Angular momentum analysis on Karate roundhouse kicks: a longitudinal case study

Jan C. L. Lau, Christian Mele, Jonathan Feng-Shun Lin, Katja Mombaur · N/A · 2026

Summary

Abstract Summary

Human gait in reality extends beyond straight-line walking, with some situations even requiring drastic back-and-forth rotations. A smooth and stable execution may seem intuitive, but the underlying mechanics remains unknown. The Karate roundhouse kick may be an extreme case of exhibiting dynamic back-and-forth rotations, but investigating the angular momentum (AM) management can potentially inform stability analysis in dynamic human motions and smoother gait in robots and exoskeletons. This paper introduces two new AM-based measures and analyzes AM-related variables to study the target-less retractable back-leg Karate roundhouse kick. The purpose is to understand the underlying AM management, analyze the differences between stable and unstable kicks, and investigate how these variables and measures change over time with improvement. A one-year longitudinal study was conducted with the first author as a Karate student, and a Karate instructor was also recruited for one session as an expert, whose data is used for comparison. Results show that unstable kicks have higher peak total AM before Strike and smaller braking peak after Strike. The proposed AM-based measures are able to identify the cause of some unstable kicks, though no clear distinction could be made between stable and unstable kicks since kicks can be unstable for different reasons. Nonetheless, the proposed measures can be applied as performance measures to analyze other types of dynamic motions. To incorporate them as stability criteria, however, it is recommended to also consider their coordination with time, kinematics, and center of pressure.

Key Points

Human gait in reality extends beyond straight-line walking, with some situations even requiring drastic back-and-forth rotations.
A smooth and stable execution may seem intuitive, but the underlying mechanics remains unknown
The Karate roundhouse kick may be an extreme case of exhibiting dynamic back-and-forth rotations, but investigating the angular momentum (AM) management can potentially inform stability analysis in dynamic human motions and smoother gait in robots and exoskeletons.
This paper introduces two new AM-based measures and analyzes AM-related variables to study the target-less retractable back-leg Karate roundhouse kick.
The purpose is to understand the underlying AM management, analyze the differences between stable and unstable kicks, and investigate how these variables and measures change over time with improvement.

Methods

The first author (female, age 25, $1.68m$, $55.44kg\pm 1.86$) participated as a Karate student and trained 3-4.5 hours per week. The second author (male, age 25, $1.83m$, $87.6kg$), who is also a black belt Karate instructor with 12 years of training, participated as an expert. Both practice Goju-Ryu Karate.

Eight sessions were collected with the student for one year, with each collection showing belt development over this time.

Methods — Angular momentum analysis on Karate roundhouse kicks: a longitudinal case study — Figure 1 : Sequential illustration of the Karate right back-leg roundhouse kick, with indication of start and end instances of all phases. This figure demonstrates the setup with force plates but without motion capture markers. The darker red line represents the Strike instance. Informed consent was obtained to publish the images above in an online open access publication.

Results

The figures presented have time scaled for each phase via 1D interpolation. The average values presented are computed based on the true non-interpolated data. The Cartesian coordinates are defined based on the ready-pose assumed during Preparation (see Fig. 1 , with X pointing to the right of the person, Y pointing forward, and Z pointing up. As mentioned, all AM variables presented are w.r.t. COM.

Except for the total AM inclination angle and angular velocity, values are normalized to body mass and height squared.

Results — Angular momentum analysis on Karate roundhouse kicks: a longitudinal case study — Figure 2 : Top : Summary of stable, marginally stable, and unstable kicks across all student sessions and expert’s single session. Middle : Breakdown of instability occurrence in unstable kicks. Bottom : Mean (star) and standard deviation of all kick durations in all sessions.

Author contributions statement

J.C.L.L., C.M., and J.F.-S.L. conceived and conducted the experiment. J.C.L.L. and K.M. developed the proposed AM measures and analyzed the results. C.M. provided Karate expertise. J.C.L.L. curated the data and wrote the original draft. K.M. acquired funding, provided supervision, reviewed and curated the manuscript. All authors reviewed the manuscript.

Additional information

Competing interests The authors declare no competing interests. Supplementary Information The online version contains supplementary material available at (link from Scientific Reports). We are continuing to improve HTML versions of papers, and your feedback helps enhance accessibility and mobile support.

To report errors in the HTML that will help us improve conversion and rendering, choose any of the methods listed below: ) button, located in the page header. Tip: You can select the relevant text first, to include it in your report.

Additional information — Angular momentum analysis on Karate roundhouse kicks: a longitudinal case study — Figure 4 : Top : AMRCz w.r.t. COM in stable kicks of all sessions. Bottom : AMRCz w.r.t. COM in unstable kicks of all sessions. Values are normalized to body mass and height squared. Positive means counterclockwise rotation, and negative means clockwise rotation. Mean and standard deviation are represented by solid line and shaded region respectively. Dotted trajectory means there is only one kick in the session. The darker vertical line represents the Strike instance.

Sources and Demonstrations

Figures are reproduced from Lau et al. See the full paper for experimental details and the project page, when the paper links one, for demonstrations and videos.