22 Fundamental concepts
(a)
Figure 2.14 The Goldberg 5R linkages obtained by (a) summation; (b) subtraction.
An extended Myard linkage has been proposed by Chen and You (2008a)
obtained by combining two Bennett linkages as Myard did in the creation
of his 5R linkage. Unlike the original Myard linkage, the angle of twists in
the extended Myard linkage, α 23 and α 45 are not necessary to be π/2 but
the sum of these two twists remains to be π. And the two general Bennett
linkages that have two equal lengths and one identical twist and one complimentary twist. As a result, the extended Myard linkage does not have
plane symmetry. Similar to the Myard linkage, the extended one is also a
special case of the generalised Goldberg 5R linkage.
Goldberg (1943) also reported a family of 6R linkages which were later
named after him. Similar to the Goldberg 5R linkage, the Goldberg 6R linkages are also produced by combining Bennett linkages. There are a total of
four types of Goldberg 6R linkages, see Figure 2.16. The first Goldberg 6R
linkage is formed by arranging three Bennett linkages in series. The first two
Bennett linkages have a link in common, and the opposite link of one of them
is common with a link of a third Bennett linkage. The second Goldberg 6R