A Parametric Optimized Method for Three-Dimensional Corner Joints in Wooden Furniture: Fid-Bau Portal

A Parametric Optimized Method for Three-Dimensional Corner Joints in Wooden Furniture

Xiutong Xu / Xianqing Xiong / Xinyi Yue / Mei Zhang

The three-dimensional corner joint is a type of joint in wooden furniture structures with complex parameter relationships and many constraints. Traditional furniture structure design requires repeated modifications of geometric models to determine parameter dimensions, which is inefficient and challenging and severely impacts the development of the digital design and manufacture process. Based on the ideal value range of mortise–tenon joints, this study derived a parametric optimized method of three-dimensional corner joints in wooden furniture and refined the theoretical value range of at least four main parameters: the width of the beneficial mortise ( $B_{2}$ ), the depth of the cede mortise ( $C_{1}$ ), the margin thickness from the cede tenon to the rail₁ reference edge ( $b_{t 1}$ ), and the margin thickness from the beneficial tenon to the rail₂ reference edge ( $b_{t 2}$ ). With case verification, the results show that in the axial direction of the cede tenon, the $m a x C_{1}$ decreased by 5.4 mm and the combination of $(B_{2}, C_{1})$ reduced at least 23 kinds. In the cases of different post widths and the margin thickness from rail₂’s reference edge to the post’s reference edge ( $B_{t m 2}$ ), the value range and value quantity of $b_{t 2}$ were narrowed and decreased in various degrees. In the axial direction of the beneficial tenon, the value range and quantity of available values of the margin thickness from the cede tenon to the rail₁ reference edge ( $b_{t 1}$ ) decrease with decreasing margin thickness from the rail₁ reference edge to the post reference edge ( $B_{t m 1}$ ) when $B_{t m 1}$ is less than constant z. The parametric optimized method of three-dimensional corner joints in wooden furniture can effectively reduce the parameter dimensional value range, both theoretically and practically, and more refined value ranges can be obtained by setting more standard values. This method also provides ideas for the digital and standardized design of wooden furniture structures.