Kinematics of A 3-PRP planar parallel robot

Articolul prezintă o modelare recurentă pentru cinematica unui robot paralel plan 3-PRP. Trei lanţuri cinematice plane ce conectează platforma mobilă a manipulatorului sunt situate in plan vertical. Cunoscând miscarea platformei, se dezvoltă cinematica inversă si se determină poziţiile, vitezele si acceleraţiile robotului. Unele ecuaţii matriceale oferă expresii iterative si grafice pentru deplasările, vitezele si acceleraţiile celor trei acţionori de translaţie. Recursive modelling for the kinematics of a 3-PRP planar parallel robot is presented in this paper. Three planar chains connecting the moving platform of the manipulator are located in a vertical plane. Knowing the motion of the platform, we develop the inverse kinematics and determine the positions, velocities and accelerations of the robot. Several matrix equations offer iterative expressions and graphs for the displacements, velocities and accelerations of the three prismatic actuators.

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

[2]  Lung-Wen Tsai,et al.  A Parallel Manipulator with Only Translational Degrees of Freedom , 1997 .

[3]  Dasgupta Bhaskar,et al.  A Newton-Euler formulation for the inverse dynamics of the Stewart platform manipulator , 1998 .

[4]  Stefan Staicu Inverse dynamics of a planetary gear train for robotics , 2008 .

[5]  Gordon R. Pennock,et al.  Kinematic Analysis of a Planar Eight-Bar Linkage: Application to a Platform-Type Robot , 1992 .

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

[7]  Stefan Staicu,et al.  Dynamic analysis of Clavel's Delta parallel robot , 2003, 2003 IEEE International Conference on Robotics and Automation (Cat. No.03CH37422).

[8]  Weihai Chen,et al.  A geometrical method for the singularity analysis of 3-RRR planar parallel robots with different actuation schemes , 2002, IEEE/RSJ International Conference on Intelligent Robots and Systems.

[9]  Jean-Pierre Merlet,et al.  Direct kinematics of planar parallel manipulators , 1996, Proceedings of IEEE International Conference on Robotics and Automation.

[10]  Hassan Zohoor,et al.  Comments to the: “Closed-form dynamic equations of the general Stewart platform through the Newton–Euler approach” and “A Newton–Euler formulation for the inverse dynamics of the Stewart platform manipulator” , 2008 .

[11]  C. Gosselin,et al.  On the quadratic nature of the singularity curves of planar three-degree-of-freedom parallel manipulators , 1995 .

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

[13]  Damien Chablat,et al.  Kinematics and workspace analysis of a three-axis parallel manipulator: the Orthoglide , 2005, Robotica.

[14]  Clément Gosselin,et al.  A New Approach for the Dynamic Analysis of Parallel Manipulators , 1998 .

[15]  Raffaele Di Gregorio,et al.  A New Algorithm Based on Two Extra-Sensors for Real-Time Computation of the Actual Configuration of the Generalized Stewart-Gough Manipulator , 2000 .

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

[17]  StaicuStefan,et al.  Dynamic modelling of a 3-DOF parallel manipulator using recursive matrix relations , 2006 .

[18]  Jean-Pierre Merlet,et al.  Parallel Robots , 2000 .

[19]  P. Zsombor-Murray,et al.  Singularity analysis of planar parallel manipulators , 1995 .

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

[21]  Leonard S. Haynes,et al.  On the dynamic model and kinematic analysis of a class of Stewart platforms , 1992, Robotics Auton. Syst..

[22]  C. Gosselin,et al.  Singularity Analysis of 3-DOF Planar Parallel Mechanisms via Screw Theory , 2003 .

[23]  Wisama Khalil,et al.  Modélisation Dynamique d'un Robot Parallèle à 3-DDL : l'Orthoglide , 2007, ArXiv.

[24]  S. Staicu,et al.  A novel dynamic modelling approach for parallel mechanisms analysis , 2008 .

[25]  C. Gosselin,et al.  The optimum kinematic design of a spherical three-degree-of-freedom parallel manipulator , 1988 .

[26]  Xin-Jun Liu,et al.  Inverse dynamics of the HALF parallel manipulator with revolute actuators , 2007 .

[27]  R. Clavel,et al.  A Fast Robot with Parallel Geometry , 1988 .

[28]  D. Stewart,et al.  A Platform with Six Degrees of Freedom , 1965 .

[29]  P. Zsombor-Murray,et al.  The Kinematics of 3-DOF Planar and Spherical Double-Triangular Parallel Manipulators , 1993 .

[30]  Liping Wang,et al.  Inverse dynamics and simulation of a 3-DOF spatial parallel manipulator , 2003, 2003 IEEE International Conference on Robotics and Automation (Cat. No.03CH37422).

[31]  Dan Zhang,et al.  Dynamic modelling of a 3-DOF parallel manipulator using recursive matrix relations , 2005, Robotica.