Linear dynamic modeling of parallel kinematic manipulators from observable kinematic elements

This paper presents a linear method for kinematic and dynamic modeling of parallel kinematic manipulators. This method is simple, compact and clear. One can write all the equations from the beginning till the end with pen and paper. It is thus well suited to mechanical understanding and computer implementation. We can apply it to many parallel robots. This method relies on a body-oriented representation of observable rectilinear kinematic structures (kinematic elements) which form the robot legs.

[1]  Philippe Martinet,et al.  Image-based Visual Servoing of a Gough—Stewart Parallel Manipulator using Leg Observations , 2007, Int. J. Robotics Res..

[2]  Richard M. Murray,et al.  A Mathematical Introduction to Robotic Manipulation , 1994 .

[3]  Jorge Angeles,et al.  The direct kinematics of parallel manipulators under joint-sensor redundancy , 2000, IEEE Trans. Robotics Autom..

[4]  C. Gosselin,et al.  Constraint Singularities as C-Space Singularities , 2002 .

[5]  Erol Özgür,et al.  From lines to dynamics of parallel robots , 2012 .

[6]  Nicolas Andreff,et al.  Vision-based Kinematic Modelling of Some Parallel Manipulators for Control Purposes , 2006 .

[7]  R. Paul Robot manipulators : mathematics, programming, and control : the computer control of robot manipulators , 1981 .

[8]  L. Ribeiro SCREW-BASED RELATIVE JACOBIAN FOR MANIPULATORS COOPERATING IN A TASK , 2007 .

[9]  Herman Bruyninckx,et al.  Unified Kinetostatics for Serial, Parallel and Mobile Robots , 1998 .

[10]  Kenneth J. Waldron,et al.  Series-Parallel Dualities in Actively Coordinated Mechanisms , 1988, Int. J. Robotics Res..

[11]  Jean le Rond d'Alembert,et al.  Traite De Dynamique , 2009 .

[12]  Philippe Martinet,et al.  A Review on the Dynamic Control of Parallel Kinematic Machines: Theory and Experiments , 2009, Int. J. Robotics Res..

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

[14]  J. Y. S. Luh,et al.  On-Line Computational Scheme for Mechanical Manipulators , 1980 .

[15]  Atsushi Konno,et al.  Design and control of a novel 4-DOFs parallel robot H4 , 2003, 2003 IEEE International Conference on Robotics and Automation (Cat. No.03CH37422).

[16]  L. W. Tsai The Jacobian Analysis of a Parallel Manipulator Using the Theory of Reciprocal Screws , 1998 .

[17]  Alon Wolf,et al.  Screw theory tools for the synthesis of the geometry of a parallel robot for a given instantaneous task , 2006 .

[18]  Federico Thomas,et al.  Analytic formulation of the kinestatics of robot manipulators with arbitrary topology , 2002, Proceedings 2002 IEEE International Conference on Robotics and Automation (Cat. No.02CH37292).

[19]  Herman Bruyninckx Dualities between serial and parallel "321" manipulators , 1999, Proceedings 1999 IEEE International Conference on Robotics and Automation (Cat. No.99CH36288C).

[20]  Philippe Poignet,et al.  Predictive functional control for a parallel robot , 2003, Proceedings 2003 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2003) (Cat. No.03CH37453).

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

[22]  Philippe Poignet,et al.  On the Design of a Fast Parallel Robot Based on Its Dynamic Model , 2006, ISER.

[23]  Thomas R. Kane,et al.  Motion Variables Leading to Efficient Equations of Motion , 1996, Int. J. Robotics Res..

[24]  Tao Zhang,et al.  Dynamic modeling of a 6-degree-of-freedom Stewart platform driven by a permanent magnet synchronous motor , 2009, Journal of Zhejiang University SCIENCE C.

[25]  Wisama Khalil,et al.  General Solution for the Dynamic Modeling of Parallel Robots , 2004, IEEE International Conference on Robotics and Automation, 2004. Proceedings. ICRA '04. 2004.

[26]  Joseph Duffy,et al.  A Direct Determination of the Instantaneous Kinematics of Fully Parallel Robot Manipulators , 1985 .

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

[28]  Tej Dallej Contributions à un modèle générique pour l'asservissement visuel des robots parallèles par l'observation des éléments cinématiques , 2007 .