Integrating Dynamics into Design and Motion Optimization of a 3-PRR Planar Parallel Manipulator with Discrete Time Transfer Matrix Method

This paper presents a novel method of dynamic modeling and design optimization integrated with dynamics for parallel robot manipulators. Firstly, a computationally efficient modeling method, the discrete time transfer matrix method (DT-TMM), is proposed to establish the dynamic model of a 3-PRR planar parallel manipulator (PPM) for the first time. The numerical simulations are performed with both the proposed DT-TMM dynamic modeling and the ADAMS modeling. The applicability and effectiveness of DT-TMM in parallel manipulators are verified by comparing the numerical results. Secondly, the design parameters of the 3-PRR parallel manipulator are optimized using the kinematic performance indices, such as global workspace conditioning index (GWCI), global condition index (GCI), and global gradient index (GGI). Finally, a dynamic performance index, namely, driving force index (DFI), is proposed based on the established dynamic model. The described motion trajectory of the moving platform is placed into the optimized workspace and the initial position is determined to finalize the end-effector trajectory of the parallel manipulator by the further optimization with the integrated kinematic and dynamic performance indices. The novelty of this work includes (1) developing a new dynamic model method with high computation efficiency for parallel robot manipulators using DT-TMM and (2) proposing a new dynamic performance index and integrating the dynamic index into the motion and design optimization of parallel robot manipulators.

[1]  Xianmin Zhang,et al.  A New Calibration Method for a Directly Driven 3PRR Positioning System , 2017, J. Intell. Robotic Syst..

[2]  Kenneth J. Waldron,et al.  The Workspaces of a Mechanical Manipulator , 1981 .

[3]  Doina Pisla,et al.  Development of inverse dynamic model for a surgical hybrid parallel robot with equivalent lumped masses , 2012 .

[4]  E. Amezua,et al.  Obtaining configuration space and singularity maps for parallel manipulators , 2009 .

[5]  Clément Gosselin,et al.  Singularity analysis and representation of planar parallel manipulators , 1992, Robotics Auton. Syst..

[6]  Ryan W Krauss.  Computationally efficient modeling of flexible robots using the transfer matrix method , 2012 .

[7]  Ryo Kurazume,et al.  A new index of serial-link manipulator performance combining dynamic manipulability and manipulating force ellipsoids , 2006, IEEE Transactions on Robotics.

[8]  Dieter Bestle,et al.  A new version of transfer matrix method for multibody systems , 2016 .

[9]  J. Gallardo-Alvarado,et al.  A Parallel Manipulator with Planar Configurable Platform and Three End-Effectors , 2019, Mathematical Problems in Engineering.

[10]  Jiasi Mo.  Control Strategy Research on Avoid and Escape the Singular Area of the 3PRR Parallel Platform Based on SEM Environment , 2015 .

[11]  Xu Zhang,et al.  Synchronized motion control and precision positioning compensation of a 3-DOFs macro–micro parallel manipulator fully actuated by piezoelectric actuators , 2017 .

[12]  Jeha Ryu,et al.  A geometrical method for computing the constant-orientation workspace of 6-PRRS parallel manipulators , 2001 .

[13]  Xiaoting Rui,et al.  Discrete Time Transfer Matrix Method for Launch Dynamics Modeling and Cosimulation of Self-Propelled Artillery System , 2013 .

[14]  Songtao Liu,et al.  Optimal design of a 2-DOF pick-and-place parallel robot using dynamic performance indices and angular constraints , 2013 .

[15]  Alberto Trevisani,et al.  Optimal robot positioning using task-dependent and direction-selective performance indexes: General definitions and application to a parallel robot , 2013 .

[16]  Juan A. Carretero,et al.  3-PRRR redundant planar parallel manipulator: Inverse displacement, workspace and singularity analyses , 2007 .

[17]  Cornel Brisan,et al.  Computation and analysis of the workspace of a reconfigurable parallel robotic system , 2011 .

[18]  Jan A. Snyman,et al.  Methodologies for the optimal design of parallel manipulators , 2004 .

[19]  Chun-Ta Chen,et al.  Singularity-free trajectory planning of platform-type parallel manipulators for minimum actuating effort and reactions , 2008, Robotica.

[20]  Zafer Bingul,et al.  Comparative study of performance indices for fundamental robot manipulators , 2006, Robotics Auton. Syst..

[21]  Yimin Song,et al.  Rigid-flexible coupling dynamic modeling and investigation of a redundantly actuated parallel manipulator with multiple actuation modes , 2017 .

[22]  Jianshu Zhang,et al.  Transfer matrix method for multibody systems (Rui method) and its applications , 2019, Science China Technological Sciences.

[23]  Xuping Zhang,et al.  Computationally efficient dynamic modeling of robot manipulators with multiple flexible-links using acceleration-based discrete time transfer matrix method , 2018 .

[24]  Xin-Jun Liu,et al.  Parameter Optimization for the Driving System of a 5 Degrees-of-Freedom Parallel Machining Robot With Planar Kinematic Chains , 2019, Journal of Mechanisms and Robotics.

[25]  Guoping Wang,et al.  A novel method for the dynamic modeling of Stewart parallel mechanism , 2018 .

[26]  Jun Wu,et al.  Workspace and singularity analysis of a 3-DOF planar parallel manipulator with actuation redundancy , 2009, Robotica.

[27]  Chris K. Mechefske,et al.  Modeling of a Fully Flexible 3PRS Manipulator for Vibration Analysis , 2006 .

[28]  S. Ebrahimi,et al.  Dexterity characterization of the RPR parallel manipulator based on the local and global condition indices , 2017 .

[29]  Xiaoting Rui,et al.  Riccati discrete time transfer matrix method for elastic beam undergoing large overall motion , 2007 .

[30]  Vincent Hayward,et al.  Multiple-goal kinematic optimization of a parallel spherical mechanism with actuator redundancy , 1992, IEEE Trans. Robotics Autom..

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

[32]  Clément Gosselin,et al.  Workspace analysis and optimal design of a 3-leg 6-DOF parallel platform mechanism , 2003, IEEE Trans. Robotics Autom..

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

[34]  Clément Gosselin,et al.  On the Kinematic Design of Spherical Three-Degree-of- Freedom Parallel Manipulators , 1993, Int. J. Robotics Res..

[35]  Xiaoting Rui,et al.  Transfer matrix method for linear multibody system , 2008 .

[36]  Jun Wu,et al.  Review: An overview of dynamic parameter identification of robots , 2010 .

[37]  Didier Dumur,et al.  Multi-Objective Design of Parallel Manipulator Using Global Indices , 2010 .

[38]  William L. Cleghorn,et al.  Trajectory tracking and vibration suppression of a 3-PRR parallel manipulator with flexible links , 2015 .

[39]  Javad Enferadi,et al.  The Performance Indices Optimization of a Symmetrical Fully Spherical Parallel Mechanism for Dimensional Synthesis , 2018, J. Intell. Robotic Syst..