cs.ROSep 21, 2026

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

Authors: Jan C. L. Lau, Christian Mele, Jonathan Feng-Shun Lin, Katja Mombaur

Organizations: BioRobotics Lab, Optimization and Biomechanics for Human-Centred Robotics (HCR), Institute for Anthropomatics and Robotics (IAR), Karlsruhe Institute of Technology, 76131 Karlsruhe, Germany · Canada Excellence Research Chair in Human-Centred Robotics and Machine Intelligence, Systems Design & Mechanical and Mechatronics Engineering, University of Waterloo, Waterloo, N2L3G1, Ontario, Canada

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Abstract

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.

Figures & tables

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.
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.
Figure 3 : Top : Kick leg AMz w.r.t. COM in stable kicks of all sessions. Bottom : Kick leg AMz w.r.t. COM in unstable kicks of all sessions. Values are normalized to body mass and height squared. 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.
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.
Figure 5 : Top : Total AM magnitude w.r.t. COM in stable kicks of all sessions. Bottom : Total AM magnitude w.r.t. COM in unstable kicks of all sessions. 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.
Figure 6 : Inclination angle, inclination velocity, and COM path with total AM vector in example stable and unstable kicks.
Figure 7 : Top : Kick leg AMA in stable kicks of all sessions. Middle : Kick leg AMA in unstable kicks of all sessions. Mean and standard deviation are represented by solid line and shaded region respectively. Dotted trajectory means there is only one kick in the session. Bottom : An example from a stable kick illustrating the total AM magnitude (solid line) and breakdown of body part AMAs (shaded regions). The darker vertical line represents the Strike instance.
Figure 8 : Top : Kick leg AMO in stable kicks of all sessions. Bottom : Kick leg AMO in unstable. kicks of all sessions. Values are normalized to body mass and height squared. 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.

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