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

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 (B2), the depth of the cede mortise (C1), the margin thickness from the cede tenon to the rail1 reference edge (bt1), and the margin thickness from the beneficial tenon to the rail2 reference edge (bt2). With case verification, the results show that in the axial direction of the cede tenon, the maxC1 decreased by 5.4 mm and the combination of B2,C1 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 (Btm2), the value range and value quantity of bt2 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 (bt1) decrease with decreasing margin thickness from the rail1 reference edge to the post reference edge (Btm1) when Btm1 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.