<p>For the safe lifting of oversized and heavy equipment on floating platforms at sea, a double-boom lifting system with anti-swing function is introduced based on the multi-loop mechanism theory, which is a typical floating-base, cable-suspended, spatial multi-loop, underdactuated mechanism system. A 51-DOF rigid-flexible coupling mechanism, predominantly comprising UPPeS elastic branches, is obtained via equivalence. To decrease the modelling difficulty, the displacement decoupling of actual inputs and unactuated DoFs is achieved by constructing 3P3R generalised nominal branches with nominal inputs. On this basis, the velocity and acceleration models of a nominal mechanism, containing S3R closed-loops, floating-base, and multi-base <i>n</i>-UPS/3P3R loops, are built using the screw theory. The mechanism by which cable-suspension topology affects motion transfer characteristics is studied by the influence coefficient method. A dynamics modelling method using nominal constraint wrenches is proposed for a floating-base {2-[(3-UPS/3P3R)(2-UPS/3P3R)]}(4-UPS/3P3R) cable-suspension system with 16 unactuated DoFs and piecewise non-smooth characteristic. Singularity analysis and simulations validate the theoretical model and reveal the problem of large out-plane inclination of hoisting cables and resonance. A refined cable-suspension topology with a double-hook tensioning cable is presented. This study lays a foundation for dynamic characteristic analysis and anti-swing control.</p>