Kinematic and Dynamic Analysis of the Gantry-tau, a 3-DoF Translational Parallel Manipulator

Abstract This paper deals with the mathematical modeling of kinematics and dynamics of the 3-degrees-of-freedom Gantry-Tau manipulator. Compared to many other parallel robots, Gantry-Tau offers a large accessible workspace and high stiffness. The kinematics of Gantry-Tau is presented which includes inverse kinematics formulation for the position, velocity and acceleration of the mechanism. Also, based on the obtained Jacobin matrices, singular configurations of the robot are studied. Afterwards, the equations of the inverse dynamic model of the Gantry-Tau are obtained through two different methods, i.e., virtual work and Newton–Euler. Finally, a case study is performed to verify the correctness of the derived models and investigate their computational efficiency.

[1]  Bhaskar Dasgupta,et al.  Closed-Form Dynamic Equations of the General Stewart Platform through the Newton–Euler Approach , 1998 .

[2]  J Zahariev,et al.  Dynamics of over-constrained rigid and flexible multibody systems , 2007 .

[3]  K. Srinivasan,et al.  Kinematic and dynamic analysis of Stewart platform-based machine tool structures , 2003, Robotica.

[4]  Chao Chen,et al.  Inverse dynamic modelling of a three-legged six-degree-of-freedom parallel mechanism , 2017 .

[5]  Viktor Berbyuk,et al.  Gantry-Tau A New Three Degrees of Freedom Parallel Kinematic Robot , 2003 .

[6]  Torgny Brogårdh,et al.  Kinematic optimisation of the gantry-tau parallel kinematic manipulator with respect to its workspace , 2007 .

[7]  Z. M. Bi,et al.  Dynamic modeling and validation of a tripod-based machine tool , 2008 .

[8]  Yangmin Li,et al.  Dynamic analysis of a 3-DOF 3-PUU parallel manipulator based on the principle of virtual work , 2015, 2015 IEEE International Conference on Advanced Intelligent Mechatronics (AIM).

[9]  Alireza Akbarzadeh,et al.  Dynamics analysis of a 3-RRP spherical parallel manipulator using the natural orthogonal complement , 2013 .

[10]  Ilya Tyapin,et al.  Kinematic and Elastostatic Design Optimisation of the 3-DOF Gantry-Tau Parallel Kinematic Manipulator , 2009 .

[11]  Geir Hovland,et al.  Benchmark of the 3-DOF Gantry-Tau Parallel Kinematic Machine , 2007, Proceedings 2007 IEEE International Conference on Robotics and Automation.

[12]  Clément Gosselin,et al.  Singularity analysis of closed-loop kinematic chains , 1990, IEEE Trans. Robotics Autom..

[13]  Anders Robertsson,et al.  A kinematic error model for a parallel Gantry-Tau manipulator , 2010, 2010 IEEE International Conference on Robotics and Automation.

[14]  Anders Robertsson,et al.  Accuracy of Kinematic and Dynamic Models of a Gantry-Tau Parallel Kinematic Robot , 2007, Proceedings 2007 IEEE International Conference on Robotics and Automation.

[15]  L. Tsai.  Solving the Inverse Dynamics of a Stewart-Gough Manipulator by the Principle of Virtual Work , 2000 .

[16]  Jian S. Dai,et al.  Joint force decomposition and variation in unified inverse dynamics analysis of a metamorphic parallel mechanism , 2016 .

[17]  Shin-Min Song,et al.  An efficient method for inverse dynamics of manipulators based on the virtual work principle , 1993, J. Field Robotics.

[18]  Clément Gosselin,et al.  Parallel Mechanisms and Robots , 2008, Springer Handbook of Robotics.

[19]  Alain Codourey,et al.  Dynamic Modeling of Parallel Robots for Computed-Torque Control Implementation , 1998, Int. J. Robotics Res..

[20]  L. W. Tsai,et al.  Robot Analysis: The Mechanics of Serial and Parallel Ma-nipulators , 1999 .

[21]  Saeid Nahavandi,et al.  Mathematical modelling of linear motion error for Hexarot parallel manipulators , 2016 .

[22]  Clément Gosselin.  Compact dynamic models for the tripteron and quadrupteron parallel manipulators , 2009 .

[23]  Saeid Nahavandi,et al.  The Octahedral Hexarot — A novel 6-DOF parallel manipulator , 2012 .

[24]  Geir Hovland,et al.  Kinematic error calibration of the Gantry-Tau parallel manipulator , 2006, Proceedings 2006 IEEE International Conference on Robotics and Automation, 2006. ICRA 2006..

[25]  Yang Li,et al.  Configuration and singularity analysis of a parallel hip joint simulator based on the forward kinematics , 2016 .

[26]  Geir Hovland,et al.  Application-oriented development of parallel kinematic manipulators with large workspace , 2005 .

[27]  Ilya Tyapin,et al.  MULTI-OBJECTIVE DESIGN OPTIMISATION OF A CLASS OF PKMS - THE 3-DOF GANTRY-TAU , 2010, ICMIC 2010.

[28]  C. Reboulet,et al.  Dynamic models of a six degree of freedom parallel manipulators , 1991, Fifth International Conference on Advanced Robotics 'Robots in Unstructured Environments.

[29]  Saeid Nahavandi,et al.  Parallel Manipulators With a Rotation-Symmetric Arm System , 2012 .

[30]  Saeid Nahavandi,et al.  A method for extending planar axis-symmetric parallel manipulators to spatial mechanisms , 2015 .

[31]  Zhuming Bi,et al.  An Inverse Dynamic Model of Over-Constrained Parallel Kinematic Machine Based on Newton–Euler Formulation , 2014 .

[32]  Mohsen Shahinpoor,et al.  Inverse dynamics of a parallel manipulator , 1994, J. Field Robotics.

[33]  Bhaskar Dasgupta,et al.  A Newton-Euler Formulation for the Inverse Dynamics of the Stewart Platform Manipulator , 1998 .

[34]  Torgny Brogårdh,et al.  Kinematic analysis and error modeling of TAU parallel robot , 2005 .

[35]  Hui Zhang,et al.  Kinematic and dynamic modelling for real-time control of Tau parallel robot , 2005 .

[36]  Reymond Clavel,et al.  The Lagrange-based model of Delta-4 robot dynamics , 1992, Robotersysteme.

[37]  J. Angeles,et al.  The Formulation of Dynamical Equations of Holonomic Mechanical Systems Using a Natural Orthogonal Complement , 1988 .

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

[39]  Min-Jie Liu,et al.  Dynamics analysis of the Gough-Stewart platform manipulator , 2000, IEEE Trans. Robotics Autom..

[40]  Bo Hu,et al.  Unified solving inverse dynamics of 6-DOF serial–parallel manipulators , 2015 .