Kinematic Modeling of a Novel (31)-Degree-of-Freedom Planar Parallel Manipulator Using Screw Theory+

This work presents the kinematic analysis of a redundant planar parallel manipulator within the framework of screw theory. The main contribution of this work is the introduction and kinematic modeling of a novel redundant planar parallel manipulator topology composed exclusively of revolute joints. The proposed architecture is motivated by the search for structurally simple mechanisms with favorable analytical properties for screw-theoretic formulation and potential applications in robotic systems requiring compact and efficient planar motion. For completeness, the displacement analysis is included. Thanks to the simple topology of the otherwise complex mechanism, the inverse–forward displacement problem is resolved through straightforward quadratic equations. The velocity input–output relationship is derived without reliance on passive joint rate velocities, and the acceleration input–output equation is obtained independently of passive joint rate accelerations. These simplifications are achieved by exploiting reciprocal line properties. Numerical examples are provided to illustrate the robustness and effectiveness of the proposed kinematic analysis method across the main topics addressed in this contribution.