Feet Part 5: Shock-Absorbing Feet

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.

Like how post-holing in deep snow is exhausting, robots with damped, shock-absorbing feet require more power to walk

• 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?

Imagine how much more violent this Klann robot's shaking could be if it had long, un-damped springs for feet

​

• 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):

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.

Smoother, non-LEGO version of Strider's linkage

Below tests how much an 8-legged Strider's gait is smoothed by adding thick foam pads to its feet:

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: