24 Fundamental concepts
linkage is the subtraction of the first Goldberg 6R linkage from another
Bennett linkage resulting in a syncopated linkage. The third Goldberg 6R
linkage is built by an L- shaped arrangement of three Bennett linkages. The
last of the four types is produced by subtracting the Goldberg L- shaped 6R
linkage from another Bennett linkage.
Other 6R overconstrained linkages based on the Bennett linkage also
exist, among which the most common one is the double- Hooke’s-joint
linkage (Baker, 2002), which we briefly touched upon earlier. It is a 6R
linkage obtained from two spherical 4R linkages. This linkage is in fact a
special case of the Bennett 6R hybrid linkage, which is a combination of
two spherical 4R linkages. Two further special forms are the Bennett
plano- spherical hybrid linkage, Figure 2.17, and the Sarrus linkage, Figure
2.11. Wohlhart (1991) described a 6R overconstrained linkage, the synthesis of which was achieved by coalescing two appropriate generalised
Goldberg 5R linkages and removing the two common links, Figure 2.18.
(a)
Figure 2.16 The Goldberg 6R linkages and their construction: (a) series; (b) syncopated; (c) L-shaped and (d) syncopated of L-shaped.