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Angular momentum analysis on Karate roundhouse kicks: a longitudinal case study
Jan C. L. Lau, Christian Mele, Jonathan Feng-Shun Lin, Katja Mombaur
TL;DR
The paper investigates how angular momentum is managed in dynamic back-and-forth motion, using target-less retractable Karate roundhouse kicks. It proposes AM measures and finds that unstable kicks often have higher pre-Strike total AM, while distinct instability causes limit threshold-based classification.
Problem
Angular-momentum management in dynamic back-and-forth rotations is not well understood, despite its relevance to human movement stability and robot and exoskeleton control.
Source: Introduction · pp. 1–2Method
The study analyzes AM-related variables and proposes AMA and AMO to compare stable and unstable target-less retractable back-leg roundhouse kicks across a student’s year of training and an expert session.
Source: Introduction · p. 2, Proposed Angular Momentum Measures and… · pp. 3–4Results
Unstable kicks showed higher peak total AM before Strike in 6 of 7 sessions with unstable kicks, while AMA and AMO indicated instability in only some kicks.
Source: Discussion · p. 13, Conclusion · p. 14Takeaways & Limitations
AMA and AMO can help describe kick-leg AM and indicate instability in some kicks, but dynamic-motion stability analysis should also consider time, kinematics, and center of pressure.
Source: Conclusion · p. 14, Discussion · p. 14Because kicks can be unstable for different reasons, AM-related variables alone do not clearly distinguish stable from unstable kicks; the analysis recommends combining them with time, kinematics, and potentially center of pressure.
Source: Discussion · p. 14
Abstract
from arXiv · showhide
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.
Introduction
Dynamic rotations matter for human stability and robot control, but angular-momentum management in back-and-forth motion remains underexplored. The paper studies a target-less retractable Karate roundhouse kick as a demanding example.
Introduction
- The paper analyzes angular momentum (AM) management in a dynamic kick to inform understanding of human movement and robot and exoskeleton control.Rotations during daily activities can challenge stability in older adults with decreased mobility, while healthy adults often execute them stably.Source: Introduction · pp. 1–2
- The target-less retractable back-leg roundhouse kick requires performers to stop their own rotation and retract, making it a demanding back-and-forth rotation task.The kick involves a chamber, body and support-foot turn, knee extension to strike, and retraction to the starting pose.Source: Introduction · p. 1
- Prior roundhouse-kick studies largely examined performance and kinematics, while the target-less variation had not been studied for AM or back-and-forth rotational stability.Earlier work examined Karate balance and stability using COM kinematics, limb angular motion, or COP measures.Source: Introduction · p. 2
- Research links AM to balance in walking, slackline performance, and humanoid-robot instability, motivating its examination in dynamic human motion.The cited slackline comparison associated lower normalized AM and COM acceleration with fewer recovery movements and better stability.Source: Introduction · p. 2
- The paper proposes AMA and AMO to compare stable and unstable kicks and examine training-related change in AM management.It hypothesizes that unstable kicks have higher total AM, and that stable kicks show bounded kick-leg AMO and positive kick-leg AMA leading up to Strike.Source: Introduction · p. 2
Methods
The study tracks a Karate student over one year and compares her kicks with one expert session. It combines motion capture and force-plate data with proposed AM measures and related variables.
Methods
- The protocol collected eight student sessions over one year and one expert session, with ten target-less right back-leg roundhouse kicks per session.The expert was a black belt instructor with 12 years of training; both participants practiced Goju-Ryu Karate.Source: Experiment Protocol · p. 2, Methods · p. 2
- Participants prioritized stability over kick height and speed, stopped the kick without a target, and retracted to the initial position.Full-power kicks were not required for safety; the study used 12 Vicon cameras, two force plates, and a 53-marker modified IOR set.Source: Experiment Protocol · p. 2
- An in-house pipeline derived joint kinematics and segmental and total angular momenta from motion-capture data, with kick phases identified using video, joint angles, and force-plate data.The pipeline used de Leva anthropometric values and Python tools; the first and last phases were visually identified.Source: Post-processing · p. 3
- Kicks were labeled stable, marginally stable, or unstable by expert visual assessment; unstable kicks required a jump or step for balance recovery.Stable kicks showed whole-body control and completed the planned motion.Source: Post-processing · p. 3
- AMA measures a body part’s AM in the direction of total AM, while AMO measures its orthogonal AM and influence on changing total-AM direction.The measures share AM units; a positive AMA indicates alignment with total AM, while a negative value indicates the opposite direction.Source: Proposed Angular Momentum Measures and… · pp. 3–4
- The analysis also examined vertical-axis total-AM rate of change and total AM in spherical coordinates; proposed measures aim to add physically interpretable information beyond percentages and PCA.AM rate of change describes net external torques, here from ground-reaction forces and moments; force-plate data were excluded from analysis because they were too noisy.Source: Proposed Angular Momentum Measures and… · p. 4
Results
Unstable kicks generally had larger total angular momentum peaks before Strike, while stable kicks usually showed stronger braking. Across the year, the student’s kicks became smoother and shorter on average, though angular-momentum patterns varied across measures and sessions.
