MiGumi: Making Tightly Coupled Integral Joints Millable

2025-10-15

AI Summary

Traditional solid-wood joinery suffers from high manual fabrication costs and geometric deviations—such as interior corner rounding—introduced by CNC milling, leading to assembly gaps or interference and hindering industrial adoption. This paper proposes a tightly coupled, manufacturability-aware wood joint design method. Its core innovation is the “millable extrusion geometry” (MXG) modeling language, which jointly optimizes part geometry and toolpaths. Leveraging subtractive extrusion modeling based on flat-end mills, the method incorporates differentiable contact-surface proximity constraints and a toolpath-aware loss function to ensure tight surface mating after milling. Evaluated on 30 classic joints, the generated designs exhibit zero assembly gaps, seamless assembly, and high geometric fidelity. The approach significantly enhances the CNC manufacturability and precision controllability of traditional mortise-and-tenon joints.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization
• Cognitive Modeling & Cognitive Systems: Computational Creativity

Application Category

• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

Traditional integral wood joints, despite their strength, durability, and elegance, remain rare in modern workflows due to the cost and difficulty of manual fabrication. CNC milling offers a scalable alternative, but directly milling traditional joints often fails to produce functional results because milling induces geometric deviations, such as rounded inner corners, that alter the target geometries of the parts. Since joints rely on tightly fitting surfaces, such deviations introduce gaps or overlaps that undermine fit or block assembly. We propose to overcome this problem by (1) designing a language that represent millable geometry, and (2) co-optimizing part geometries to restore coupling. We introduce Millable Extrusion Geometry (MXG), a language for representing geometry as the outcome of milling operations performed with flat-end drill bits. MXG represents each operation as a subtractive extrusion volume defined by a tool direction and drill radius. This parameterization enables the modeling of artifact-free geometry under an idealized zero-radius drill bit, matching traditional joint designs. Increasing the radius then reveals milling-induced deviations, which compromise the integrity of the joint. To restore coupling, we formalize tight coupling in terms of both surface proximity and proximity constraints on the mill-bit paths associated with mating surfaces. We then derive two tractable, differentiable losses that enable efficient optimization of joint geometry. We evaluate our method on 30 traditional joint designs, demonstrating that it produces CNC-compatible, tightly fitting joints that approximates the original geometry. By reinterpreting traditional joints for CNC workflows, we continue the evolution of this heritage craft and help ensure its relevance in future making practices.

Problem

• Traditional wood joints are difficult to fabricate using CNC milling
• Milling causes geometric deviations that prevent tight coupling of parts
• A new method co-optimizes part geometries to restore joint integrity

Innovation

• Develops Millable Extrusion Geometry language for milling
• Co-optimizes part geometries to restore tight coupling
• Uses differentiable losses for efficient joint optimization