Axis Constraint Analysis and Its Resultant 6R Double-Centered Overconstrained Mechanisms
- 19 July 2011
- journal article
- Published by ASME International in Journal of Mechanisms and Robotics
- Vol. 3 (3), 031004
- https://doi.org/10.1115/1.4004225
Abstract
This paper investigates the 6R overconstrained mechanisms by looking at an arrangement that axes intersect at two centers with arbitrary intersection-angles. From the close-loop matrix equation of the mechanism, the paper develops a set of geometric constraint equations of the 6R double-centered overconstrained mechanisms. This leads to the axis constraint equation after applying the Sylvester’s dialytic elimination method. The equation reveals the geometric constraint of link and axis parameters and identifies three categories of the 6R double-centered overconstrained mechanisms with arbitrary axis intersection-angles. The first two categories present two 6R double-centered overconstrained mechanisms and a 6R spherical mechanism. The last category evolves into the 6R double-spherical overconstrained mechanism with arbitrary axis intersection-angles at each spherical center. This further evolves into Baker’s double-Hooke mechanism and his derivative double-spherical mechanism with orthogonal axis intersection. The paper further develops the joint-space solution of the 6R double-centered overconstrained mechanisms based on the geometric constraint equation and verifies the result with a numerical example.Keywords
This publication has 31 references indexed in Scilit:
- Geometry and Constraint Analysis of the Three-Spherical Kinematic Chain Based Parallel MechanismJournal of Mechanisms and Robotics, 2010
- Myard linkage and its mobile assembliesMechanism and Machine Theory, 2009
- Myard’s first five-bar linkage as a degeneracy of a plane-symmetric six-bar loopMechanism and Machine Theory, 2008
- Mobility analysis of a complex structured ball based on mechanism decomposition and equivalent screw system analysisMechanism and Machine Theory, 2004
- Displacement–closure equations of the unspecialised double-Hooke's-joint linkageMechanism and Machine Theory, 2002
- Overconstraint analysis on spatial 6-link loopsMechanism and Machine Theory, 2002
- Interrelationship between screw systems and corresponding reciprocal systems and applicationsMechanism and Machine Theory, 2001
- Mobility in Metamorphic Mechanisms of Foldable/Erectable KindsJournal of Mechanical Design, 1999
- Movable Spatial 6R Mechanisms With Three Adjacent Parallel AxesJournal of Mechanical Design, 1993
- Inverse Kinematics of the General 6R Manipulator and Related LinkagesJournal of Mechanical Design, 1993