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Parallelotriangular Mechanisms and Line Contact Constraint

V. Karakusevic, J. Angeles, P.J. Zsombor-Murray 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 inhibits 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 the 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 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.

Thierry Baron
Mon Apr 7 12:54:24 EDT 1997