深蹲动作下三连杆模型的对比分析

目的 探讨三连杆模型用于深蹲动作互动动力学分析的合理性，明确三连杆模型与Visual 3D计算关节力矩的差异来源。方法 选取8名受试者，通过Vicon获取深蹲动作运动学数据，采用拉格朗日第二类方程建立三连杆动力学方程，基于Mathematica编程计算获取关节力矩，与Visual 3D下肢链节段模型计算结果进行对比分析，并采用复相关系数（coefficient of multiple correlation, CMC）评价两者的相似程度。结果 8名受试者髋、膝关节CMC均大于0.85，踝关节CMC在0.50～0.85之间，三连杆动力学方程和Visual 3D计算的关节力矩在髋、膝关节处高度相似，在踝关节处仅呈现中度相似性。结论 三连杆模型可用于深蹲动作的关节力矩分析以及进一步的环节互动动力学分析，但应当考虑由地面反作用力引起的互动力矩（外力矩）对踝关节力矩的影响。

Comparative Analysis of Three-Link Model in Deep Squatting

Objective To discuss rationality of the three-link model used in analysis on interactive dynamics of deep squatting, and clarify the source of differences in calculation of joint torque by three-link model and Visual 3D. Methods Eight subjects were selected to obtain kinematic data of the squat motion through Vicon. The second Lagrangian equation was used to establish the three-link dynamic equation. The joint torque was calculated based on the Mathematica programming. The results were compared with the calculation results of lower limb chain segment model by Visual 3D, and the similarity between the two results was evaluated by the coefficient of complex correlation (CMC). Results The CMC of hip joint and knee joint from 8 subjects was larger than 0.85, and the CMC of ankle joint was between 0.50-0.85. The joint torque calculated by three-link dynamic equation and Visual 3D was highly similar in hip joint and knee joint, and there was only a moderate similarity in ankle joint. Conclusions The three-link model can be used in further analysis on interactive dynamics of deep squatting, but the influence of interactive moment caused by ground reaction force (external moment) on ankle torque should be considered.