How Accurate Is Symmetry?

In previous articles, we spoke about the undeniable use and help the notion of symmetry brings to a mechanical design. It is a powerful tool, and everyone has always used it intrinsically, if not explicitly.

The need for radial, spherical or even bilateral symmetry arose with the advent of mechanisation, due to the need for ease of manufacturing and straightforward geometry.


Do we over-rely on symmetry?

Everyday symmetry can be observed in nature on a large scale, which is in many ways where the idea of using symmetry in mechanical design came from. If our environment contributes to the shaping of our ideas and concepts, there is no denying as to how much symmetry is depicted around us. Symmetry can be visible on a big scale but it is by using a smaller scale you notice that symmetry is at best a blur at the horizon. The body is not symmetrical, not only because you don’t have two pancreas or livers, but because even symmetrical organs – kidneys, lungs, feet, breasts, etc – are asymmetrical and you can observe it with the naked eye. The face is an area we often assume to be symmetrical but try reflecting half of you face onto a mirror and you will be surprised – our faces are far from symmetrical!

Challenging assumptions on symmetry

The gravity centre of your body is not, as we often assume, conveniently located at the centre of the line you ideally picture when splitting yourself in half. In fact, your centre of gravity changes position depending on weight fluctuation, adopted motion or position, sickness, etc. In the same fashion, plants and animals might seem symmetrical but they’re not. You can’t fold a leaf and find it symmetrical on its median line, and you don’t even have to use a very small scale for such an observation: the naked eye will easily note the phenomena. Is this our brain playing games with our eyes? Do we see what we want to see in its purest form?

Extensive examples could be provided but it all leads to a reasonable conclusion: nature is not symmetrical. It might use a very general one to help with balance but it is not an inherent feature of a working system.

Real-life symmetry

I still have a clear experience in my head as to the concept of symmetry in everyday life:-

While I could see how German automotive machinery can be an example of robustness through the use of symmetry, I noted that Japanese automotive machinery is even more symmetrical (to an obsessive scale). However, still Japanese automotive machinery couldn’t outreach the performances of the famous German brand I was working for.

This difference was clear despite the fact that CAD models weren’t too dissimilar when it came to the philosophy of design. The features studied were solely the mobile ones and the methodologies of CAD and FEA, simulations and calculations were similar if not the same. This was mainly due to the fact that while German designers took symmetry into account, they didn’t completely embrace the gestaltism to the extent of having one referential for a CAD vehicle that could neatly cut it in half. Rather, they had several referentials for different parts and worked on the overall balance of the vehicle, seeking stability of the system over easiness or symmetry. In summary, they were creating products which focused on what they were supposed to do as opposed to simply looking the part.

As I mentioned above, symmetry is encouraged for many reasons but the core of this ideal is easiness. It’s easier to work with symmetry, to modify symmetry and it’s even easier to appeal to the public with symmetrical features. However, does symmetry give us the perfect results which we all strive for?

Perfect symmetry can have weaknesses

Nature is a very powerful force which seeks to save energy and create as little waste as possible. Therefore, if there is an easier way to achieve a certain process you can bet your bottom dollar that nature will surely find it and follow it. However, nature doesn’t fall into two traps:

  • Making symmetry a purpose if not a requirement
  • Applying the concept or extrapolating it on the other aspects of life

When I started studying about the several manifestations of mechanics in the physical realm, such as thermodynamics or electricity… I had to unlearn the concept of “you harvest what you sow”. That is the symmetry applied to the moral code of work and re-educate myself about its more subtle less symmetrical form.

No, if you send X0K V to a house, you do not get X0K. Thermal loss, static electricity, cables materials, etc, are to be taken into account. You end up with a loss ranging from 8% – 30%. Maybe the electricity will not reach you even though you paid your bill because of some random event?

No, if you achieve an optimal FE Analysis on a part that says your system can stand 300MPa, you don’t get a system that withstands 300MPa. You end up at best with one that can bear 240MPa or so, if not less considering the defects of materials and manufacturing. The load cases that it will experience and all the random events – impact, vibrations, other forces applied from someplace else, moisture and heat…that will probably befall upon it.

Symmetry is not always the perfect answer

In short, you can’t extrapolate such a concept onto every possible aspect of science and art. You have to be extremely mindful about how you apply this and perhaps use symmetry as a possible answer but not as the favourite methodology to go with.

Use symmetry but use it mindfully…

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