<p>The introduction of the Delta parallel robot and the SCARA serial manipulator marked a significant milestone in the evolution of industrial robotics. Since then, there has been a growing wave of innovative proposals for robots capable of executing Schönflies motion. Parallel manipulators with identical limbs have played a crucial role in shaping these robotic topologies. However, maintaining symmetry presents crucial challenges, particularly due to the complexity of mechanical assembly and the high precision required in manufacturing. This work explores the kinematics of an innovative Schönflies-motion parallel manipulator through the application of screw theory, an algebraic framework with profound geometric significance. The manipulator is composed of serial kinematic chains with two distinct degrees of freedom. While this design compromises symmetry, it significantly streamlines both kinematic analysis and overall construction. By eliminating passive kinematic chains, it offers a practical alternative to traditional parallel manipulators constructed from closed kinematic chains incorporating parallelogram-type linkages. To ensure the reliability of the proposed kinematic analysis method, numerical validation is performed using an alternative approach: an algorithm based on numerical data fitting.</p>