Yoshihuku Y, Herzog W
Department of Natural Sciences, College of Engineering, Chubu University, Aichi, Japan.
J Sports Sci. 1996 Apr;14(2):139-57. doi: 10.1080/02640419608727696.
This study sought to find the optimal design parameters for a bicycle-rider system (crank length, pelvic inclination, seat height and rate of crank rotation) that maximise the power output from muscles of the human lower limb during cycling. The human lower limb was modelled as a planar system of five rigid bodies connected by four frictionless pin joints and driven by seven functional muscle groups. The muscles were assumed to behave according to an adapted form of Hill's (1938) equation, incorporating the muscle force-length relation. The force-length relation and the values of length that served as input into the relations of the various muscles were defined in the following two ways: (1) the force-length relation was parabolic, based on the experiment of Woittiez et al. (1984), and the length was defined as the whole muscle length; and (2) the force-length relation was expressed as a combination of lines, based on the cross-bridge theory, and the length was defined as muscle fibre length. In the second definition, the joint configurations at which four of the seven muscle groups reached optimal length (i.e. the length at which the muscle can exert maximal isometric force) were further given in two ways. The first way was consistent with a previous study from this laboratory (Yoshihuku and Herzog, 1990); the second way relied on unpublished experimental data. The dependence of the average power on the design parameters and definitions of the force-length relation and muscle length was examined. Maximal average power for one full crank rotation with a crank length of 0.17 m was found to be about 1300 W for definition 1 and 1000 W for definition 2. The average power was more sensitive to changes in design parameters in definition 2 than definition 1. The optimal rate of crank rotation with a crank length of 0.17 m was 18.4 rad s-1 (176 rev min-1) for definition 1 (this value is different from the result of the previous study due to revisions in input for two muscle groups), and 15.2 rad s-1 (145 rev min-1) and 14.6 rad s-1 (139 rev min-1) for definition 2.
本研究旨在找出自行车骑行者系统（曲柄长度、骨盆倾斜度、座椅高度和曲柄旋转速率）的最佳设计参数，以在骑行过程中使人类下肢肌肉的功率输出最大化。人类下肢被建模为一个平面系统，由五个刚体通过四个无摩擦销关节连接，并由七个功能性肌肉群驱动。假设肌肉根据希尔（1938年）方程的一种改编形式表现，纳入了肌肉力-长度关系。力-长度关系以及作为各种肌肉关系输入的长度值通过以下两种方式定义：（1）基于沃伊蒂兹等人（1984年）的实验，力-长度关系为抛物线形，长度定义为整个肌肉长度；（2）基于横桥理论，力-长度关系表示为直线的组合，长度定义为肌纤维长度。在第二种定义中，七个肌肉群中的四个达到最佳长度（即肌肉可施加最大等长力的长度）时的关节构型又进一步通过两种方式给出。第一种方式与该实验室之前的一项研究（吉福库和赫尔佐格，1990年）一致；第二种方式依赖未发表的实验数据。研究了平均功率对设计参数以及力-长度关系和肌肉长度定义的依赖性。对于定义1，曲柄长度为0.17 m时，一次完整曲柄旋转的最大平均功率约为1300瓦，对于定义2为1000瓦。定义2中的平均功率对设计参数变化比定义1更敏感。对于定义1，曲柄长度为0.17 m时的最佳曲柄旋转速率为18.4弧度/秒（176转/分钟）（由于两个肌肉群输入的修订，该值与之前研究的结果不同），对于定义2为15.2弧度/秒（145转/分钟）和14.6弧度/秒（139转/分钟）。
