数值求解人体上肢两刚体系统

目的 简化人体上肢结构，建立两刚体系统动力学模型，并对其进行数值求解。方法 以卡尔登角为广义坐标，运用多刚体动力学理论，建立上肢的动力学方程；运用MATHEMATICA计算软件对方程进行正、反数值求解并进行了比较。结果 得到了上肢的两刚体动力学方程和数值解，对比计算结果表明，将已知运动带入方程求得的主动力作为已知力反求得的卡尔登角与已知运动的卡尔登角基本一致，而且在反解时会出现奇点。结论 运用MATHEMATICA计算软件求解复杂的上肢两刚体系统方程，相当方便，为免奇点出现，应在适当范围内进行求解，在误差允许的范围内，求得的解是可以接受的。

Numeric Evaluation of a Two Rigid-Body System in Human Upper Extremity

Objective To simplify the structures of human upper extremity into a two rigid-body system by establishing a dynamic model based on a numerical equation approach. Methods Using Carerden angle as the generalized coordinates and applying the multi-rigid-body dynamic theory to establish dynamic equation; Using the MATHEMATICA calculation software to solve the equation numerically in the active and the converse solution, respectively and results were subsequently compared. Results The dynamic equation of the upper extremity with two rigid-body and numeric solution were obtained. The Carerden angle calculated by the known active force, which was calculated in the equation as the known motion, was accordance with that which was given when the motion was known. At one time the peak point appeared in the converse solution. Conclusion The MATHEMATICA software was a convenient approach, which was able to resolve the complex two rigid-body system equations in the upper extremity. In order to avoid the peak point, the evaluation should be conducted within a defined range with confined error range so that the solution obtained was acceptable.