Theo Jansen’s Strandbeest

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Theo Jansen is a Dutch artist who, for the last couple of decades, has been building increasingly elaborate kinetic sculptures that he calls strandbeesten (beach-animals). Constructed out of plastic tubing, these wind-powered mechanisms walk sideways on legs built from simple mechanical linkages.

His early models, such as the one illustrated in the video below right, could only walk downwind, driven by rigid sails. Later models have wing-like sails that provide propulsion regardless of the wind direction. Still later models use the sails to store compressed air that continues to drive the mechanism during short lulls in the wind.

Jansen has a cute way of describing these kinetic sculptures as if they are living things. From his website:

Since 1990 I have been occupied creating new forms of life. Not pollen or seeds but plastic yellow tubes are used as the basic material of this new nature. I make skeletons that are able to walk on the wind, so that they don’t have to eat. Over time, these skeletons have become increasingly better as surviving the elements such as storm and water and eventually I want to put these animals out in herds on the beaches, so they will live their own lives.

The key to the construction of the beasts is Jansen’s linkage, a simple mechanical linkage that uses eleven linked rods to convert circular motion of a crank to a smooth walking motion of a foot. Jansen describes the discovery of the linkage:

The ideal walking curve [is] a flat base with rounded corners. The curve this produces is dependent on the ratio between the lengths of the 11 small rods. Another ratio gives an entirely different curve, a figure 8 for example. Of course, I had no idea beforehand which ratio between the lengths I needed for the ideal walking movement. Which is why I developed a computer model to find this out for me.

But even for the computer the number of possible ratios between 11 rods was immense. Suppose every rod can have 10 different lengths, then there are 10,000,000,000,000 possible curves. If the computer were to go through all these possibilities systematically, it would be kept busy for 100,000 years. I didn’t have this much time, which is why I opted for the evolutionary method.

Fifteen hundred legs with rods of random length were generated in the computer. It then assessed which of these approached the ideal walking curve. Out of the 1,500, the computer selected the best 100. These were awarded the privilege of reproduction. Their rods were copied and combined into 1,500 new legs. These 1,500 new legs exhibited similarities with their parent legs and once again were assessed on their resemblance to the ideal curve. This process went through many generations during which the computer was on for weeks, months even, day and night. It finally resulted in eleven numbers denoting the ideal lengths of the required rods.

The demonstration below (based on code by Stack Overflow user heltonbiker) illustrates the evaluation of candidate linkages. You can specify the lengths of each of the eleven rods. (Try out different numbers to see what kinds of motion you can get: CD=55.3 is quite entertaining, for example.)

When the crank AC has turned through a full circle the shape traced by the foot H is given two scores. The ground score is the fraction of the cycle that the foot spends on the ground, which I take to be all points whose y-coordinate is within some tolerance of the lowest point. The drag score is the biggest difference between any two horizontal velocities while the foot is on the ground. (It’s always negative, so that higher values correspond to small differences in velocities, which are better.)

What I don’t know how to do, and what Jansen elides in his description, is how to balance these factors against each other? The Jansen magic numbers give me ground score 0.520 and drag score −0.285. If I set AC=10, GH=65, EH=50, I get ground score 0.688 and drag score −0.661. Nearly 70% of the time the foot is on the ground, but the take-off is rather draggy. Is it better or worse than Jansen’s linkage? Probably worse, but without actual engineering feedback it’s hard for me to know.