基于四元数的肌肉骨骼模型中肌肉作用力效应的计算
Calculation of a force effect from muscle action to a quaternion-based musculoskeletal model
AI总结：
针对生物力学中欧拉角描述旋转存在万向节锁的问题，提出基于四元数的肌肉作用数学框架，可估算肌肉力矩并实现肌力臂转换，适用于肩关节等复杂大活动度肌肉骨骼的动态建模。
摘要：
生物力学分析中的欧拉角表示法可直观描述关节旋转，但因存在名为万向节锁的奇异性问题，其应用可能受到限制。四元数为描述旋转提供了另一种方法，但由于其复杂性且本身不够直观，尤其是在由肌肉驱动的动态模型中，在生物力学领域大多未被采用。本研究提出了一个数学框架，用于在基于四元数的动态肌肉骨骼模拟中描述肌肉作用。该方法可估算基于四元数的肌肉骨骼模型中的肌肉力矩，并在由肌肉单元驱动的三维双摆系统上展示了其应用。此外，本文还提出了将基于欧拉角的肌肉路径得到的肌力臂转换为四元数描述的方法。该方法适用于具有复杂运动学和大运动范围的肌肉骨骼模型（如肩关节）的动态建模。
英文摘要：
Euler angle representation in biomechanical analysis allows straightforward description of joints rotations. However, application of Euler angles could be limited due to singularity called gimbal lock. Quaternions offer an alternative way to describe rotations but they have been mostly avoided in biomechanics as they are complex and not inherently intuitive, specifically in dynamic models actuated by muscles. This study introduces a mathematical framework for describing muscle actions in dynamic quaternion-based musculoskeletal simulations. The proposed method estimates muscle torques in quaternion-based musculoskeletal model. Its application is shown on three-dimensional double-pendulum system actuated by muscle elements. Furthermore, transformation of muscle moment arms obtained from muscle paths based on Euler angles into quaternions description is presented. The proposed method is advantageous for dynamic modeling of musculoskeletal models with complex kinematics and large range of motion like the shoulder joint.
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