统一分析刚性折纸结构的运动，自动生成约束矩阵。
A Unified Framework for Kinematic Simulation of Rigid Foldable Structures
- 基于螺钉理论构建速度层级约束矩阵，捕捉旋转与平移耦合。
- 从最小扩展数据模式提取最小环基，覆盖所有结构约束。
- 支持多类刚性折纸结构的自动仿真与可视化，免去手工推导。
受折纸启发的刚性面板结构已拓展至厚板、剪切折纸及多层实现，亟需统一的运动学分析方法。现有方法缺乏对各类结构环约束的通用建模手段。本文提出一种自动化框架，可为任意刚性可折叠结构（RFS）生成Pfaffian约束矩阵。该工具基于最小扩展数据模式构建面-铰链图，提取最小环基以捕获全部约束，并利用螺钉理论在速度层级组装约束矩阵，精确编码旋转与平移的闭环关系。框架能高效计算并可视化多种RFS的展开与折叠过程，彻底避免繁琐且易错的手动约束推导。
原文摘要 · Abstract (English)
Origami-inspired structures with rigid panels now span thick, kirigami, and multi-sheet realizations, making unified kinematic analysis essential. Yet a general method that consolidates their loop constraints has been lacking. We present an automated approach that generates the Pfaffian constraint matrix for arbitrary rigid foldable structures (RFS). From a minimally extended data schema, the tool constructs the facet-hinge graph, extracts a minimum cycle basis that captures all constraints, and assembles a velocity-level constraint matrix via screw theory that encodes coupled rotation and translation loop closure. The framework computes and visualizes deploy and fold motions across diverse RFS while eliminating tedious and error-prone constraint calculations.
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