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Legs = Springs?

Writer: Bobby Zhu ‘26

Editor: Jasmine Shum ‘24


Source: Amazon.com


When thinking about our legs, does the word “spring” ever come to mind? You may be familiar with the common phrase, “She has a spring to her step,” or when basketball commentators say that an athlete has “bunnies” after flying in for a poster dunk. Whatever the case, these sayings are somewhat correct in that the leg, while not a spring itself, has spring-like properties, notably in the tendons[1].


Tendons are the connective tissue that joins the muscle to the bone in any organism. They specialize in moving the bone along when the muscle contracts, allowing the organism to move in the direction of the muscle[2]. However, another property of the tendon is its ability to store energy as potential energy, which can be released at a later time to increase the amount of force produced[1]. With this ability, tendons enable us to run and jump, movements that would otherwise be much more difficult on the muscles without the presence of tendons to store the force they generate. Furthermore, the next time a muscle contracts to generate force, the energy can be released from the tendon, which results in a maximum amount of force that far exceeds the capabilities of the muscle when generating force by itself (and that's why Michael Jordan could fly across the air and make dunks from the free throw line). All of this is to say that tendons not only help an organism move by acting as attachments from the muscle to the skeleton but also act as springs that can store energy to be used at a later time.


As a result of the spring-like properties of tendons, the legs are considered to be part of a spring-mass model where they follow a resonant frequency of around 2.2 Hz3. This is also known as the preferred hopping frequency. This model represents the leg as a coiled, massless spring with the weight of the person being held up by this spring[4]. While this model may seem intuitive and very likely due to the spring-like properties of the tendons, there are still many factors to consider, including the fact that the torque applied differs between specific joints, like the hip, knee, and ankle. This is due to changes in the distance and angle of the force applied when moving. In addition, our legs have mass which may cause a skew away from the spring-mass system. However, researchers like CT Farley, a retired University of Colorado professor, have done studies where they show that the people who jump higher still maintain a resemblance to the spring-mass model,[3] which encourages the idea that the leg can be represented by the spring-mass model, even if the leg deviates from its supposed normal use. As such, from this study and other similar ones, the spring-mass model still stands strong, which has allowed many researchers to experiment with the idea of leg stiffness. 


Leg stiffness stems from the representation of legs as springs according to the simple spring-mass model. From this theory, we can measure how our legs change due to an increase in stride frequency when we run. Based on another paper by Farley, if the subjects increased their stride frequency but maintained the same running speed during a run, meaning that they take shorter but faster steps, then their legs would become stiffer[5]. One reason for this is that when subjects take shorter but faster steps, they have less contact time with the ground, which causes them to increase their legs’ stiffness so that they can continue at the same quick frequency[5]. To visualize this, imagine a pogo stick that has a stiff spring and a pogo stick that has a compliant spring. It’s harder to compress a stiffer pogo stick than a compliant one meaning that it would take a longer time for the compliant spring to come back up from being compressed. As a result, a stiffer spring would have less time touching the ground as it can’t be compressed all the way down. Our legs act in the same manner and when given the condition that their ground contact time is short due to a higher frequency, they will increase their stiffness as a response, as shown in the study done by Farley[5]


Therefore, our legs can be considered biological springs with the capability to increase the amount of force production and change given varying conditions. So the next time someone tells you that you have a “springy” gait, tell them that they do as well. 


Works Cited

1. E; RT. Flexible mechanisms: The diverse roles of Biological Springs in vertebrate movement [Internet]. U.S. National Library of Medicine. Available from: https://pubmed.ncbi.nlm.nih.gov/21228194/


2. Bordoni B, Black AC, Varacallo M [Internet]. Available from: https://www.ncbi.nlm.nih.gov/books/NBK513237/ 


3. CR; FCRJ. Hopping frequency in humans: A test of how springs set stride frequency in Bouncing Gaits [Internet]. U.S. National Library of Medicine. Available from: https://pubmed.ncbi.nlm.nih.gov/1778902/ 


4. R; B. The spring-mass model for running and hopping [Internet]. U.S. National Library of Medicine. Available from: https://pubmed.ncbi.nlm.nih.gov/2625422/ 


5. O; FC. Leg stiffness and stride frequency in human running [Internet]. U.S. National Library of Medicine. Available from: https://pubmed.ncbi.nlm.nih.gov/8849811/ 



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