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This paper describes the optimal design of a 3-DOF redundant planar parallel kinematic mechanism (PKM) based finishing cut stage to improve the surface roughness of FDM 3D printed sculptures. First, to obtain task-optimized and singularity minimum workspace of the redundant PKM, a weighted grid map based design optimization was applied for a task-optimized workspace without considering the redundancy. For the singularity minimum workspace, the isotropy and manipulability of the end effector of the PKM were carefully modeled under the previously obtained redundancy for optimality. It was confirmed that the workspace size increased by 81.4%, and the internal singularity significantly decreased. To estimate the maximum rated torque and torsional stiffness of all active joints and prevent an undesired end effector displacement of more than 200 μμm, a kinematic stiffness model composed of active and passive kinematic stiffness was derived from the virtual work theorem, and the displacement characteristic at the end effector was examined by applying the reaction force for the PLA surface finishing as an external force acting at the end effector. It was confirmed that the displacement of the end effector of a 1-DOF redundant PKM was not only less than 200 μμm but also decreased from 40.9% to 67.4% compared to a nonredundant actuation.

mathematics

Design Optimization of 3-DOF Redundant Planar Parallel Kinematic Mechanism Based Finishing Cut Stage for Improving Surface Roughness of FDM 3D Printed Sculptures