﻿ 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

Vol.04 No.03(2015), Article ID:15828,8 pages
10.12677/AAM.2015.43030

Mathematical Description of the Creative Folding Table’s Dynamic Change Process

Ying Wang*, Jiang Qian, Fumou Duan

College of Science, Hohai University, Nanjing Jiangsu

Email: *15951707381@163.com

Received: Jul. 15th, 2015; accepted: Aug. 4th, 2015; published: Aug. 10th, 2015

ABSTRACT

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.

Keywords:Parameterization, The Related Point Method, Cubic Spline Interpolation, Folding Table, Similar Triangles, The Pythagorean Theorem

Email: *15951707381@163.com

1. 引言

Rising Side Table来自设计师Robert van Embricqs的创意，与其说这是一款精妙的设计，还不如说它是一种数学宅的炫耀。简约与时尚已成为当代设计的潮流[1] 。相比普通折叠桌，创意平板桌的美观艺术性，在折叠的动态变化过程可很好展示，同时对加工进行参数优化设计，使它兼具稳定性好、加工方便、用材最少等特点[2] [3] 。

2. 模型建立

2.1. 模型假设

(1) 不考虑各木条间的缝隙；

(2) 不考虑加工时的木料磨损；

(3) 长方形木板刚好加工成整数根木条，无木料剩余；

(4) 加工时，保证桌腿上的滑槽宽度小于桌腿厚度，同时大于钢筋直径；

(5) 不考虑由于加工桌子所用的木板的材质以及钢筋的质量问题所导致的折叠桌不稳定的情况。

2.2. 预备知识说明

(1)

(2)

2.3. 参数化模型

(3)

(4)

Figure 1. Wood corresponding location coordinate

Figure 2. Coordinate diagram

Figure 3. Length scale diagram

(5)

2.4. 相关点法模型

(6)

(7)

(8)

(9)

3. 模型求解

Table 1. Board design and processing parameter list

Figure 4. h = 3 Simplified model diagram

Figure 5. h = 20 Simplified model diagram

Figure 6. h = 53 Simplified model diagram

Figure 7. Simplified figure of interpolation table leg edge line

4. 结论

Mathematical Description of the Creative Folding Table’s Dynamic Change Process[J]. 应用数学进展, 2015, 04(03): 238-245. http://dx.doi.org/10.12677/AAM.2015.43030

1. 1. 王新业 (2013) 折叠家具: “叠”出品质生活. 销售与市场(管理版), 10, 56-58.

2. 2. 韩佳成, Van Embricqs, R. (2012) 平板折叠边桌. 设计, 8, 24.

3. 3. 郑路通, 郭志鹏 (2014) 创意平板折叠桌的数学模型. 运城学院学报, 5, 1-2.

4. 4. 李庆扬, 王能超, 易大义 (2008) 数值分析. 第5版, 清华大学出版社, 北京.