Feet Part 5: Shock-Absorbing Feet

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.

Smoother, non-LEGO version of Strider's linkage