

Department of Engineering  
University of Cambridge > Engineering Department > Research > Structures Group > Research Students 
Tensegrity structures with point group symmetry, T , will have the symmetries of rotations, but not reflections, of a tetrahedron. Since this T group tensegrity structure originates from tetrahedron, this structure has 7 symmetry axes, which are along the vertices and vertex diagonals of tetrahedron. The twelve symmetry operations; the identity, E, rotations by 120° and 240° about the vertices, 1, 2, 3 and 4; { C_{31}, C_{32}, C_{33}, C_{34}, C^{2}_{31}, C^{2}_{32}, C^{2}_{33}, C^{2}_{34} }, and rotation by 180° about the a, b, and c axes, { C_{2a}, C_{2b}, C_{2c} }, form the symmetry group of the example structure. These twelve symmetry operations constitute the symmetry group T. We assume one regular orbit of nodes: there are 12 nodes, which have one to one correspondence with the 12 symmetry operations.
If we choose to have:
1) a strut connecting node E to node C_{2a} with tension coefficient t_{s};
2) cable 1 connecting nodes E to node C_{31}, and node C^{2}_{31} with tension coefficient t_{t}; and
3) cable 2 connecting nodes E to node C_{32}, and node C^{2}_{32} with tension coefficient t_{d};
then solution t_{t}/t_{s} = t_{d}/t_{s} = 1 gives the tensegrity structure T_{1}.
If we choose to have:
1) a strut connecting node E to node C_{2a} with tension coefficient t_{s};
2) cable 1 connecting nodes E to node C_{31}, and node C^{2}_{31} with tension coefficient t_{t}; and
3) connecting nodes E to node C_{33}, and node C^{2}_{33} with tension coefficient t_{d};
then solution t_{t}/t_{s} = t_{d}/t_{s} = 0.67 gives the tensegrity structure T_{2}.
If we choose to have:
1) a strut connecting node E to node C_{2a} with tension coefficient t_{s};
2) cable 1 connecting nodes E to node C_{31}, and node C^{2}_{31} with tension coefficient t_{t}; and
3) cable 2 connecting node E to node C_{2b} with tension coefficient t_{d},
then solution t_{t}/t_{s} = t_{d}/t_{s} = 1.74 gives the tensegrity structure T_{3}.
If we choose to have:
1) a strut connecting nodes E to node C_{31}, and node C^{2}_{31} with tension coefficient t_{s};
2) cable 1 connecting nodes E to node C_{32}, and node C^{2}_{32} with tension coefficient t_{t}; and
3) cable 2 connecting nodes E to node C_{33}, and node C^{2}_{33} with tension coefficient t_{d};
then solution t_{t}/t_{s} = t_{d}/t_{s} = 1.5 gives the tensegrity structure T_{4}.
If we choose to have:
1) a strut connecting nodes E to node C_{31}, and node C^{2}_{31} with tension coefficient t_{s};
2) cable 1 connecting nodes E to node C_{32}, and node C^{2}_{32} with tension coefficient t_{t}; and
3) cable 2 connecting node E to node C_{2a} with tension coefficient t_{d},
then solution t_{t}/t_{s} = t_{d}/t_{s} = 3 gives the tensegrity structure T_{5}.
If we choose to have:
1) a strut connecting nodes E to node C_{31}, and node C^{2}_{31} with tension coefficient t_{s};
2) cable 1 connecting nodes E to node C_{32}, and node C^{2}_{32} with tension coefficient t_{t}; and
3) cable 2 connecting node E to node C_{2b} with tension coefficient t_{d},
then solution t_{t}/t_{s} = t_{d}/t_{s} = 2.47 gives the tensegrity structure T_{6}.