The physics of transporting a cup of coffee without spilling it

Despite what that long-forgotten stain on your white shirt might lead you to believe, humans are pretty good at walking around with a cup of coffee and avoiding spills, even if our success rate isn’t quite 100% . Each time you manage to move your cup of coffee from one point to another without spilling any, you intuitively accomplish a little-understood feat of physics: manipulating a complex object such as a liquid.

That’s according to a group of researchers at Arizona State University (ASU) who modeled the phenomenon of coffee transport in an effort to imbue robots with the same smoothness. In a world of increasing automation, machines are expected to perform more dexterous movements, says Brent Wallace, Ph.D. student at ASU’s School of Electrical, Computer, and Power Engineering who participated in the work. “But even for simple tasks, like carrying a cup of water or a cup of coffee, the robot struggles. Every day you and I make a cup of coffee, and 99 days out of 100 we don’t spill it,” Wallace says. “So how can we benefit from solving these kinds of problems? Well, let’s study how humans behave in these situations.

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Building on previous work at Northeastern University, which revealed that humans have two main approaches to manipulating a complex object like a fluid, the ASU team simulated these responses, focusing on the phase of transition between the two to understand why humans exhibit a binary response—and to see how robots might learn to do the same in the future. The results were published in the journal Applied physical examination end of 2021.

Approach #1 is called the low-frequency strategy and involves human participants exerting a constant, slow back-and-forth force on the cup of coffee. So if you swing your mug to the left, the java inside follows suit, like a pendulum. This is called phase synchronization. Alternatively, approach #2 is a high-frequency strategy in which people exert a jerky, rapidly changing force on the cup. Following this approach, if you swing your cup to the left, the java inside moves to the right side of the cup. This is called antiphase synchronization.

Since both strategies worked, albeit at opposite ends of the spectrum, Wallace surmised that some Northeastern study participants moved back and forth between the two approaches, moving the cup enthusiastically in some situations, and more gently at other times. This led him to ask: where does the transition between in-phase and out-of-phase synchronization occur?

To test his hypothesis, Wallace set up a simulated mechanical experiment so he could use an unlimited number of test subjects. He chose to set up a non-linear model of a pendulum attached to a moving cart. The trolley replaces the cup and the pendulum represents the lapping coffee. A nonlinear system takes into account all the chaotic behaviors that may exist in our cup of coffee, Wallace explains. Most real world systems are nonlinear because they are hard to define and do not exist in a vacuum. When you’re driving a car, for example, it will go 50 mph if you press the accelerator pedal, but it won’t go 5,000 mph if you keep pressing it. A linear system, on the other hand, is much more predictable: a spring system or a clock will always move in the same regular way. Thinking mathematically, this holds true. The Linear Equation Graph there = X is always a straight line; Meanwhile, the graph for there = X2 is a nonlinear equation that looks like a curve, representing various solutions, not just one.

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Wallace and his team found that the transition phase between each of the strategies was varied, but that in both cases, humans could switch between the approaches “abruptly and efficiently,” according to their paper. The transition phase, as expected, was the most chaotic, or unpredictable. But humans have moved away from this common ground, sticking closely to one approach or the other.

Researchers believe they can implement these controls in robots to make their movements more predictable and reliable, adaptively manipulating complex objects in ever-changing environments. Although it is currently possible to program machines to operate on a binary basis, like humans vigorously slapping their cups of coffee or walking gently with them, robots are still not refined enough to handle the switching between two modes. On a production line, for example, hanging pendulum systems are quite common, Wallace says. By controlling the internal degrees of freedom in a manufacturing system like this, a robotic arm can more reliably weld the right part without overshooting and merging another section.

“If you have an idea of ​​what you want the prosthesis to do, like making the cup of coffee, you can incorporate those kind of natural intuitions that the human has.”

This paradigm could also lead to better prostheses, according to Ying-Cheng Lai, a professor at ASU’s School of Electrical, Computer and Energy Engineering who participated in the work. Let’s say you have a prosthesis and want to make a cup of coffee. You have to send a signal from your brain to the prosthesis, but matching the two is difficult. “If you have an idea of ​​what you want the prosthesis to do, like make the cup of coffee, you can integrate these kinds of natural intuitions that the human has into a regular script to filter the reference commands coming from the brain. “, he explains.

To make all of this a reality, further work is still needed to better quantify the subtle changes between the approaches. Wallace says the team will try to study systems with more degrees of freedom, like a pendulum with another pendulum suspended. If all works out, we might one day see robots moving around with careful intent, just like us.


🍳 More Kitchen Physics: Here’s Why Food Sticks to Your Frying Pan

You can thank thermocapillary convection for making your food stick to your favorite frying pan. That’s right, physics can explain why sometimes your meats and vegetables get stuck while cooking. The phenomenon causes hot oil to bead, rupture, and spread to the outer edges of a pan, leaving the dreaded dry spot in the middle.

Research by Alexander Fedorchenko of the Czech Academy of Sciences found that this type of convection is the result of uneven heating. Once the cooking oil reaches a thin critical point—which in this study consistently occurred in the middle of the pan—it breaks down due to loss of surface tension. To alleviate the problem, try using a little more oil to make it harder to reach that critical breaking point.

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