Matrix modeling of inverse dynamics of spatial and planar parallel robots

Recursive matrix relations for kinematics and dynamics analysis of two known parallel mechanisms: the spatial 3-PRS and the planar 3-RRR are established in this paper. Knowing the motion of the platform, we develop first the inverse kinematical problem and determine the positions, velocities, and accelerations of the robot’s elements. Further, the inverse dynamic problem is solved using an approach based on the principle of virtual work, and the results can be verified in the framework of the Lagrange equations with their multipliers. Finally, compact matrix equations and graphs of simulation for power requirement comparison of each of three actuators in two different actuation schemes are obtained. For the same evolution of the moving platform, the power distribution upon the three actuators depends on the actuating configuration, but the total power absorbed by the set of three actuators is the same, at any instant, for both driving systems. The study of the dynamics of the parallel mechanisms is done mainly to solve successfully the control of the motion of such robotic systems.

[1]  D. Stewart.  A Platform with Six Degrees of Freedom , 1965 .

[2]  Thomas R. Kane,et al.  THEORY AND APPLICATIONS , 1984 .

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[18]  Clément Gosselin,et al.  Kinematic Analysis and Optimization of a New Three Degree-of-Freedom Spatial Parallel Manipulator , 2000 .

[19]  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 .

[20]  Jean-Pierre Merlet,et al.  Micro parallel robot MIPS for medical applications , 2001, ETFA 2001. 8th International Conference on Emerging Technologies and Factory Automation. Proceedings (Cat. No.01TH8597).

[21]  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.

[22]  Wisama Khalil,et al.  A novel solution for the dynamic modeling of Gough-Stewart manipulators , 2002, Proceedings 2002 IEEE International Conference on Robotics and Automation (Cat. No.02CH37292).

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

[24]  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).

[25]  T. Shiau,et al.  Direct kinematic analysis of a 3-PRS parallel mechanism , 2003 .

[26]  Qingsong Xu,et al.  Kinematics and inverse dynamics analysis for a general 3-PRS spatial parallel mechanism , 2005, Robotica.

[27]  J. Angeles,et al.  Recursive Kinematics and Inverse Dynamics for a Planar 3R Parallel Manipulator , 2005 .

[28]  J. Angeles,et al.  Modular and Recursive Kinematics and Dynamics for Parallel Manipulators , 2005 .

[29]  Qingsong Xu,et al.  Kinematic analysis of a 3-PRS parallel manipulator , 2007 .

[30]  Yonggang Li,et al.  Inverse Dynamics of 3-RPS Parallel Mechanism Based on Virtual Work Principle , 2007 .

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

[32]  P. Xirouchakis,et al.  Dynamics analysis of a 3-DOF parallel manipulator with R–P–S joint structure , 2007 .

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

[34]  Wisama Khalil,et al.  General Solution for the Dynamic Modeling of Parallel Robots , 2007, J. Intell. Robotic Syst..

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

[36]  Stefan Staicu,et al.  Power requirement comparison in the 3-RPR planar parallel robot dynamics , 2009 .

[37]  Stefan Staicu.  Recursive modelling in dynamics of Delta parallel robot , 2009, Robotica.

[38]  S. Staicu.  Recursive modelling in dynamics of Agile Wrist spherical parallel robot , 2009 .

[39]  Sherman Y.T. Lang,et al.  Joint workspace of parallel kinematic machines , 2009 .

[40]  Stefan Staicu,et al.  Inverse dynamics of the 3-PRR planar parallel robot , 2009, Robotics Auton. Syst..

[41]  S. Staicu,et al.  Explicit dynamics equations of the constrained robotic systems , 2009 .

[42]  Juan A. Carretero,et al.  Architecture optimisation of three 3- P RS variants for parallel kinematic machining , 2009 .