This paper analyzes the kinematics of planar tensegrity ma-nipulators made of two Snelson's X-shape mechanisms in series. The variable instantaneous center of rotation of each mechanism renders the kinematic analysis of the resulting manipulator more challenging. A general formulation of the direct kinematics is set. A method is proposed to solve the inverse kinematic problem in a symbolic way and up to four inverse kinematic solutions are found. The singularities of the manipulator are shown to divide the joint space into two singularity-free components, showing for the first time a planar positioning manipulator that can be cuspidal. The workspace is determined and plotted for different values of the geometric parameters.