クアテニオンベースの筋骨格モデルによる力効果の計算
Ondrej Zoufaly1, Edward K Chadwick2, Dimitra Blana3
1Czech Technical University in Prague, Department of Mechanics, Biomechanics and Mechatronic, Technicka 1902/4, Prague 6, 16000, Czech Republic.
Journal of biomechanics
|August 22, 2025
まとめ
この研究は,オイラー角に共通するギンバルロック問題を克服して,筋肉で動作する筋骨組みシミュレーションのためのクォーターニオンベースのフレームワークを提示します. 複雑な関節の動きの ダイナミックモデリングを より正確に可能にします
科学分野:
- バイオメカニクス
- 筋骨格モデリング
- 計算ダイナミクス
背景:
- オイラー角とカルダン角は,バイオメカニクスにおける関節の回転を記述する際に一般的であるが,ギンバル・ロック・シンギュラリティに苦しんでいる.
- クォーターニオンはギンバルロックを避けますが,直感性が低く,複雑な動的筋骨格モデルでは広く採用されていません.
- 既存のダイナミックモデルは 筋肉の動作を直感的に表現するのに苦労します 特に複雑な運動力学を持つモデルでは
研究 の 目的:
- クアターニオンベースの動的筋骨格シミュレーションのための数学的枠組みを導入する.
- 筋肉のトルクをクォーターニオン枠内で推定する方法を開発する.
- 筋肉のモメントアームを 伝統的な角度システムからクアテルニオンに 変換する.
主な方法:
- クアターニオンベースの筋肉の動作の記述のための新しい数学的枠組みを開発した.
- クアテニオンベースの筋骨格モデルを用いて推計された筋肉のトルク.
- 3Dのダブルペンデュラムシステムで筋肉の要素と変形モメントアームを演示した.
主要な成果:
- 動的筋骨格シミュレーションのクォーターニオンベースのアプローチを成功裏に実装しました.
- この方法は筋肉のトルクを効果的に推定し,ギンバルのロック問題を回避します.
- オイラー/カルダン角度からクアテルニオンへの筋肉モメントアームの変換を証明した.
結論:
- 提案されている四次元の方法は,動的筋骨格モデル化のための有利な代替案を提供します.
- このアプローチは,肩のような複雑な運動学と大きな関節範囲を持つモデルにとって特に有益です.
- このフレームワークは,バイオメカニクスにおけるダイナミックシミュレーションの正確性と適用性を高めます.
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