Fundamental concepts 31
The Bricard linkages also appear in other objects or linkages. A linkage
popularly known as the kaleidocycle is one example. A kaleidocycle is a
three dimensional ring made from a chain of identical tetrahedra, each of
which is linked to an adjoining one along an edge. The ring can be turned
through its centre continuously. At least six tetrahedra are required in
order to form a mobile closed ring (Schattschneider and Walker, 1977). In
fact when the number of tetrahedra is six, the loop becomes a trihedral
case of the Bricard linkage. A model is shown in Figure 2.23, which is constructed from a toy commonly known as Flexistar 6.
1
Its geometrical properties are as follows.
,
,
,
(2.36)
(i = 1, 2, . . ., 6).
The other example is the Altmann 6R linkage (1954), which also turned
out to be a special case of the line- symmetric and trihedral case Bricard
linkage. Moreover, the Schatz linkage, reported and patented by Schatz,
was derived from a special trihedral Bricard linkage (Phillips, 1990). The
new 6R linkage reported by Wohlhart (1987) can be regarded as a generalisation of the Bricard trihedral 6R linkage.
(a)
(b)
Figure 2.22 More Bricard linkages: (a) trihedral and (b) line-symmetric octahedral
cases.
The Bricard linkages also appear in other objects or linkages. A linkage
popularly known as the kaleidocycle is one example. A kaleidocycle is a
three dimensional ring made from a chain of identical tetrahedra, each of
which is linked to an adjoining one along an edge. The ring can be turned
through its centre continuously. At least six tetrahedra are required in
order to form a mobile closed ring (Schattschneider and Walker, 1977). In
fact when the number of tetrahedra is six, the loop becomes a trihedral
case of the Bricard linkage. A model is shown in Figure 2.23, which is constructed from a toy commonly known as Flexistar 6.
1
Its geometrical properties are as follows.
,
,
,
(2.36)
(i = 1, 2, . . ., 6).
The other example is the Altmann 6R linkage (1954), which also turned
out to be a special case of the line- symmetric and trihedral case Bricard
linkage. Moreover, the Schatz linkage, reported and patented by Schatz,
was derived from a special trihedral Bricard linkage (Phillips, 1990). The
new 6R linkage reported by Wohlhart (1987) can be regarded as a generalisation of the Bricard trihedral 6R linkage.
(a)
(b)
Figure 2.22 More Bricard linkages: (a) trihedral and (b) line-symmetric octahedral
cases.