Static and dynamic stiffness analyses of cable-driven parallel robots with non-negligible cable mass and elasticity

Abstract This paper focuses on the stiffness analysis of cable-driven parallel robots (CDPRs), including the static stiffness and the dynamic stiffness analyses. Static and dynamic cable models are introduced considering the effect of both cable mass and elasticity. Based on these models, the static stiffness of CDPRs is evaluated by the variation of the end-effector pose error, and the dynamic stiffness of CDPRs is analyzed by identifying the robot natural frequencies. Simulations and experiments are made on a 6-DOF prototype to validate the theoretical models. Comparison with other methods available in literature is presented. Results show the important effect of cable mass and elasticity on the static and dynamic stiffness of CDPRs.

[1]  Manfred Hiller,et al.  Workspace, Stiffness, Singularities and Classification of Tendon-Driven Stewart Platforms , 1998 .

[2]  Giuseppe Carbone,et al.  Stiffness analysis and experimental validation of robotic systems , 2011 .

[3]  Marc Gouttefarde,et al.  Simplified static analysis of large-dimension parallel cable-driven robots , 2012, 2012 IEEE International Conference on Robotics and Automation.

[4]  Ou Ma,et al.  Vibration analysis of cable-driven parallel manipulators , 2009 .

[5]  Clément Gosselin,et al.  Stiffness mapping for parallel manipulators , 1990, IEEE Trans. Robotics Autom..

[6]  Placid Mathew Ferreira,et al.  Computation of stiffness and stiffness bounds for parallel link manipulators 1 This research was sup , 1999 .

[7]  Hamid D. Taghirad,et al.  Modeling and Control of Cable Driven Parallel Manipulators with Elastic Cables: Singular Perturbation Theory , 2011, ICIRA.

[8]  Uwe Starossek,et al.  Dynamic stiffness matrix of sagging cable , 1991 .

[9]  Gilles Trombettoni,et al.  Confirmation of Hypothesis on Cable Properties for Cable-Driven Robots , 2013 .

[10]  Hong Bao,et al.  Cable Vibration Analysis for Large Workspace Cable-Driven Parallel Manipulators , 2013 .

[11]  Manfred Hiller,et al.  A real-time capable force calculation algorithm for redundant tendon-based parallel manipulators , 2008, 2008 IEEE International Conference on Robotics and Automation.

[12]  Saeed Behzadipour,et al.  Stiffness of Cable-based Parallel Manipulators With Application to Stability Analysis , 2006 .

[13]  Sadao Kawamura,et al.  Development of an ultrahigh speed robot FALCON using wire drive system , 1995, Proceedings of 1995 IEEE International Conference on Robotics and Automation.

[14]  Hong Bao,et al.  Dynamic analysis of cable-driven parallel manipulators with time-varying cable lengths , 2012 .

[15]  Moharam Habibnejad Korayem,et al.  Workspace analysis of cable-suspended robots with elastic cable , 2007, 2007 IEEE International Conference on Robotics and Biomimetics (ROBIO).

[16]  Eric Courteille,et al.  Design optimization of a Delta-like parallel robot through global stiffness performance evaluation , 2009, 2009 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[17]  Sadao Kawamura,et al.  High-speed manipulation by using parallel wire-driven robots , 2000, Robotica.

[18]  Yan Li,et al.  Vibration Analysis of Tendon-Based Parallel Robot for Processing , 2013 .

[19]  James S. Albus,et al.  Stiffness Study of a Parallel Link Robot Crane for Shipbuilding Applications , 1988 .

[20]  Philippe Martinet,et al.  Vision-based modeling and control of large-dimension cable-driven parallel robots , 2012, 2012 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[21]  Qian Zhou,et al.  Static analysis of cable-driven manipulators with non-negligible cable mass , 2004, IEEE Transactions on Robotics.

[22]  Andreas Pott,et al.  Closed-form Force Distribution for Parallel Wire Robots , 2009 .

[23]  Andreas Pott,et al.  An Algorithm for Real-Time Forward Kinematics of Cable-Driven Parallel Robots , 2010 .

[24]  Jean-Pierre Merlet,et al.  Solving the Direct Geometrico-Static Problem of 3-3 Cable-Driven Parallel Robots by Interval Analysis: Preliminary Results , 2013 .

[25]  Anders Ansell,et al.  The dynamic element method for analysis of frame and cable type structures , 2005 .

[26]  Honghai Liu,et al.  Intelligent Robotics and Applications , 2014, Lecture Notes in Computer Science.

[27]  Hamid D. Taghirad,et al.  Dynamics analysis of a redundant parallel manipulator driven by elastic cables , 2008, 2008 10th International Conference on Control, Automation, Robotics and Vision.

[28]  Dominique Deblaise,et al.  A systematic analytical method for PKM stiffness matrix calculation , 2006, Proceedings 2006 IEEE International Conference on Robotics and Automation, 2006. ICRA 2006..

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

[30]  B. Y. Duan,et al.  Dynamic modeling and active control of a cable-suspended parallel robot , 2008 .

[31]  C. Gosselin,et al.  On the determination of the force distribution in overconstrained cable-driven parallel mechanisms , 2011 .

[32]  Robert Riener,et al.  Forward kinematics of redundantly actuated, tendon-based robots , 2010, 2010 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[33]  H. D. Taghirad,et al.  Robust PID control of cable-driven robots with elastic cables , 2013, 2013 First RSI/ISM International Conference on Robotics and Mechatronics (ICRoM).

[34]  Marc Gouttefarde,et al.  Effects of non-negligible cable mass on the static behavior of large workspace cable-driven parallel mechanisms , 2009, 2009 IEEE International Conference on Robotics and Automation.

[35]  Marc Arsenault,et al.  Workspace and stiffness analysis of a three-degree-of-freedom spatial cable-suspended parallel mechanism while considering cable mass , 2013 .

[36]  Christian Sturm,et al.  Wire Robot Suspension Systems for Wind Tunnels , 2011 .

[37]  Sung Pil Chang,et al.  Dynamic stiffness matrix of an inclined cable , 2001 .

[38]  Ou Ma,et al.  Dynamics analysis of a cable-driven parallel manipulator for hardware-in-the-loop dynamic simulation , 2005, Proceedings, 2005 IEEE/ASME International Conference on Advanced Intelligent Mechatronics..