Accuracy and stiffness analysis of a 3-RRP spherical parallel manipulator

In this paper, accuracy and stiffness analysis of a 3-RRP spherical parallel manipulator (SPM) (Enferadi and Tootoonchi, A novel spherical parallel manipulator: Forward position problem, singularity analysis and isotropy design, Robotica, vol. 27, 2009, pp. 663–676) with symmetrical geometry is investigated. At first, the 3-RRP SPM is introduced and its inverse kinematics analysis is performed. Isotropic design, because of its design superiority, is selected and workspace of the manipulator is obtained. The kinematics conditioning index (KCI) is evaluated on the workspace. Global conditioning index (GCI) of the manipulator is calculated and compared with another SPM. Unlike traditional stiffness analysis, the moving platform is assumed to be flexible. A continuous method is used for obtaining mathematical model of the manipulator stiffness matrix. This method is based on strain energy and Castigliano's theorem. The mathematical model is verified by finite element model. Finally, using mathematical model, kinematics stiffness index (KSI), and global stiffness index (GSI) are evaluated.

[1]  Feng Gao,et al.  The global conditioning index in the solution space of two degree of freedom planar parallel manipulators , 1995, 1995 IEEE International Conference on Systems, Man and Cybernetics. Intelligent Systems for the 21st Century.

[2]  Jorge Angeles,et al.  The Computation of All 4R Serial Spherical Wrists With an Isotropic Architecture , 2007, ArXiv.

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

[4]  Charles A. Klein,et al.  Dexterity Measures for the Design and Control of Kinematically Redundant Manipulators , 1987 .

[5]  Charles W. Wampler,et al.  On a Rigid Body Subject to Point-Plane Constraints , 2006 .

[6]  Lung-Wen Tsai,et al.  Kinematic Analysis of 3-DOF Position Mechanisms for Use in Hybrid Kinematic Machines , 2002 .

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

[8]  Jorge Angeles,et al.  Fundamentals of Robotic Mechanical Systems: Theory, Methods, and Algorithms , 1995 .

[9]  C. Gosselin.  The optimum design of robotic manipulators using dexterity indices , 1992, Robotics Auton. Syst..

[10]  Qingsong Xu,et al.  An investigation on mobility and stiffness of a 3-DOF translational parallel manipulator via screw theory , 2008 .

[11]  J. Kenneth Salisbury,et al.  Articulated Hands , 1982 .

[12]  Qingsong Xu,et al.  Stiffness analysis for a 3-PUU parallel kinematic machine , 2008 .

[13]  Jorge Angeles,et al.  Fundamentals of Robotic Mechanical Systems , 2008 .

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

[15]  Clément Gosselin,et al.  A Global Performance Index for the Kinematic Optimization of Robotic Manipulators , 1991 .

[16]  Feng Gao,et al.  Criteria based analysis and design of three degree of freedom planar robotic manipulators , 1997, Proceedings of International Conference on Robotics and Automation.

[17]  Clément Gosselin,et al.  Determination of the workspace of planar parallel manipulators with joint limits , 1996, Robotics Auton. Syst..

[18]  M. Ceccarelli,et al.  A stiffness analysis for CaPaMan (Cassino Parallel Manipulator) , 2002 .

[19]  John J. Craig,et al.  Introduction to Robotics Mechanics and Control , 1986 .

[20]  Michael M. Stanišić,et al.  Design of an Overconstrained and Dextrous Spherical Wrist , 2000 .

[21]  Phillip J. McKerrow,et al.  Introduction to robotics , 1991 .

[22]  Clément Gosselin,et al.  Workspaces of Planar Parallel Manipulators , 1998 .

[23]  John J. Craig Zhu,et al.  Introduction to robotics mechanics and control , 1991 .

[24]  Feng Gao,et al.  Optimum design of 3-DOF spherical parallel manipulators with respect to the conditioning and stiffness indices , 2000 .

[25]  John J. Craig,et al.  Articulated hands: Force control and kinematic issues , 1981 .

[26]  Soumya Bhattacharya,et al.  On the optimum design of Stewart platform type parallel manipulators , 1995, Robotica.

[27]  Raffaele Di Gregorio.  The 3-RRS Wrist: A New, Simple and Non-Overconstrained Spherical Parallel Manipulator , 2004 .

[28]  Placid Mathew Ferreira,et al.  Computation of stiffness and stiffness bounds for parallel link manipulators 1 This research was sup , 1999 .

[29]  K. C. Gupta,et al.  On the Nature of Robot Workspace , 1986 .

[30]  Roger Boudreau,et al.  Synthesis of Planar Parallel Mechanisms While Considering Workspace, Dexterity, Stiffness and Singularity Avoidance , 2006 .

[31]  Feng Gao,et al.  Performance evaluation of two-degree-of-freedom planar parallel robots , 1998 .

[32]  Carl D. Crane,et al.  Stiffness mapping of planar compliant parallel mechanisms in a serial arrangement , 2006, ARK.

[33]  Raffaele Di Gregorio.  A new family of spherical parallel manipulators , 2002, Robotica.

[34]  Ilian A. Bonev,et al.  Geometric approach to the accuracy analysis of a class of 3-DOF planar parallel robots , 2008 .

[35]  Vijay Kumar,et al.  Characterization of Workspaces of Parallel Manipulators , 1992 .

[36]  Javad Enferadi,et al.  A novel spherical parallel manipulator: forward position problem, singularity analysis, and isotropy design , 2009, Robotica.

[37]  Xiaoqiang Tang,et al.  A novel 2-DOF parallel mechanism based design of a new 5-axis hybrid machine tool , 2003, 2003 IEEE International Conference on Robotics and Automation (Cat. No.03CH37422).

[38]  J. Merlet.  Jacobian, Manipulability, Condition Number and Accuracy of Parallel Robots , 2005, ISRR.