The pair of tetrahedra that move with intersecting edges is a parallel
mechanism with six line contact constraints; the six R-P-R-P-R joints.
It is also a six legged platform that moves, albeit with legs of zero length.
Such five degree of freedom joints or, conversely, ones that inhibit only
one degree of freedom, are conveniently studied with simple double triangular
mechanisms, of planar, spherical and spatial variety, which use them. Forward
kinematics, singularity and isotropy of all three types have been obtained.
However, much remains to be done concerning analysis of the spatial variety.
Of particular interest is an analytical approach based on the observation
that each edge of the movable triangle occupies a line complex whose axis
is a circle and whose axis, in turn, is an edge of the fixed triangle.
Furthermore, one observes that in the case of intersecting tetrahedral
edges this complex degenerates to a congruence of lines in the point of
intersection as the circle assumes zero radius. In fact the double tetrahedron
may be thought of as a Siamese, antisymmetric pair of special spatial triangles
with only one dual angle vertex.