Negative Curvature Surfaces from Flat Strips
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Solution Overview
Problem
There is no efficient means to construct surfaces of controlled or constant negative curvature by assembling flat materials, which are dynamically unique and offer significant surface area in a small volume, limiting their application in various fields.
Innovation Solution
A method of assembling surfaces of negative curvature by forming flat materials like steel, paper, or foam into strips with varying attachment spacings, allowing for precise control of curvature through interlocking shapes and openings, enabling the creation of materials with negative curvature without requiring computer-controlled fabrication or 3D printing.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Volume of moving object
If flat materials are assembled to construct surfaces of negative curvature, then surface area in a small volume is achieved, but manufacturing complexity and difficulty increase
Solution Approach 1:
The flat material is divided into multiple strips with interlocking features. Each strip contains a series of openings and attachment points that can be connected to adjacent strips, allowing the material to be segmented into manageable units that collectively form the complex negative curvature surface without requiring complex single-piece fabrication
Solution Approach 2:
The invention transitions from 2D flat material to 3D negative curvature surface by introducing interlocking strips with varying attachment spacings. The strips are arranged in multiple dimensions with different spacing patterns, enabling the flat material to buckle and form three-dimensional saddle-shaped surfaces with controlled negative curvature
2Manufacturing precision
If computer-controlled fabrication or 3D printing is used to create negative curvature surfaces, then manufacturing precision is improved, but device complexity and cost increase
Solution Approach 1:
The attachment spacings are predetermined during the cutting or forming of the strips, with specific patterns of openings and attachment points designed in advance. This preliminary configuration of geometric parameters allows the strips to self-assemble into negative curvature surfaces with controlled precision without requiring complex real-time control systems
Solution Approach 2:
The interlocking strip structure is designed to self-assemble into negative curvature surfaces through inherent geometric constraints. The varying attachment spacings and interlocking features guide the material to naturally buckle and form the desired saddle-shaped geometry without requiring external computer-controlled manipulation or 3D printing processes
3Area of moving object
If flat material is manipulated to form negative curvature surfaces, then surface area is increased, but material stress increases
Solution Approach 1:
By dividing the material into multiple strips with interlocking features, the stress that would concentrate in a continuous bent surface is distributed across many small connection points. Each strip experiences localized bending rather than the entire surface bearing the stress of forming the negative curvature
Solution Approach 2:
The invention uses flexible flat materials that can bend and buckle to form negative curvature surfaces. The interlocking strip structure allows the material to flex and adapt to the curved geometry, reducing stress concentrations that would occur with rigid materials or single-piece constructions
Data Source
AI summary
An object having a plurality of negative curvatures comprising a plurality of planar sections adjoined together by locking segments.