一种描述人体头部运动范围的数学方法

One Novel Methodology for the Description of Human Head Motion Scope

基于头盔伺服系统执行机构的结构优化设计需求,提出了一种用六维空间超椭球体描述人体头部运动范围的方法;该方法主要由二维包络椭圆的计算和六维超椭球体的计算两部分组成。首先,总结和归纳了包络椭圆的定义,提出了包络椭圆的计算方法。在计算过程中提出了椭圆中心坐标修正步长、包络椭圆的两半轴长修正因子以及纵轴半轴长修正步长等概念。实现了对椭圆中心和半轴长的动态修正,提高了包络椭圆计算的准确性和智能化水平。其次,给出了判定包络椭圆的条件和准则,方便了对计算方法可行性的验证。再次,提出了根据投影面内包络椭圆几何信息求解六维超椭球体的方法。最后,对包络超椭球体的计算方法进行了理论分析和实例计算。结果表明:对包络椭圆与超椭球体的计算是准确的,采用超椭球体来描述头部运动范围是可行的。

One method for the description of human head motion scope using six-dimensional hyperellipsoid is proposed based on structural optimization requirements of helmet mounted display servo system. The method is made up of two parts the calculation of two-dimensional circling ellipse and the computation of corresponding hy- perellipsoid. The former part is developed firstly, the definition of circling ellipse and corresponding conceptions are proposed also, such as modification step of the center and the longitudinal axis of circling ellipse, the modifica- tion factor of the axes length of circling ellipse, and so on. The dynamical modifications of the center and axes length of circling ellipse are implemented, and the accuracy and intellectual ability of the method is improved. Sec- ondly, two identification norms about circling ellipse are developed, and the calculation method of hyperellipsoid based on fifteen circling ellipse is also proposed. Finally, theory analysis and example test of the novel method are carried out, and the accuracy and feasibility of the methodology are also demonstrated better by the results.