Mobility of Overconstrained Parallel Mechanisms
- 14 October 2004
- journal article
- Published by ASME International in Journal of Mechanical Design
- Vol. 128 (1), 220-229
- https://doi.org/10.1115/1.1901708
Abstract
The Kutzbach–Grübler mobility criterion calculates the degrees of freedom of a general mechanism. However, the criterion can break down for mechanisms with special geometries, and in particular, the class of so-called overconstrained parallel mechanisms. The problem is that the criterion treats all constraints as active, even redundant constraints, which do not affect the mechanism degrees of freedom. In this paper we reveal a number of screw systems of a parallel mechanism, explore their inter-relationship and develop an original theoretical framework to relate these screw systems to motion and constraints of a parallel mechanism to identify the platform constraints, mechanism constraints and redundant constraints. The screw system characteristics and relationships are investigated for physical properties and a new approach to mobility analysis is proposed based on decompositions of motion and constraint screw systems. New versions of the mobility criterion are thus presented to eliminate the redundant constraints and accurately predict the platform degrees of freedom. Several examples of overconstrained mechanisms from the literature illustrate the results.Keywords
This publication has 46 references indexed in Scilit:
- Mobility in Metamorphic Mechanisms of Foldable/Erectable KindsJournal of Mechanical Design, 1999
- Kinematic Analysis and Singularity Loci of Spatial Four-Degree-of-Freedom Parallel Manipulators Using a Vector FormulationJournal of Mechanical Design, 1998
- Kinematic characteristics analysis of 3 DOF in-parallel actuated pyramid mechanismMechanism and Machine Theory, 1996
- Characterization of Workspaces of Parallel ManipulatorsJournal of Mechanical Design, 1992
- The Synthesis of Point Contact Restraint of a Rigid BodyJournal of Mechanical Design, 1985
- The Elliptic Polarity of ScrewsJournal of Mechanical Design, 1985
- A Direct Determination of the Instantaneous Kinematics of Fully Parallel Robot ManipulatorsJournal of Mechanical Design, 1985
- Structural Kinematics of In-Parallel-Actuated Robot-ArmsJournal of Mechanical Design, 1983
- Some Kinematic Structures for Robot Manipulator DesignsJournal of Mechanical Design, 1983
- Mechanism and MotionJournal of Applied Mechanics, 1960