A general method for the creation of dilational surfaces

Area of Science:

• Mechanical Engineering
• Materials Science
• Geometry

Background:

• Existing dilational structures have limitations in shape adaptability and can obstruct enclosed volumes.
• Current designs are often restricted to specific curvatures and require perpendicular movements.

Purpose of the Study:

• To present a universal method for designing dilational structures applicable to arbitrary surfaces.
• To enable surface dilation with movements exclusively tangent to the surface, preserving enclosed volume.

Main Methods:

• Triangulating arbitrary target surfaces (2-manifolds).
• Replacing triangular faces with pantograph mechanisms using a collision-avoiding tiling algorithm.
• Demonstrating the method with examples of varying complexity and Gaussian curvature.

Main Results:

• A generalizable method for creating dilational structures from any surface was established.
• The method allows for tangent-only surface motion, preventing volume obstruction.
• Theoretical scalability from full expansion to a single point is achieved.

Conclusions:

• The proposed method offers a versatile solution for designing dilational structures for diverse applications.
• This technique overcomes limitations of current designs, enabling efficient and adaptable shape-changing mechanisms.
• The approach is theoretically applicable to any surface, paving the way for novel engineering designs.