Comparative Kinematics and Static Analysis of Regular and Irregular Hexagonal Stewart–Gough Platform Configurations

The Stewart–Gough Platform (SGP) is a spatial parallel manipulator offering high accuracy, rigidity, and adaptability, with applications spanning medical systems, marine engineering, agriculture, manufacturing, entertainment, aerospace, and architectural installations. This paper presents a comparative analytical and computational study of three SGP configurations: the regular SGP, with regular hexagonal base and top platforms; the Irregular-Parallel SGP, derived from the regular SGP by a novel graphical decomposition-and-modification procedure and characterized by similar symmetric hexagonal platforms with limbs preserved parallel; and the Irregular-Skewed SGP, in which the irregular hexagonal platforms of the Irregular-Parallel SGP are retained, but the limbs are connected in an inclined, alternating clockwise (or anticlockwise) topology. The Irregular–Skewed SGP is free from the constraint singularity that persists in the first two configurations and requires the shortest maximum actuator stroke. Static force analysis shows that the regular SGP and the Irregular–Parallel SGP both exhibit a rank-deficient rigidity matrix (rank = 3) across the geometric scaling range tested (radius ratios 1:2 to 1:10; inter-platform distances 100–1000 mm), whereas the Irregular-Skewed SGP achieves full rank (rank = 6) through inclined limb connectivity and is the only configuration capable of sustaining static equilibrium under the loading conditions examined. The forward kinematics of the Irregular-Parallel SGP is verified against a SolidWorks model: under a 9 mm uniform limb extension, the MATLAB and SolidWorks positions of node 7 agree to within 1.27 mm. The rotational workspace volume is equivalent across the three configurations, but the density of valid solution points within that workspace differs. The workspace within joint limits, alternating compression–tension force partition, and asymmetric stroke economy of the Irregular-Skewed SGP indicate applicability to kinetic facades and transformable interiors in architectural-robotics deployment.