid.

However, pushing a Klann robot with the crank in the below position would cause the crank to rotate:

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 variation of Strider's legs 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 linkage variation #6's foot-speed varying a little.

Strider's legs can also be driven by pushing the robot when built in an 8-leg version, although not as efficiently as 12-leg versions:

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 increase the percentage of ground-contact of each leg enough 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 can also increase the percentage of ground contact of each leg.  For example, feet with very long springs could theoretically increase a 12-legged Strider's  ground-contact of each leg to 50% of the crank's rotation, like is required by 8-legged Striders graphed in red below, but do so without causing the robot to drop at the two ends of the foot-path (where the red dots curl up).  

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 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):

Maybe the smoothest solution for Strider 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.

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. 

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 rotating feet to Strandbeest? ( Jeez that thing is cool!)

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

​​I rushed my Klann Ver 2 build and didn't build the outer frames in an optimal way:

The only thing keeping this frame's corners at right angles are the two 3x5 L-shaped LEGO parts.  If this frame were put under a lot of force, like would happen at a larger scale, the corners would be subjected to torque that could easily cause the rectangle to collapse. To avoid this diagonals need to be added, which will convert the rectangles into triangles and lock the corner's angles.
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The challenge with walkers in LEGO is we often need diagonals for rectangles that define the linkage's parameters.  In other words, these diagonals often need to be the hypotenuses of right triangles.   As you can see below, my Klann's upper support rods are 7 holes above the motor's axle, and the lower support rods are 2 holes below the motor's axle.  Neither of these lengths work with a 3-4-5 or 6-8-10 right triangle with LEGO parts for hypotenuses. What can we do using the integer lengths of LEGO's beams?  

NOTE:  When determining the length of LEGO beams the first hole is always counted as 0!  If you don't measure LEGO beam lengths in this way you won't be able to use the Pythagorean theorem to calculate which beams to use as hypotenuses.
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Fortunately, with LEGO we don't have to be at precise integer numbers, and we can use hypotenuses that are close enough. 
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1.  Hypotenuses for rectangles of height 7. 
Plugging in a 90 degree angle with a side length of 7, plus a few other whole number sides into the Pythagorean theorem yields this near integer number triangle:

​I used this triangle for Klann's inner frame where two 9 hole beams create hypotenuses of length 8:

I also used this triangle for TrotBot's frame:

​2. Hypotenuses for rectangles of height 9. 
We can also connect the top and bottom beams of Klann's frame with a hypotenuse:

Plugging a 90 degree angle with a side length of 9, plus a few other whole number sides into the Pythagorean theorem yields another near integer number triangle:

So, 13 hole LEGO beams can be used to lock Klann's outer frames into triangles, like this:

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Here are a few other useful triangles for LEGO frames:

​​Also, the below 5-3 bent beam can be used as a hypotenuse.

You can create more triangles by lengthening a side of the above parts by attaching a LEGO beam to it.

Klann's Mechanical Spider was the first walker I ever built.  I like it since it's robust and not too complicated (as mechanical walkers go).  

Here's a simulation using the ver 2 LEGO beams as the bar lengths.  The python script that made this sim can be downloaded here.

The Mechanical Spider can bear more stress than other walking mechanisms, why?