In this paper, the use of the Kresling tower origami as a building block for compliant mechanism design is considered. Two contributions are introduced to develop a synthesis method of such a building block. First, models to link the origami pattern geometry to the Kresling tower kinematics are derived. The position of stable configurations, the lead angle of its helical motion are expressed as functions of the pattern parameters. Experimental validation of the models is performed. Second, a modification of pattern by local adjustment of fold geometry is introduced. This aims at modifying the origami stiffness without affecting the kinematics. The use of modified fold geometries is experimentally investigated. The capacity to strongly modify the stiffness level is observed, which is encouraging to go towards a synthesis method with decoupling of kinematics and stiffness selection.