创意平板折叠桌的数学模型
本文首先从几何学角度建立数学模型用以讨论折叠桌上关键点的动态变化过程，然后我们将模型连续化，进一步获得了桌脚边缘线和桌腿曲面的参数方程.再从几何要求和力学的稳定性要求两个方面研究了最优开槽长度的设计方案。本文还给出了一个具体设计实例验证了本文提出的模型和算法具有一定的实用性。最后，对本文提出的模型进行了推广，证明了只要桌脚边缘线恰好在桌腿直纹曲面上，那么这个折叠桌就是可以生产的.
Abstract
The design of foldable furniture is a multi-subject innovation connects realms such as industrial design, structure design, mechanical structure, engineering material and material processing. It is a method of conceptual furniture design. Along with technological development, foldable furniture is not limited to traditional forms. Creative furniture products greatly satisfy people’s material and emotional needs by adapting to limited spaces that city people are subjected to. It helps people reaching their goal of comfortable living circumstances, and creating hominy life.
Firstly, a mathematical model based on geometry analysis which describes the dynamical process of foldable table of key points is built in this article. Then a serialization method is used in the discrete model to acquire the parametric equations about the edge line of legs and curved surface of legs. A designing scheme of the optimal length slot is also studied from geometrical and mechanical stable requirements. A specific design example is also given to demonstrate the practicality and effectiveness of the model and the algorithm. Finally, the model is generalized, it proved that if the edge line of legs is just on curved surface of legs, the foldable table can be produced.
毕业论文关键词：数学建模、空间几何学、三角函数、约束条件、刚体力学
目录
一、问题描述 1
1.1引言 1
1.2问题的提出 1
二、问题分析 1
三、模型假设与约定 2
四、 符号说明及名词定义 2
五、 模型建立 2
5.1折叠桌几何模型 2
5.2桌脚边缘线及桌面曲线 5
5.3约束条件 7
5.4最优开槽长度 8
5.5模型实例 8
5.6力学分析 11
优尔、 模型结果的分析与改进 13
6.1模型的分析结果 13
6.2模型的改进 13
七、 参考文献 15
八、 附录 15
致谢 17
一、问题描述
1.1引言
人类所特有的创造性劳动的体现是创新，它是人类社会进步的源泉和核心动力.创新是人类在认识世界和改造世界的过程中，对原有理论、观点的超越和对过去实践的突破.折叠式家具的创新更是对人们居家生活具有巨大的影响.
折叠家具的研究目的之一是有效地利用空间，并且能够在有限空间中追求舒适、美观的效果；其二在于借助新的技术手段发现新的家具折叠方式，既可以丰富家具品种，又能够改良用户体验；其三在于寻找折叠式产品设计的新概念，为设计师提供展示才华和实现设计的平台，当然最终目的就是为了提高产品设计的整体水平.
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