Scissor mechanisms are used as deployable structures in industrial products, architecture, and aerospace structures. In general, tubular scissor mechanisms (TSMs), composed of scissor-like elements on their surrounding facets, extend collinearly to serve as lifters, masts, and bridges. Furthermore, curved TSMs can form circular arches to serve as spatial frames and space antennas. However, previous studies proposed limited configurations of TSM models and did not present detailed geometrical formulations. This paper presents new compositions of curved TSMs that can extend by winding two-dimensionally or twisting three-dimensionally. Detailed geometrical formulations of the scissor-like elements were analytically derived to generate a variety of extended shapes. In addition to the numerical simulations using 3D CAD, physical models were assembled to verify their deployability considering realistic sizes of bars and joints. This work widens the deployability of extendable scissors mechanisms, which will eventually broaden the usage of this structure in practical applications.