What is a mechanism?

A mechanism is a mechanical device used to transfer or transform motion, force, or energy. Mechanisms typically use links and pin joints to achieve their motion.

What is a developable surface?

A developable surface is a surface with curvature in a single direction. The four types of developable surfaces are planes, cylinders, cones, and tangent-developed surfaces.

Developable Mechanisms

A developable mechanism is a mechanism that, at some point in its motion, conforms to a developable surface. In other words, it is a device that can move and that is shaped to match a curved surface in a certain position. A simple example of a developable mechanism is shown below.

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In the left image, the mechanism is conformed to the developable surface (in this case, a cone).  In the right image the mechanism has been deployed off the surface.  

Groundbreaking research was recently published on developable mechanisms in the Science Robotics academic journal.

To allow motion, the mechanism's joint axes (where the pin joints are) must be along the ruling lines on the developable surface. Developable mechanisms are possible on all types of developable surfaces.  Below is an animation showing developable mechanisms on cylindrical, conical, and tangent developed surfaces. 

Developable Mechanisms moving
Advantages of Developable Mechanisms

Developable mechanisms are useful because they can be compactly stored and they can exhibit predictable motion.  This means we can mathematically model and plan their movement.

Another advantage is that they can be contained within (or placed on) developable surfaces.  Developable surface are very common in engineering applications, but currently those surfaces are static and don't move.


Developable mechanisms can give increased functionality to common surfaces and can be compactly stored when not in use.

Challenges of Developable Mechanisms

Traditional mechanism design assumes that the shape of the links does not matter.  But for developable mechanisms, the shape of the links does matter because the links must conform to the developable surface.

As noted above, another challenge is where the joint axes can be placed. The joint axes must be coincident with the ruling lines on the developable surface.