Spatial 6R linkages supposedly fixed:
W= 6(m – 1) –5p1 = 6(6 -1) – 5•6 = 0.
m - the number of links, p1 - the number of one movable joints.
However, some of 6R linkages are mobile. The Brikard linkage (Fig. 1a) is mobile because of satisfying additional conditions. To determine these conditions, build this linkage based on the cube figure. Line UL connecting the vertices of the cube is the main diagonal (Fig. 1b). Figure 1. a - Brikard linkage, b - building linkage based on the cube figure, a-f - experimental models of new linkage modifications.
Analysis of 6R mechanisms mobility depending on the orientation of joints axes relatively to the main diagonal allowed us to determine conditions of mobility and synthesize new mobile modifications of Brikard linkages (Fig. 1b):
1. Linkage contains three pairs of identical links: AB = DE = L1, CB = EF = L2, CD = FA = L3.
2. Three joints axes intersect the main diagonal at one point.
3. Other joints axes intersect the main diagonal (optionally at one point).
According to these conditions, we synthesize 18 new mobile modifications of Brikard linkage (Fig. 1c-d).