Does swing leg angular acceleration increase at foot strike?

[Ted Andresen]

Hello All,

I work with the spring-mass model (1). I use it to study how gait and power expenditure depend on running velocity.

I coupled the motion of the CM in the Lab-frame with a swing leg model (2). I find that there is a slight increase in the hip angle acceleration at foot strike. Unfortunately, I do not have access to experimental data, so I can’t confirm this finding.

Do researchers with motion capture systems observe a sudden increase in hip angle acceleration at foot strike (FS) similar to the one shown in the attached plot?

Sincerely,

Ted Andresen

(1) The Spring-Mass Model for Running and Hopping, R. Blickhan
(2) The SL model uses a 2-segment DA Winter leg in the moving CM-frame. It employs a Newton-Raphson algorithm to iterate an RK4 integration of the Euler equations until the FS conditions mirror the TO conditions.

[Ross Miller]

Re: Does swing leg angular acceleration increase at foot strike?

Hi Ted,

Here's a graph of some "normal" running data (means over 13 subjects, speed ~ 3.2 m/s). I don't have accelerations handy but the "slope of the slope" of the hip around the timing of ipsilateral heel-strike (~ 50% of the stride) doesn't look to me like it changes much, but it does appear to be increasing a bit (slope is getting higher between 40-60%).

Actually this was barefoot running so most of them weren't "heel" striking.

Ross

[Ted Andresen]

Re: Does swing leg angular acceleration increase at foot strike?

Hi Ross,

That is great data! By the way it is almost impossible to look at straight regions of angle or position data and see small changes in the acceleration. In fact the parent data for the acceleration curve I posted above looks smooth and does indicate the bumps in acceleration.

There is a trick, described below, for extracting the acceleration from the straight region of the mean Hip (deg) data that might work.

If you would consider sending me just the data columns for the darker mean curve and, maybe, one individual’s run in the Hip (deg) plot, I’d like to try to extract any acceleration from the straight region near FS.

If it comes together, I’ll post the findings here and layout the procedure, so others can use it. That would be a very interesting experiment.

Sincerely,

Ted

The trick involves fitting the straight-ish region with a least-squares high degree polynomial and taking the derivative of the poly twice to extract the acceleration.

As an experiment I corrupted my original angle data with Gaussian noise, so it looked like yours. I applied the procedure and came up with a bump in the acceleration curve. The resolution of the dip suffered a bit, but the trough-and-peak signature came through.

[Ross Miller]

Re: Does swing leg angular acceleration increase at foot strike?

Ted, I sent you a PM just now.

Ross

[Ted Andresen]

Re: Does swing leg angular acceleration increase at foot strike?

Hello Ross,

Thank you for sharing your data with me. This was a wonderful opportunity to revisit some useful analytical and graphical tools for visualizing the affect of acceleration on angular or linear displacement.

It’s easy to generate the angular acceleration from the angular displacement by building a difference table (1). Here the acceleration is in units of deg/%^2 (2)

Typically the acceleration shown in blue does not make much sense at first glance. Fortunately, it becomes more intuitive as in the lower plot, if it is added to the angular displacement curve (red) as if it is a positive error bar (black). Then it is possible to see when and in which direction the acceleration acts on the displacement.

During its stance phase the ipsilateral leg’s angular acceleration (blue) is pretty small. The acceleration becomes more significant during the stance phase (50% to 90% of gait cycle) of the contralateral leg. Before mid-stance (MS) the GRF’s combine to decelerate the CM and slow it down. This increases the forward angular acceleration of the swing leg creating the upward hump in the angular acceleration. After mid-stance the GRF’s accelerate the CM forward and decelerate or slow it down the leg’s swing. This creates the downward hump in the acceleration curve.

In summary: Yes, swing leg angular acceleration does increase at foot strike. Now, I feel more confident in the Swing Leg model.

Ted Andresen
St. Petersburg, FL

(1) There a good diagram to the table’s construction for n=5 halfway down the page at the link below. Of course the acceleration only requires n=2.

http://ecourses.vtu.ac.in/nptel/courses/Webcourse-contents/IIT-KANPUR/Numerical%20Analysis/numerical-analysis/Rathish-kumar/rathish-oct31/fratnode6.html

(2) Degrees/%GaitTime^2 can be converted to degrees/sec^2 by multiplying by 10,000/GaitTime^2 or to radians/sec^2 by multiplying Degrees/%GaitTime^2 by 175/GaitTime^2.