The invention provides an
extension method for constructing a rigid foldable multi-tubular structure and a tubular structure. The
extension method comprises the following steps: constructing a three-dimensional
tetrahedron by setting the side length, the interior angle and the
dihedral angle of a planar triangle; extending the bottom edges of the tetrahedrons, and determining new vertexes through geometric constraints to generate adjacent transverse extension tetrahedrons; then determining a heterogeneous
tetrahedron of the basic
tetrahedron through geometric constraint of a BOIII mechanism, and determining an axially extending tetrahedron based on the heterogeneous tetrahedron; the multiple foldable tubular structures are generated by repeating the steps of transverse extension and axial extension and modifying initial side length angle parameters in a matched mode. According to the method, through the steps of basic tetrahedron construction, transverse extension, axial extension and iterative expansion, a set tetrahedron relational expression is met in the process of executing the extension step, so that the problem that the shape complexity of a bent section of the foldable tubular structure needs to be simplified is solved, and the foldable tubular structure which is more flexible and reliable is provided; and the requirements of different
engineering fields are met.