Hoeken’s linkage consists of three links and is driven by the
rotary motion of the shortest one (yellow). The proportions
of the following three dimensions are crucial to make this
linkage work: the length of the shortest link (yellow), the
length of the medium link (light grey), and the distance
between points of attachment to the supporting structure.
The proportions should be 2 to 5 to 4. The longest link (blue)
can be extended to any length beyond its upper joint. The
tip of this link traces the shape of a flattened oval cut in half
(the dotted line in the illustration), and the size of this oval
is determined by the extended link’s length. A little less than
half of this link’s movement is linear. Such an unusual motion
pattern can be used, for example, to drive the legs of walking
vehicles.