Planar Expandable Structure via Tessellation Hinges
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Solution Overview
Problem
Existing three-dimensional movable structures are complex, energy-intensive, and costly, with limited design types and stability issues, making them unsuitable for universal and systematic applications.
Innovation Solution
A method for generating a planar expandable structure by adding hinged points and hinged rods based on uniform tessellation, utilizing geometric tessellation principles and duality principles to create a systematic and innovative design.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of operation
If three-dimensional folding or rotation mechanisms are used to create movable structures, then the structures can achieve dynamic changes and movement, but the structure becomes complex, occupies large space, requires many driving mechanisms, consumes much energy, and has high construction and operation costs
Solution Approach 1:
The patent transitions from three-dimensional folding mechanisms to two-dimensional planar expansion mechanisms. By changing the dimensional approach from 3D rotation to 2D tessellation-based expansion, the structure achieves movability through a fundamentally different geometric principle that reduces complexity and space requirements.
Solution Approach 2:
The structure is divided into multiple identical basic units that can be systematically arranged through tessellation. Each basic unit contains the necessary hinged points and rods, allowing the entire structure to be constructed from repeating modular elements rather than complex custom components.
2Ease of operation
If three-dimensional folding or rotation mechanisms are used, then dynamic changes can be achieved, but the construction and operation costs increase and stability decreases
Solution Approach 1:
Instead of using rotation mechanisms that pivot around points, the patent inverts the approach by using expansion mechanisms that radiate from central points. The hinged rods expand outward from hinged points in a planar configuration, fundamentally inverting the traditional rotational paradigm to achieve both stability and dynamic capability.
Solution Approach 2:
The geometric constraints of the tessellation pattern and hinged connections provide inherent structural stability without requiring additional bracing or stabilization mechanisms. The structure's own geometry and connection system serve to maintain stability during expansion and contraction.
3Ease of operation
If three-dimensional movable structures are used, then movement is achieved, but the design types are limited and the system is not universal or systematic
Solution Approach 1:
The patent creates a universal design system based on planar uniform tessellation that can generate a wide variety of structures by changing the basic unit configuration. The same fundamental principles apply across different designs, making the system universally applicable while allowing for diverse outcomes through parameter variation.
Solution Approach 2:
The design system allows for variation in parameters such as the number of basic units, the configuration of hinged points, and the arrangement of rods within each unit. By changing these parameters while maintaining the fundamental tessellation-based expansion mechanism, a wide range of design types can be generated from a single systematic approach.
Data Source
AI summary
The present disclosure discloses a systematic method for generating a planar expandable structure by adding hinged points and hinged rods based on uniform tessellation, including: establishing a database of planar uniform tessellation graphs; selecting, inputting a graph of arbitrarily size range, naming it Graph A; drawing a dual tessellation graph of the Graph A, and extracting a basic unit b from it; determining whether the basic unit b has rotational symmetry, if not, then expanding the basic unit b to adjacent units, and denoting a final combined unit as Graph C; choosing to add hinged points or hinged rods, adjusting a length of each side of the Graph C, making Graph C′; adding original tessellation polygons in the Graph A to corresponding angular points of the Graph C′, rotating at a predetermined angle; hinging adjacent polygons by the hinged points or hinged rods together to obtain an expandable structural unit.