SNG 9: Foldable Umbrella

I own a foofoo non-circular umbrella from Senz. My defense for the foofoo-ness is that I got it as a gift through my frequent flyer program. But it does work quite well on two counts:

  1. It behaves like an airfoil whose geometry you can adjust by tilting the umbrella differently. This makes it a lot easier to hold on to in high winds
  2. The asymmetrical design is ergonomically sound. My view is that unless it is part of an umbrella hat, there aren’t many good functional reasons why umbrellas should be circular.

This week, I geek out on the folding mechanism in this umbrella. Each arm of the umbrella is made up of a series of pin-ended aluminum members (C-channel sections in pictures) joined in series. Each alternate member is then connected with a slender spring tempered wire. Basically, each section is part of a local 4-bar linkage.

Buckling

The interesting thing about this mechanism is that it exploits the buckling behavior of the spring tempered wires in its design. This marks a departure from the traditional “classroom” engineering approach where buckling is not considered until late in the design process when one verifies that the specified members are not going to buckle. This approach reminds me of a piece of MIT IP from Prof. Brian Wardle’s lab that I wrote about at work (as a technology licensing intern for the MIT TLO), where buckling is exploited to create 3D MEMS geometry using conventional 2D microfabrication workflows such as CMOS.

Bi-stable Mechanism

Back to the umbrella. In the folded configuration, the spring wires are in a relaxed state, free to rattle around in the pin-supports at their ends. In the fully open configuration, they are under tension — applying the preload to hold the mechanism in the open position and keep the fabric web taut. In between these two configurations, the wires experience compression loads large enough to cause them to buckle but not enough to cause them to yield. This allows them to act as compressive springs in this intermediate region. The result, then, is a bi-stable mechanism that stays fully open or fully closed, but is unstable in intermediate states. This is great design, and I believe not something every umbrella does! The stability of the 2 functionally relevant positions means that the latches and ball detents used to keep the umbrella open or closed actually experience very little load, allowing lighter and more easily actuated components to be used.

Variable Spring Rate

Another benefit of exploiting buckling is that you can get the spring wires to act as springs with different stiffnesses in tension vs. compression. When the umbrella is open, the wires are under axial tension with very high stiffness — great for standing up against wind loads and keeping the umbrella open. Conversely, when the mechanism is neither fully open nor fully closed, you want a spring that is strong enough to nudge it towards a stable conformation, but not one that would poke a user’s eye out. This is achieved by allowing the wires to enter the buckled state, which places them under pin-ended bending instead of axial compression — significantly reducing stiffness.  This is an excellent example of the use of self-help in mechanical design!

Buckling Direction

We have seen how buckling can be used to great effect, but it is fundamentally a phenomenon drive by instability. This makes the math a bit more complicated (i suspect this is why it isn’t classically popular in “school” engineering design) and means that it is not straightforward to predict the buckled shape of structural members. In an umbrella, this poses a number of risks, including the creation of unpredictable pinch points and inadvertent puncturing of the fabric web by a wire buckling in the wrong direction. The way the designers of this umbrella have dealt with this is by entrapping the spring wires within the adjacent channel at their midpoints using a tab. This biases the members and forces them to buckle in a predictable direction. Again, a nice touch. A minor drawback to this is that it sets up a sliding contact between the aluminum channel and the hardened steel wire in the middle of the umbrella-opening stroke, which is starting to create squeaking noises as repeated use starts to wear through the phosphate coating on the wires. On the bright side, that squeak was what prompted me to grease the contact points and, in the process, geek out about this mechanism!

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