Cognate linkage
From original triangle, ΔA1DB1: The lengths of the four members can be found by using the law of sines.
Because both parallelograms were constructed off of the center coupler link, the new links connected to the ground share identical rotational motion functions, allowing for a 1:1 gear train to be used to connect them together.
However, an alternative to using a gear train to achieve 1:1 rotation is to connect them together using a parallelogram linkage, adding one additional link.
One characteristic with cognate linkages is that they often share at least two links in identical configuration.
Appending onto the method of the six-bar pairings, the links do not necessarily have to overlap, but rather just need to meet the criterion such that: Rather than overlapping the paired links, they can be attached in a fashion which forms a parallelogram, resulting in eight-bar cognate linkages.
Top row: Four-bar cognate linkages .
Middle row: Geared five-bar cognate linkages , derived from top row.
Bottom row: Closely related six-bar cognate linkages , derived from middle row.
