Abstract The bench press exercise on a Smith machine, frequently used in training programs, can be analyzed as a redundantly actuated biomechanical system. In this exercise, a simplified model having one degree of freedom, actuated at the shoulder and the elbow, provides a meaningful representation of its dynamics. Due to the actuation redundancy, many different combinations of actuations that lead to the same motion can be found. The present optimization framework for the bench press exercise is intended at understanding the appropriate performance of this exercise when it is used to gain endurance or to perform the exercise in the safest manner, that is, avoiding overloads. The dynamic simulation is solved by parameter optimization and direct collocation. The kinematics of the bench press exercise performed by a trained subject and recorded with an electro-goniometer is used as a reference motion for the optimization. The results show that it is possible to mathematically obtain better realizations of the exercise, what suggests the potential of this methodology in the design of training programs in sports or rehabilitation exercises.

中文翻译：

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通过参数优化在 Smith 机器上进行卧推练习的轨迹和扭矩设计

摘要 在训练计划中经常使用的史密斯机器上的卧推练习可以被分析为一个冗余驱动的生物力学系统。在本练习中，在肩部和肘部处驱动的具有一个自由度的简化模型为其动力学提供了有意义的表示。由于致动冗余，可以找到导致相同运动的许多不同的致动组合。当前的卧推练习优化框架旨在了解当使用该练习获得耐力或以最安全的方式（即避免超负荷）进行练习时，该练习的适当表现。动态仿真通过参数优化和直接搭配求解。由受过训练的受试者执行并用电子测角仪记录的卧推运动的运动学被用作优化的参考运动。结果表明，可以在数学上更好地实现锻炼，这表明这种方法在设计运动或康复锻炼的训练计划方面具有潜力。