Synthesis and Networking of Spaceborne Deployable Prismatic Antenna Mechanisms Based on Graph Theory

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Spaceborne deployable cylindrical antennas have broad application prospects in the fields of space earth observation and remote-sensing detection because of their significant advantages of ultralong aperture, high gain, and flexible beam scanning. As application requirements rapidly develop, a new type of spaceborne deployable cylindrical antenna mechanism with a large diameter and deployability is urgently needed. This paper presents an innovative design for a cylindrical deployable antenna mechanism based on 18R triangular prism elements based on graph theory. The correctness of the configuration is verified by developing a prototype. First, four kinds of nonoverconstrained 12-bar triangular prism-stabilized truss structure configurations and their corresponding topological diagrams are constructed. Second, based on graph theory, three types of 102 triangular prism-stabilized truss mechanism configurations that can be folded into linear mechanisms are derived. Third, the kinematic pair configuration is established to achieve a single-degree-of-freedom 7R2U9S triangular prism deployable unit. Fourth, combined with the geometric topology characteristics of the unit network, a triangular prism unit networking method is proposed, and a cylindrical network mechanism configuration based on 18R triangular prism units is obtained. A prototype was fabricated by 3D printing, and an expansion and retraction function test was conducted, which verified the correctness of the theoretical analysis in this paper. Finally, a new concept configuration for a parabolic cylindrical antenna is proposed. This paper provides a reference for the configuration of large-scale folding truss structures with unit expansion.