AAM  >> Vol. 4 No. 3 (August 2015)

    创意折叠桌的动态变化过程的数学描述
    Mathematical Description of the Creative Folding Table’s Dynamic Change Process

  • 全文下载: PDF(708KB) HTML   XML   PP.238-245   DOI: 10.12677/AAM.2015.43030  
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作者:  

王 莹,钱 江,段付谋:河海大学理学院,江苏 南京

关键词:
参数化相关点法三次样条插值折叠桌相似三角形勾股定理Parameterization The Related Point Method Cubic Spline Interpolation Folding Table Similar Triangles The Pythagorean Theorem

摘要:

采用参数化–相关点法模型对折叠桌的动态变化过程进行数学描述。首先通过分析木条在桌面边缘铰接处的坐标、木条与钢筋的交点坐标以及桌脚边缘点坐标三者和桌面铰接处与x轴的夹角θ、桌面半径r之间的关系,将各坐标变量用参数表示,通过参数值的变化观测相应坐标变量的变化,进而用此参数方程对折叠桌的动态变化过程进行数学描述。而具体解决问题时,也可以直接利用桌面边缘铰接处的坐标、木条与钢筋的交点的坐标表示出桌脚边缘线上各点的坐标,根据三者的函数关系式来描述折叠桌的动态变化过程。

Parametric-related point method model is used to give a mathematical description of the dynamic table folding process. Firstly by analyzing the relationship between the coordinate of the batten on the edge of the table articulated point, the intersection point coordinates of batten and steel and the coordinates of leg edge points and the inclined angle—θ of table articulated point and the x axis, and radius of the table—r, we can conclude the equation of coordinate variables indicated by parameters and observe the change of the corresponding coordinate variables through the change of parameter values. This parametric equation of folding table is used to give a mathematical description for the process of dynamic change. When solving specific problems, we can also directly use the coordinate of the batten on the edge of the table articulated point and the coordinate of the intersection between batten and steel to calculate the coordinate of leg edge points. Using these three function formulas, the folding process is described.

文章引用:
王莹, 钱江, 段付谋. 创意折叠桌的动态变化过程的数学描述[J]. 应用数学进展, 2015, 4(3): 238-245. http://dx.doi.org/10.12677/AAM.2015.43030