Forward kinematics analysis and experimental validation of a four-cable-driven under-constrained parallel mechanism

Taking the sinking winch mechanism as prototype, this paper studies the forward kinematics problem of a four-cable-driven under-constrained parallel mechanism. The tension states (slackness and tautness) and properties of the cables are incorporated into the forward kinematics model. We propose a new algorithm (named traversal algorithm) to solve the tensions in cables and the pose of platform, under the condition that only the lengths of four cables are known. The simulation and experimental results on forward kinematics demonstrate the effectiveness and correctness of the model and the traversal algorithm. The results of this paper can be used to evaluate the effect of the unequal cables’ lengths to the tension distribution of cables and pose of the platform for sinking winch mechanism.

[1]  Jian S. Dai,et al.  Forward displacement analysis of the general 6–6 Stewart mechanism using Gröbner bases , 2009 .

[2]  Erika Ottaviano,et al.  Analysis and design of a four-cable-driven parallel manipulator for planar and spatial tasks , 2008 .

[3]  Marcus Frean,et al.  Hybrid MetaHeuristic Paradigm for the Forward Kinematics of 6-6 General Parallel Manipulator , 2009 .

[4]  Mjd Powell,et al.  A Fortran subroutine for solving systems of non-linear algebraic equations , 1968 .

[5]  Guohua Cao,et al.  Forward Kinematics Analysis of a Four-Cable-Driving Parallel Robot , 2011 .

[6]  Vijay R. Kumar,et al.  The Direct Kinematics of Objects Suspended From Cables , 2010 .

[7]  Jean-Pierre Merlet,et al.  Geometrico-Static Analysis of Under-Constrained Cable-Driven Parallel Robots , 2010 .

[8]  M. Carricato,et al.  Real solutions of the direct geometrico-static problem of under-constrained cable-driven parallel robots with 3 cables: a numerical investigation , 2012 .

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

[10]  Eldon Hansen,et al.  Global optimization using interval analysis , 1992, Pure and applied mathematics.

[11]  M. Ceccarelli,et al.  A 4–4 cable-based parallel manipulator for an application in hospital environment , 2007, 2007 Mediterranean Conference on Control & Automation.

[12]  Mohammad Eghtesad,et al.  Neural Network Solution for Forward Kinematics Problem of Cable Robots , 2010, J. Intell. Robotic Syst..

[13]  Qi Lin,et al.  Analysis of inverse kinematics and dynamics of a novel 6-degree-of-freedom wire-driven parallel gantry crane robot , 2009, 2009 IEEE/ASME International Conference on Advanced Intelligent Mechatronics.

[14]  Jean-Pierre Merlet,et al.  Kinematic analysis of a spatial four-wire driven parallel crane without constraining mechanism , 2009 .

[15]  M. Hiller,et al.  Design, analysis and realization of tendon-based parallel manipulators. , 2005 .

[16]  Wilgo Moreira Nunes,et al.  Cable-based parallel manipulator for rehabilitation of shoulder and elbow movements , 2011, 2011 IEEE International Conference on Rehabilitation Robotics.

[17]  Qiyuan Liu,et al.  Chaotic Finding Method of Position Forward Kinematics of 3-DOF Parallel Robot , 2009, 2009 Third International Symposium on Intelligent Information Technology Application.

[18]  Jean-Pierre Merlet,et al.  Stability Analysis of Underconstrained Cable-Driven Parallel Robots , 2013, IEEE Transactions on Robotics.

[19]  Yoon Keun Kwak,et al.  Kinematics and Workspace Analysis of a Parallel Wire Mechanism for Measuring a Robot Pose , 1999 .

[20]  Developments in Reliable Computing, International Symposium on Scientific Computing, Computer Arithmetic, and Validated Numerics, SCAN 1998, Szeged, Hungary, September 22-25, 1998 , 1999, SCAN.

[21]  Mohammad Eghtesad,et al.  Neural network solution for forward kinematics problem of HEXA parallel robot , 2008, ACC.

[22]  Jan Verschelde,et al.  Advances in Polynomial Continuation for Solving Problems in Kinematics , 2002 .

[23]  Jean-Pierre Merlet,et al.  Solving the Forward Kinematics of a Gough-Type Parallel Manipulator with Interval Analysis , 2004, Int. J. Robotics Res..

[24]  Jae Kyung Shim,et al.  Forward kinematics of the general 6–6 Stewart platform using algebraic elimination , 2001 .

[25]  Xuesong Wang,et al.  On the use of differential evolution for forward kinematics of parallel manipulators , 2008, Appl. Math. Comput..

[26]  James S. Albus,et al.  The NIST robocrane , 1993, J. Field Robotics.

[27]  Robert L. Williams,et al.  Cable-suspended robotic contour crafting system , 2007 .

[28]  Siegfried M. Rump,et al.  INTLAB - INTerval LABoratory , 1998, SCAN.

[29]  Jing Xu,et al.  Combined kinematic and static analysis of a cable-driven manipulator with a spring spine , 2011, 2011 IEEE International Conference on Robotics and Automation.

[30]  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.

[31]  Guilin Yang,et al.  Kinematics and singularity analysis of a planar cable-driven parallel manipulator , 2004, 2004 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) (IEEE Cat. No.04CH37566).

[32]  Jean-Pierre Merlet,et al.  Direct geometrico-static problem of under-constrained cable-driven parallel robots with three cables , 2011, 2011 IEEE International Conference on Robotics and Automation.

[33]  Saeed Behzadipour,et al.  Cable-based Robot Manipulators with Translational Degrees of Freedom , 2006 .