A new bicycle reinvents the wheel, with a pentagon and triangle

·Guan’s bicycle isn’t the first to exploit these shapes — they have been used by urban planners as manholes.

It seems a bit crazy to reinvent the wheel, but that is precisely what the Chinese inventor Guan Baihua has done. Although his new set of wheels have a little twist to them. The 50-year-old military officer from Qingdao has devised a rather curious new bicycle. Instead of circular wheels the bike has a pentagonal wheel at the front and a triangular wheel at the back.
Those who have tried it have been surprised at how smooth the ride is.
That is because the edges of the pentagonal and triangular wheels are not perfectly straight. The sides of the shapes bulge outwards in such a way that the wheels share an important feature with the circle: the diameter across the shapes is the same which ever way that you measure it.
This means that as I cycle, although the wheel itself does not have a fixed centre of rotation, the saddle of the bike doesn’t bob up and down as you might expect but stays a fixed distance from the ground. To get the exact contours for the shapes, the curved edges are drawn so that they are part of a circle centred on the vertex opposite the edge. They are called Reuleaux polygons after the 19th-century German engineer Franz Reuleaux, who did pioneering work on machines that turn one type of motion into another.

A Reuleaux triangle is a curve of constant width. Opposite sides on each square are parallel supporting lines, since each touches the curve but does not intersect the interior. The fact that the Reuleaux triangle can be rotated whilst still just intersecting the boundary shows that width (separation between parallel supporting lines) is constant in all directions.
File:Rouleaux triangle Animation.gif
[Source: wikipedia.org]

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