Optimal design of a 2-DOF parallel manipulator with actuation redundancy considering kinematics and natural frequency

In this paper, a planar 2-DOF parallel manipulator with actuation redundancy is proposed and the optimal design considering kinematics and natural frequency is presented. The stiffness matrix and mass matrix are derived, and the structural dynamics is modeled. The natural frequency is obtained on the basis of dynamic model. Based on the kinematic performance, the range for link length is given. Then, considering the natural frequency, the geometry is optimized. The natural frequency is simulated and compared with the corresponding non-redundant parallel manipulator. The designed redundant parallel manipulator has desired kinematic performance and natural frequency and is incorporated into a 4-DOF hybrid machine tool. Highlights? A novel parallel manipulator with actuation redundancy is proposed. ? The natural frequency and displacement response are determined. ? Optimal design of the manipulator based on kinematics and natural frequency is presented. ? The redundant parallel manipulator has a higher natural frequency than its counterpart.

[1]  Clément Gosselin,et al.  Parametric Stiffness Analysis of the Orthoglide , 2004, ArXiv.

[2]  J Wang,et al.  Dimensional synthesis and dynamic manipulability of a planar two-degree-of-freedom parallel manipulator , 2008 .

[3]  Tatsuo Arai,et al.  A modified Stewart platform manipulator with improved dexterity , 1993, IEEE Trans. Robotics Autom..

[4]  Lung-Wen Tsai,et al.  A comparison study of two 3-DOF parallel manipulators: one with three and the other with four supporting legs , 2003, IEEE Trans. Robotics Autom..

[5]  De-Qing Kong.  Dynamic Modeling and Robust Trail Tracking Control of 3-DOF Translational Parallel Kinematic Machine Driven by AC Servo Motors , 2007 .

[6]  Sébastien Briot,et al.  On the optimal design of parallel robots taking into account their deformations and natural frequencies , 2009, ArXiv.

[7]  A. Müller,et al.  Model-based control of redundantly actuated parallel manipulators in redundant coordinates , 2012, Robotics Auton. Syst..

[8]  Tian Huang,et al.  Stiffness estimation of a tripod-based parallel kinematic machine , 2002, IEEE Trans. Robotics Autom..

[9]  Clément Gosselin,et al.  On the Kinematic Design of Spherical Three-Degree-of- Freedom Parallel Manipulators , 1993, Int. J. Robotics Res..

[10]  Carlo Menon,et al.  Geometrical Optimization of Parallel Mechanisms Based on Natural Frequency Evaluation: Application to a Spherical Mechanism for Future Space Applications , 2009, IEEE Transactions on Robotics.

[11]  J. Merlet,et al.  Multi-criteria optimal design of parallel manipulators based on interval analysis , 2005 .

[12]  Xin-Jun Liu,et al.  On the optimal kinematic design of the PRRRP 2-DoF parallel mechanism , 2006 .

[13]  Vincent Hayward,et al.  Multiple-goal kinematic optimization of a parallel spherical mechanism with actuator redundancy , 1992, IEEE Trans. Robotics Autom..

[14]  Clément Gosselin,et al.  Stiffness mapping for parallel manipulators , 1990, IEEE Trans. Robotics Autom..

[15]  K. Miller,et al.  Optimal kinematic design of spatial parallel manipulators: Application to Linear Delta robot , 2003 .

[16]  Il Hong Suh,et al.  Optimal design and development of a five-bar finger with redundant actuation , 2001 .

[17]  Jun Wu,et al.  Optimal Kinematic Design and Application of a Redundantly Actuated 3DOF Planar Parallel Manipulator , 2008 .