Geometric Determination of the Interference-Free Constant-Orientation Workspace of Parallel Cable-Driven Mechanisms

The increasing use of parallel cable-driven mechanisms calls for a better understanding of their behavior and highly efficient algorithms to attenuate their drawbacks at the design stage. One of these drawbacks is the high probability of mechanical interferences between the moving parts of the mechanism. In this paper, the phenomenon is described under the assumption that a cable is a line segment in space. When a mechanical contact occurs between two cables or between a cable and an edge of the end effector, these entities necessarily lie in the same plane, and then the three-dimensional problem becomes two-dimensional. This fact is used to simplify the equations, and leads to exhaustive descriptions of the associated interference loci in the constant-orientation workspace of a cable-driven mechanism. These results provide a fast method to graphically represent all interference regions in the manipulator workspace, given its geometry and the orientation of its end effector.

[1]  Clément Gosselin,et al.  WORKSPACE OPTIMIZATION OF A VERY LARGE CABLE-DRIVEN PARALLEL MECHANISM FOR A RADIOTELESCOPE APPLICATION , 2007 .

[2]  Peter I. Corke,et al.  Air Vehicle Simulator: an Application for a Cable Array Robot , 2005, Proceedings of the 2005 IEEE International Conference on Robotics and Automation.

[3]  Vijay R. Kumar,et al.  Workspaces of Cable-Actuated Parallel Manipulators , 2006 .

[4]  Federico Thomas,et al.  A Wire-Based Active Tracker , 2008, IEEE Transactions on Robotics.

[5]  Clément Gosselin,et al.  Cable Tension Control and Analysis of Reel Transparency for 6-DOF Haptic Foot Platform on a Cable-Driven Locomotion Interface , 2009 .

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

[7]  P. Larochelle,et al.  Self-Collision Detection in Spatial Closed Chains , 2008 .

[8]  Pascal Lafourcade.  Étude des manipulateurs parallèles à câbles : conception d'une suspension active pour soufflerie , 2004 .

[9]  Moshe Shoham,et al.  Wire-driven Parallel Robot: Permitting Collisions Between Wires , 2008, Int. J. Robotics Res..

[10]  Clément Gosselin,et al.  On the Ability of a Cable-Driven Robot to Generate a Prescribed Set of Wrenches , 2008 .

[11]  Manfred Hiller,et al.  On design of a redundant wire-driven parallel robot WARP manipulator , 1999, Proceedings 1999 IEEE International Conference on Robotics and Automation (Cat. No.99CH36288C).

[12]  C. Gosselin,et al.  Determination of the Dynamic Workspace of Cable-Driven Planar Parallel Mechanisms , 2005 .

[13]  Robert L. Williams.  PLANAR CABLE-SUSPENDED HAPTIC INTERFACE: DESIGN FOR WRENCH EXERTION , 1999 .

[14]  Mohammad Eghtesad,et al.  Workspace Analysis for Planar and Spatial Redundant Cable Robots , 2009 .

[15]  Xiaolei Yin,et al.  Dynamic Performance Limitations Due to Yielding in Cable-Driven Robotic Manipulators , 2006 .

[16]  Jean-Pierre Merlet,et al.  Legs interference checking of parallel robots over a given workspace or trajectory , 2006, Proceedings 2006 IEEE International Conference on Robotics and Automation, 2006. ICRA 2006..

[17]  Samuel Bouchard.  Géométrie des robots parallèles entraînés par des câbles , 2008 .

[18]  Rodney G. Roberts,et al.  On the inverse kinematics, statics, and fault tolerance of cable‐suspended robots , 1998 .

[19]  Sadao Kawamura,et al.  Development of a virtual sports machine using a wire drive system-a trial of virtual tennis , 1995, Proceedings 1995 IEEE/RSJ International Conference on Intelligent Robots and Systems. Human Robot Interaction and Cooperative Robots.

[20]  Richard Verhoeven,et al.  Analysis of the Workspace of Tendon-based Stewart Platforms , 2004 .

[21]  Clément Gosselin,et al.  Cable-Driven Parallel Mechanisms: Application to a Locomotion Interface , 2008 .

[22]  Saeed Behzadipour,et al.  Workspace Analysis of a Three DOF Cable-Driven Mechanism , 2009 .

[23]  Clément Gosselin,et al.  Determination and Management of Cable Interferences Between Two 6-DOF Foot Platforms in a Cable-Driven Locomotion Interface , 2009, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

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

[25]  Clément Gosselin,et al.  Analysis of the wrench-closure workspace of planar parallel cable-driven mechanisms , 2006, IEEE Transactions on Robotics.