Determination of the Dynamic Workspace of Cable-Driven Planar Parallel Mechanisms
- 1 March 2005
- journal article
- Published by ASME International in Journal of Mechanical Design
- Vol. 127 (2), 242-248
- https://doi.org/10.1115/1.1830045
Abstract
In this paper, we present a general and systematic analysis of cable-driven planar parallel mechanisms. The equations for the velocities are derived, and the forces in the cables are obtained by the principle of virtual work. Then, a detailed analysis of the workspace is performed and an analytical method for the determination of the boundaries of an x-y two-dimensional subset is proposed. The new notion of dynamic workspace is defined, as its shape depends on the accelerations of the end-effector. We demonstrate that any subset of the workspace can be considered as a combination of three-cable subworkspaces, with boundaries being of two kinds: two-cable equilibrium loci and three-cable singularity loci. By using a parametric representation, we see that for the x-y workspace of a simple no-spring mechanism, the two-cable equilibrium loci represent a hyperbolic section, degenerating, in some particular cases, to one or two linear segments. Examples of such loci are presented. We use quadratic programming to choose which sections of the curves constitute the boundaries of the workspace for any particular dynamic state. A detailed example of workspace determination is included for a six-cable mechanism.Keywords
This publication has 8 references indexed in Scilit:
- A Method for Representing the Configuration and Analyzing the Motion of Complex Cable-Pulley SystemsJournal of Mechanical Design, 2003
- Design of Continuous Backbone, Cable-Driven RobotsJournal of Mechanical Design, 2002
- Kinematics and workspace analysis of a parallel wire mechanism for measuring a robot poseMechanism and Machine Theory, 1999
- On the quadratic nature of the singularity curves of planar three-degree-of-freedom parallel manipulatorsMechanism and Machine Theory, 1995
- The NIST robocraneJournal of Robotic Systems, 1993
- A Minimal, Minimal Linkage: The Tension-Compression Parallel Link ManipulatorPublished by Elsevier BV ,1993
- Application of Multi-Dimensional Wire Cranes in ConstructionProceedings of the 37th International Symposium on Automation and Robotics in Construction (isarc), 1988
- A numerically stable dual method for solving strictly convex quadratic programsMathematical Programming, 1983