The compressibility properties of systems consisting of generic rotating rigid triangles are analyzed and discussed.It is shown that these systems which are usually associated with auxeticity can exhibit strongly anisotropic properties for certain conformations,which may give rise to the anomalous property of negative linear compressibility (NLC),that is,the system with particular geometry will expand along one direction when loaded hydrostatically.It is also shown that through carefully choosing the geometric features (i.e.the dimensions and the alignment of the rotating triangles as well as the angles between them) and the direction along which the linear compressibility is measured,one may control the magnitude and range of the NLC.All this provides a novel but effective method of manufacturing the systems which can be tailored to achieve particular values of NLC to fit particular practical applications.