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The trend toward smaller mechanism footprints and volumes, while maintaining the ability to perform complex tasks, presents the opportunity for exploration of hypercompact mechanical systems integrated with curved surfaces. Developable surfaces are shapes that a flat sheet can take without tearing or stretching, and they represent a wide range of manufactured surfaces. This work introduces “developable mechanisms” as devices that emerge from or conform to developable surfaces. They are made possible by aligning hinge axes with developable surface ruling lines to enable mobility. Because rigid-link motion depends on the relative orientation of hinge axes and not link geometry, links can take the shape of the corresponding developable surface. Mechanisms are classified by their associated surface type, and these relationships are defined and demonstrated by example. Developable mechanisms show promise for meeting unfilled needs using systems not previously envisioned.
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Developability of Triangle Meshes
Developable surfaces are those that can be made by smoothly bending flat pieces without stretching or shearing. We introduce a definition of developability for triangle meshes which exactly captures two key properties of smooth developable surfaces, namely flattenability and presence of straight ruling lines. This definition provides a starting point for algorithms in developable surface modeling—we consider a variational approach that drives a given mesh toward developable pieces separated by regular seam curves. Computation amounts to gradient descent on an energy with support in the vertex star, without the need to explicitly cluster patches or identify seams. We briefly explore applications to developable design and manufacturing.
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- Award ID(s):
- 1717320
- PAR ID:
- 10060771
- Date Published:
- Journal Name:
- ACM transactions on graphics
- Volume:
- 37
- Issue:
- 4
- ISSN:
- 0730-0301
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Accepted Manuscript1.0
- Journal Article:
- The DOI is not currently available.
