Balance Beam Recovery: Center of Mass / Base of Support Analysis
Despite the dry title, this COM/BOS analysis of two Olympic gymnasts by Imgurian Jon Matthis is wicked cool. I’m posting here with his permission (and a few edits).
So yeah, I did another center of mass analysis thing, this time of two awesome examples of gymnasts just barely not falling off of a balance beam! Just in time for the Olympics! Yay!
The first of these gifs shows Nastia Liukin and the second (the one with the Jedi) is Mykayla Skinner. So, there are a couple of things to look at here.
BOS and COM, Olympic Style
…The limits of the balance beam (dotted lines) show the extent of the base of support (BOS) available to these gymnasts. That means that the moment their center of mass (COM) travels beyond the dotted line is the moment they have begun to fall off the bar. Once their COM passes over the dotted line, the only way that that can bring it back inside is by either gripping the bar to actively *pull* their COM back into balance, or by doing some kinda crazy torquing maneuver to try to use friction against the bar to impart some lateral force onto their COM to bring it back over the bar. Both these things occur, but we’ll get to that in a second.
First, just take a moment to appreciate how amazing the first halves of both these gifs are. Watching these kinds of activities and knowing a bit about physics, you know that things *have* to be this way. The COMs of the gymnasts *must* travel in a near perfectly straight line completely within the minuscule bounds of the balance beam’s extent. And yet, seeing it play out in this gif still blew my mind. It’s just so amazing. Humans are so cool. Perceptuomotor control, man. [For real.]
But then they screw up! So what went wrong?
In the first gif, [Nastia] seems to come down unevenly after the last flip, so she rebounds from the bar at a slight angle which takes her COM out of the limits of the BOS for just a fraction of second. Her saving grace was that she seemed to realize that something was wrong right at the moment of impact, which allowed her to use the entire rebound period to execute her recovery.
Notice that when she comes down, she *grips* the bar with her hands, which gives her the control authority to allow her COM to leave the BOS on the other side of the bar. Because she can now exert a significant pulling force on the bar, she has no problem pulling her COM back in stability.
In the second gif, the gymnast also comes down a bit wrong, but her COM never really seems to cross out of the BOS, even though it gets *real* close. With her COM so close to the limits of the BOS, is it is very difficult for her to bring her COM back above the stable region at the center of the beam. All the forces from her foot are pushing her COM *away* from the center of the beam, so all that wild arm swinging is just to try to stop the COM from crossing that dotted line into oblivion.
Eventually, she’s able to duck her upper body down and pull her COM back from the edge and into a region where her feet on the bar can keep it within the BOS. It’s possible the friendly Jedi helped too, but that analysis is a bit beyond my pay grade.
So yeah! The judges may’ve been all [>:(] about it, but I, for one, am glad that these awesome gymnasts almost fell off these bars. Good for them!
Methods – I pulled the original gif into a cool piece of software called Tracker, which let me do some semi-automated tracking of main body segments. I then pulled the data from that software into Matlab and calculated the segmental centers of mass (red asterisks). The full body COM is calculate on each frame by taking the average poision of each segmental COM, weighted by that sement’s proportion of the total body mass.
The [hardest part] was that these athletes were moving REALLY fast against a textured background, so most of the tracking was by hand. Also, it was hardest to track their body parts during their flips, which is why their COMs bob around a bit when they are in the air. In reality, once they are in flight, the COM travels in a perfectly parabolic cannonball trajectory, not matter how much the other parts of their bodies waggle around. I ran a Butterworth filter over the movement data to clean it up a bit, but it’s not perfect.
Thank you, Jon, for your great analysis!