探析宋代夾頭榫案之穩固性

The Stability Analysis of Recessed-Leg Tables with Bridle-and-Tenon Joints in the Sung Dynasty

本研究旨在探討宋人畫作中，出現的四種不同結構形制的夾頭榫案之穩固性問題。為了完整描述夾頭榫案的結構構件，彼此間相互連結的拓樸幾何關係，提出以細實線條代表構件，空心圓表示連結構件的榫卯接點，利用細實線條和空心圓簡單的幾何元素，模擬了榫卯結構體構件排列連結的拓樸構造圖，應用拘束方程式計算結構體的拘束度，再以拘束度做為判定案式結構體穩固性的量化指標。根據結構體拘束度的運算結果，分析比較四種不同結構形制夾頭榫案的穩固性，再依據案式結構體的構造特性，比較了結構體使用的便利性，分析比較的結果應可提供研究宋代夾頭榫案結構形制演進的參考依據。

The purpose of this paper was to study the four various styles of recessed-leg table with bridle-and-tenon joints appearing in paintings by artists in the Sung dynasty. To depict topographically geometrical relations among parts of construction in different ages, the real lines and hollow circles were considered to be members of construction and mortise-tenon joints, respectively. To utilize simple geometrical elements such as lines and circles, the topographical construction diagrams were developed to simulate the arrangements of parts of construction with bridle-and-tenon joints. The equation of constraint was used to calculate the degrees of constraints of construction. The degrees of constraint were represented to be the quantitative index of stability of construction. The comparisons of stability of recessed-leg table with bridle-and-tenon joints were made. It is well supposed that this study would be a good reference to research the development process of recessed-leg table with bridle-and-tenon joints in the Sung dynasty.