Kinematic and static analysis of a planar two-degree-of-freedom parallel manipulator

In this paper, the kinematics and statics of a planar seven-link two-degree-of-freedom parallel manipulator are studied. After introducing the mechanism, a kinematic analysis is reported. Then, velocity equations are derived which leads to the analysis of the singularities of the manipulator. Based on the geometry of the manipulator, a workspace analysis is performed and a description of the boundaries of the workspace is provided. Finally, a static analysis is presented and algorithms to compute joint or Cartesian forces and torques are proposed. This manipulator can be used in robotic applications involving the positioning of a point on the plane with high stiffness or accuracy. Additionally, the mechanism can find applications in motion simulators or other high-precision or high-bandwidth devices.