New Delhi: How conscious are you when you walk around holding a cup of hot coffee in hand — at home, in the office or on the road? You don’t usually spill it, do you? 


Balancing the hot cup of coffee while walking is just so natural for all of us. But there is a science behind it, and it can be explained with the help of the laws of physics.


A study by researchers from Arizona State University, recently published in the Physical Review Applied journal, says the physics associated with handling a cup of coffee can be applied to soft robotics.


How does a human interact with a cup of coffee?


A cup of hot coffee, held by a human while walking, is a complex object or a system with internal degrees of freedom (independent parameters defining its configuration). The hot coffee and the human holding the cup are able to interact with each other because of these internal degrees of freedom, states the study. 


Ying-Cheng Lai, a Professor at ASU and one of the authors, says it is a gifted ability of humans to be able to interact with complex objects, but there is no understanding of these concepts, according to a statement by ASU. He added that humans can't consciously analyse the influence of external factors such as noise or climate on these interactions. 


In order to simulate the process of humans holding a cup, the researchers used two models, a conceptual model and a mechanical model. In the conceptual model, they conducted a virtual experiment, where participants were asked to hold a bowl with a rolling ball inside it. 


The mechanical model was a non-linear dynamical model, where a pendulum was attached to a moving cart, and was subjected to external forces that were periodic in nature. The researchers observed how the humans handled the bowl with the ball in the first model, and studied the motions of the cart and the pendulum in the second model, in order to understand how humans interact with, and manipulate complex objects such as a coffee cup. 


The conceptual model


The researchers found that in the conceptual model, the participants consciously rotated the cup in rhythmic motion, and exhibited the ability to vary the force and frequency to ensure that the ball did not fall from the cup. 


The study found that two strategies are employed by humans to handle a complex object. One of the strategies is a low-frequency strategy, involving in-phase synchronisation, which means that the ball and the bowl were made to oscillate with the same frequency, and in the same direction, to keep the ball from falling. The other strategy was a high frequency one, involving anti-phase synchronisation, which means that the ball and bowl oscillated at the same high frequency, but in opposite directions.


 Both these strategies prevented the ball from coming out of the bowl, and in a similar manner, coffee is prevented from spilling while a human walks with a cup of coffee. The study found that this is how the rhythmic motion of the cup is maintained with the help of low-frequency and high-frequency strategies. 


The mechanical model


The researchers observed that humans can switch abruptly from one strategy to another, and studied this transition between in-phase and anti-phase synchronisation with the help of the mechanical model, involving the cart and the pendulum.


The external driving frequency, due to the externally applied force, varied, resulting in an abrupt transition, as explained in one regime. The researchers found that the transition occurred at the point where the external frequency applied on the moving cart, and the frequency of the system, which is the pendulum, came close to each other. This frequency is called the frequency of resonance, where an object tends to vibrate at a higher amplitude. This means that when the frequency of the hot coffee, and the frequency of the cup come close to each other, the human carrier can unconsciously switch from one synchronous state to another, and involuntarily balance the cup.


The researchers explain that beyond this regime, the transition occurred at the point where there was no synchronisation between the motions of the cart and the pendulum. This means the abrupt transition took place at the point where the frequencies of the cart and the pendulum were not the same. The study also states that there were two equilibrium states, or a condition of bistability — one was at the transition point, and the other was near this point on the low-frequency side. 


These findings indicate that humans can involuntarily switch between the low-frequency and high-frequency strategies, at the point where the frequencies of the cup and the coffee are not synchronised. 


How can these findings be applied to smart prosthetics and soft robotics?


Brent Wallace, the lead author of the study, says the modes of flexibility exhibited by the natural motion of human limbs should be incorporated into smart prosthetics also, in order to make them comfortable for the user, according to the ASU statement. 


Lai explains that robots, which will be used for handling objects in future, will require the coordination that humans exhibit effortlessly. 


The study mentions that when robots take short steps to walk, they can exhibit large variations in their walking frequency, while for longer steps, there should be careful selection of the frequency. The mechanism of handling a cup of coffee and other complex behaviours adopted by humans can be exploited for inventing smart robots that can adaptively handle objects in a changing environment, the study explains.


Lai says that humans can smoothly switch between phase and anti-phase strategies, without even realising it. He explains that the findings of the study can be applied in fields such as designing soft robotics, rehabilitation and brain-machine interface. 


"By mimicking the dynamically-favorable behaviors adopted by humans in handling complex objects, we will be able to automate processes previously thought to be impossible," Wallace is quoted as saying in the statement.