Blog Details
- Member
- August 2, 2025
ANGULATED LINK MECHANISM
The Hoberman Switch Pitch ball, and Hoberman mechanisms in general, are fascinating
examples of transformable structures based on the principles of kinematic linkages. While
the common toy version is spherical, the underlying mechanism can be applied to create a
variety of polyhedral shapes.
The core of the Hoberman mechanism, often referred to as an "angulated element" or
"scissors mechanism," consists of two identical bent rods joined at a central pivot.
Multiple such elements are then connected at their ends to form a larger structure.
The key is that these linkages allow for a single degree of freedom of motion, meaning that if one part moves, the entire structure expands or contracts in a coordinated way.
Here's a breakdown of the polyhedral shapes possible with the Hoberman switching
mechanism:
● Spherical Forms (Icosidodecahedron-based):
○ The most common and iconic Hoberman Sphere (and the Switch Pitch ball) is
essentially a truncated icosahedron (like a soccer ball) or an icosidodecahedron in
its expanded state.
○ The mechanism is arranged along the edges of these polyhedra.
As the structure contracts, the panels fold inwards, and the overall shape remains generally spherical, but with a different set of exposed faces (colors in the Switch Pitch ball).
○ The "switching" action of the Switch Pitch ball involves the inversion of the faces,
essentially flipping inside out to reveal a different set of "external" faces.
This specific "switch" from one spherical configuration to another is a specialized
application of the general Hoberman mechanism.
● Platonic Solids (with modifications):
○ Research and design have explored applying the Hoberman mechanism to mobilize
the five Platonic solids:
■ Tetrahedron: While simple, it can be made transformable.
■ Cube (Hexahedron): Possible to create expanding/contracting cube structures.
■ Octahedron: Also a possibility for a transformable structure.
■ Dodecahedron: Can be designed to expand/contract.
■ Icosahedron: Closely related to the Hoberman Sphere's geometry.
○ The challenge with these is often maintaining the regular polygon faces during
expansion and contraction, which sometimes requires bent or curved members in the
linkages.
● Archimedean Solids:
○ These are convex polyhedra whose faces are regular polygons but not all the same
kind, and whose vertices are all alike. The truncated icosahedron (soccer ball) is an
Archimedean solid, which directly relates to the Hoberman sphere.
○ Other Archimedean solids, like the rhombicuboctahedron, can also theoretically be
the basis for Hoberman-like transformable structures.
● Prisms and Pyramids:
○ Simpler polyhedra like prisms (e.g., triangular prism, square prism) and pyramids can
also be made transformable using Hoberman-style linkages, allowing them to expand
or contract in height or overall volume.
● Reconfigurable Deployable Polyhedral Mechanisms (RDPMs):
○ Advanced research in robotics and mechanical engineering extends the Hoberman
principle to create more complex "reconfigurable" polyhedra. These structures can
not only expand/contract but might also have multiple stable configurations or the
ability to reconfigure their internal geometry significantly.
Key Characteristics that Allow for these Shapes:
● Scissor-like Linkages: The fundamental building block.
● Single Degree of Freedom: The entire structure moves in a coordinated fashion with
one input.
● Vertex Connectivity: The way the individual linkages connect at the vertices of the
target polyhedron is crucial for maintaining the overall shape while allowing for
transformation.
● Geometric Constraints: The design of the angulated elements (length, angles of the
bends) dictates which polyhedral forms can be successfully mobilized and how uniformly
they expand or contract.
In essence, if a polyhedron can be represented by a network of interconnected "edges" that
can change length in a synchronized way, it's a candidate for a Hoberman-style transforming
mechanism.
The Switch Pitch ball is a specific, popular example of this concept applied to
an icosidodecahedral base with a clever face-flipping mechanism.