# 基于三维建模的创意桌设计与实现Design and Implementation of Creative Table Based on 3D Modeling

DOI: 10.12677/AAM.2018.76084, PDF, 下载: 517  浏览: 809

Abstract: This paper proposes a set of circular folding table design based on three-dimensional modeling. When the folding table is propped up, the table top is round. When the table legs are flattened, the table top is a solid rectangle. Firstly, the length and width of the rectangle and the height of the ta-ble are set. The design scheme analyzes the specific scheme of the folding table by setting up the mathematical model. This process includes the design of the processing parameters and the mathematical description of the edge line of the table leg. Moreover, MATLAB is used to simulate the dynamic change of the folding table. Then, a mathematical model is established as for arbitrary rectangle length, width and table height, and an optimal design scheme is given which can design table with good stability and saving material. Ultimately, a more practical, more beautiful, and more innovative folding table is designed.

1. 引言

2. 折叠桌总方案

3. 限定条件模型

3.1. 模型建立

3.1.1. 确定滑槽模型

Figure 1. Folding table image

Figure 2. The steel bar and the empty slot position schematic diagram

Figure 3. Model diagram

$S:\left\{\begin{array}{l}x=\left({D}_{1}-a\right)\mathrm{cos}t+a\\ y=\left({D}_{1}-a\right)\mathrm{sin}t\end{array}$

${M}_{t}:\left\{\begin{array}{l}x-a=\left({D}_{1}-a\right)\mathrm{cos}t\\ y=\left({D}_{1}-a\right)\mathrm{sin}t\\ z=z\end{array}$

${M}^{\prime }{M}_{t}=\left(\left({D}_{1}-a\right)\mathrm{cos}t+a-{x}^{\prime },\left({D}_{1}-a\right)\mathrm{sin}t,0\right)$

${{x}^{\prime }}^{2}+{z}^{2}={r}^{2}$ (r为桌面半径)

${L}_{n}=\mathrm{max}|{M}^{\prime }{M}_{t}|-\mathrm{min}|{M}^{\prime }{M}_{t}|\text{\hspace{0.17em}}\left(1\le n\le 10\right)$

3.1.2. 确定桌脚模型

${M}^{\prime }M=k{M}^{\prime }{M}_{t}$

${M}^{\prime }{M}_{t}=\left(k\left(\left({D}_{1}-a\right)\mathrm{cos}t+a-{x}^{\prime }\right),k\left({D}_{1}-a\right)\mathrm{sin}t,0\right)$

${M}^{\prime }M=\left(x-{x}^{\prime },y,z\right)$

$\left\{\begin{array}{l}x-{x}^{\prime }=k\left[\left({D}_{1}-a\right)\mathrm{cos}t+a-{x}^{\prime }\right]\\ y=k\left({D}_{1}-a\right)\mathrm{sin}t\end{array}$

$\frac{y}{x-{x}^{\prime }}=\frac{\left({D}_{1}-a\right)\mathrm{sin}t}{\left({D}_{1}-a\right)\mathrm{cos}t+a-{x}^{\prime }}$

$\left\{\begin{array}{l}x=\sqrt{{r}^{2}-{z}^{2}}+k\left[\left({D}_{1}-a\right)\mathrm{cos}t-\sqrt{{r}^{2}-{z}^{2}}\right]\\ y=k\left({D}_{1}-a\right)\mathrm{sin}t\\ z=0\end{array}$

3.2. 模型求解

${x}^{\prime }=\sqrt{{r}^{2}-{z}^{2}}=\sqrt{{r}^{2}-{\left[\left(10-n\right)d\right]}^{2}}$

$a=\sqrt{{r}^{2}-{\left(r-d\right)}^{2}}=7.8\text{\hspace{0.17em}}\text{cm}$

${D}_{1}=\frac{60-a}{2}+a=33.9\text{\hspace{0.17em}}\text{cm}$

$\mathrm{sin}t=\frac{50}{60-a}=0.958$

Table 1. Slideway length table

3.3. MATLAB仿真

4. 不限条件模型

4.1. 模型建立

4.1.1. 确定滑槽模型

$S:\left\{\begin{array}{l}x=\left({D}_{1}-a\right)\mathrm{cos}t+a\\ y=\left({D}_{1}-a\right)\mathrm{sin}t\\ z=z\end{array}$

${M}_{t}:\left\{\begin{array}{l}x-a=\left({D}_{1}-a\right)\mathrm{cos}t\\ y=\left({D}_{1}-a\right)\mathrm{sin}t\\ z=z\end{array}$

${M}^{\prime }{M}_{t}=\left(\left({D}_{1}-a\right)\mathrm{cos}t+a-{x}^{\prime },\left({D}_{1}-a\right)\mathrm{sin}t,0\right)$

Figure 4. Dynamic effect diagram

Figure 5. Leg-ground intersection diagram

$\mathrm{sin}t=\frac{H-3}{\frac{L}{2}-a}$

$0\le t\le {t}_{0}$ ，则：

${t}_{0}=\mathrm{arcsin}\frac{H-3}{\frac{L}{2}-a}$

$0\le t\le \mathrm{arcsin}\frac{H-3}{\frac{L}{2}-a}$

$\partial \left(t\right)=|{M}^{\prime }{M}_{t}|=\sqrt{{\left({D}_{1}-a\right)}^{2}-2\ast \left({D}_{1}-a\right)\left({x}^{\prime }-a\right)\mathrm{cos}t+{\left({x}^{\prime }-a\right)}^{2}}$

${v}_{i}=\partial \left({t}_{0}\right)=\sqrt{{\left({D}_{1}-a\right)}^{2}-2\ast \left({D}_{1}-a\right)\left(f\left({z}_{i}\right)-a\right)\mathrm{cos}{t}_{0}+{\left(f\left({z}_{i}\right)-a\right)}^{2}}$

${u}_{i}=\partial \left(0\right)=\sqrt{{\left({D}_{1}-a\right)}^{2}-2\ast \left({D}_{1}-a\right)\left(f\left({z}_{i}\right)-a\right)+{\left(f\left({z}_{i}\right)-a\right)}^{2}}$

${L}_{p}={v}_{i}-{u}_{i}$

${z}_{1}=\frac{1}{2}d,{z}_{2}=\frac{1}{2}d+d,\cdots ,{z}_{i}=\frac{1}{2}a+\left(i-1\right)d$

Figure 6. Schematic diagram when laying flat

Figure 7. Table leg schematic diagram

4.1.2. 确定桌脚模型

，得到截痕方程：

4.2. 目标优化

Figure 8. Schematic diagram of stereogram

5. 总结

NOTES

*通讯作者。

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