A pair of congruent, equilateral tetrahedra, superposed so each edge of one intersects exactly one edge of the other, move relative to one another. Motion has been analysed in terms of 5 joint parameters of the 6 parallel PRR*RP joints representing intersections and the rotational workspace has been mapped. A 12 actuator model of this 2.5DOF mechanism and a 6DOF manipulator prototype, composed of a serial chain of 3 double tetrahedra are planned. An efficient, reliable method to analyze the local DOF of this overconstrained mechanism, even in singular regions, was developed. It uses the nullity of the 6-leg Jacobian matrix, composed of Pücker line coordinate vectors of the intersecting edge plane normals. Edge and joint configuration of a mobile pair of tetrahedra is shown in Fig. .
P. Zsombor-Murray, J. Angeles, M. Husty, F. Bulca
A double tetrahedral manipulator.