Results
- Across 91 kicks, 50 were stable, 29 marginal, and 12 unstable; kicks became smoother from Month 4, and mean duration fell 14% over the year.The student’s mean duration declined from 3.03s±0.60 to 2.60s±0.16.Source: General Observations · p. 4, Figure 2 · p. 5
- Kick-leg AMz trajectories showed an inflection around Strike in every session; Month 12’s unstable kicks had greater trajectory variation than its stable kicks.The unstable trajectories included brief negative AM and a higher Extension plateau.Source: Kick Leg Angular Momentum about… · p. 4, Figure 3 · p. 6
- In the example unstable kick, the total-AM vector was more forward-tilted at Strike and the COM’s forward-backward range was about 6.4 cm longer.The wider Retraction path followed the student’s jump to the left in response to instability.Source: Total Angular Momentum Magnitude and… · p. 8, Figure 6 · p. 10
- The expert’s unstable kick-leg AMA global peak averaged 13.3% above his stable kicks, while one student Month 12 unstable kick reached −0.05s−1 during Chamber.The student’s stable kicks showed a distinct AMA peak at the end of Preparation.Source: Angular Momentum Aligned Component of… · p. 8, Figure 7 · p. 11
- Unstable kick-leg AMO peaks were 40.9% above stable kicks in Month 4 and 35.2% above them shortly before Strike in the expert’s session.The student’s stable AMO peak increased over the year, reaching 0.13s−1 in Month 12.Source: Angular Momentum Orthogonal Component… · p. 8, Figure 8 · p. 12
- Unstable kicks had larger pre-Strike total-AM peaks in all sessions except Month 12, while stable kicks had stronger braking in 5/7 sessions.The negative AMRCz peak near Strike represents braking before Retraction.Source: Rate of Change of Total Angular… · pp. 6–7, Figure 4 · p. 7, Total Angular Momentum Magnitude and… · p. 8
Discussion
The discussion finds that unstable kicks often carry more total angular momentum before Strike, while kick-leg angular-momentum patterns suggest several possible, session-dependent instability mechanisms. Improvement was not simply a matter of moving faster, and the authors caution that angular-momentum variables alone do not establish stability.
Discussion
- The first hypothesis was only partially supported: the student became smoother and more dynamic, while the expert remained stable with smaller kick-leg AM amplitudes.The discussion interprets early motion incoherence as consistent with beginners prioritizing technique over speed.Source: Discussion · p. 13
- Among sessions with unstable kicks, 6/7 followed the trend of exerting higher peak total AM before Strike; without a kicking pad, excess AM made stable retraction challenging.Source: Discussion · p. 13
- Kick-leg AMA and AMO suggested possible instability mechanisms, but the AMO threshold varied across sessions and kicking styles.Examples include excessive kick-leg AMA before Strike for the expert and a larger pre-Strike AMO in Month 4.Source: Discussion · p. 13
- The expert’s shorter kick duration shows that faster execution can preserve stability and technique, while the student’s increasing stable-kick count and lower variability indicate improved consistency.Unstable kicks lasted longer on average because of recovery time.Source: Discussion · p. 13
- In Month 12, the student’s kick-leg AMz trajectory resembled the expert’s, but AMA and AMO still showed a larger kick-leg influence on total AM.The trajectory shift may indicate that roundhouse-kick mastery is staged rather than gradual.Source: Discussion · p. 13
- The stable example used horizontal-axis AM during retraction, but total-AM direction measures were noise-sensitive near zero crossings and did not convey AM magnitude.The authors recommend combining AM variables with timing, kinematics, and potentially center-of-pressure data when developing a stability criterion.Source: Discussion · pp. 13–14
- Supporting-foot oscillations about zero indicate continual adjustment of how ground-reaction forces and moments act on the body.The discussion notes that excessive braking can also destabilize a kick when the person approaches a full halt.Source: Discussion · pp. 13–14
Conclusion
The conclusion reports greater pre-Strike total AM and less post-Strike braking in unstable kicks, while emphasizing that instability has multiple causes. The proposed measures may describe performance, but stability criteria should coordinate them with other motion variables.
Conclusion
- Unstable kicks generally had higher total AM magnitude before Strike and less braking moment after Strike, but could arise for different reasons.Kick-leg AMA and AMO indicated instability in only some kicks.Source: Conclusion · p. 14
- AMA and AMO show potential as performance measures because they describe 3D body-part AM behavior in relation to total AM.Source: Conclusion · p. 14
- For stability criteria, the authors recommend investigating coordination of these measures with time, kinematic, and kinetic variables.Source: Conclusion · p. 14
Additional information
The authors report no competing interests and note that supplementary information is available online.
Additional information
- The authors declare no competing interests.Source: Additional information · p. 16
- The online version contains supplementary material.Source: Additional information · p. 16
- Supplementary information is available through the online version at Scientific Reports.Source: Additional information · p. 16