This research deals with the methodical derivation of single degree-of-freedom (dof) deployable and transformable linkages with antiparallelogram loops. The study starts with the review of literature on the mechanisms used in planar deployable structures, scissor mechanisms in particular. Scissor mechanisms have been subject of many research, including those that examine them in term of the loops formed. In this research, a summary of the loops observed in previous researches are mentioned. The simplest single-dof linkage is the four-bar linkage. Its loop geometry is quadrilateral. The loops defined formerly in the deployable structures literature are compared to the geometries classified under quadrilaterals and seen that use of antiparallelogram loops are yet to be discovered. While forming novel linkages with antiparallelogram loops, the loop assembly method that Hoberman utilized during his discovery of angulated scissor linkages is used. In order to lay out alternatives of loop arraying options, pattern generating methods are examined. Frieze group operations are found to be most suitable. Using those, loop assembly variations are formed. Later, links formed by these arrays are determined and linkages are formed, modelled and simulated using Solidworks®. Among many alternatives, five of them are chosen due to their novelties in specific aspects. In conclusion findings are compared to the previous research in the literature. Potentials of the novel linkages in terms of architecture are discussed and further research subjects are offered.