Triangular bipyramid

Abstract: The present invention concerns a building block toy, characterized in that a single kind of building block is used and in that the building block is of a unique shape. Specifically, the center of a flat equilateral triangular piece and the center of a flat hexagonal piece with the same thickness can be overlapped, and the three conjugated sides of the hexagonal piece can be connected to the three sides of the equilateral triangular piece upon stacking these two pieces in a parallel manner. The length of each side of the equilateral hexagonal piece is ⅓ of that of the side of the equilateral triangular piece. Thus, the parts where the equilateral triangular piece and the equilateral hexagonal piece overlap form three small equilateral triangular pieces ( 1, 2 and 3 ) of equal size. More importantly, one of the three small equilateral triangular pieces ( 1 ) is removed and transferred to the side of the hexagonal piece for connection in such a manner that the direct-view diagram of the front side or back side of the equilateral triangular block of the present invention shows an equilateral triangle. In addition, the front side of the equilateral triangular block of the present invention is equipped with projectiles ( 4, 5 and 6 ) (that is, on the three small equilateral triangles and the equilateral hexagon), and the back side is equipped with cups ( 7, 8 and 9 ) at positions opposite the projectiles, so that the equilateral triangular building blocks can be stacked together by means of the projectiles and cups.

Abstract: The complete, closed-form exact solutions for the hollow equilateral triangular waveguide are presented. Both TM and TE mode shapes are determined.

Abstract: In this paper, a tetrahedron unit constructed by connecting three links to a node via revolute joints is proposed. A closed loop mechanism is constructed by combining two tetrahedrons units to share a common face with three spherical joints such that the geometric structure of the mechanism is a triangular bipyramid. We show that the structure of the mechanism enables it possess a rolling function when proceeding on the ground. Furthermore, with the similar topology structure, two more closed-loop rolling mechanisms are obtained by combining 4 and 6 units, respectively. Due to the similar rolling principles of the proposed mechanisms, it suffices to analyze the rolling feasibility of the triangular bipyramid mechanism. By analyzing the kinematics, the deformation features of the mechanism are obtained. Upon some proper controls, we show that these features enable the mechanism to roll and switch directions when it proceeds on the ground. These functions are verified by a series of simulations with a 3D model and experiments with a prototype.

Abstract: Traditional methods and theories on synthesizing parallel mechanisms are not applicable to related researches on hybrid mechanisms, thus hampering the design of innovative coupled mechanisms. Polyh...