Minimal realizations of spatial stiffnesses with parallel or serial mechanisms having concurrent axes
- 27 February 2001
- journal article
- Published by Wiley in Journal of Robotic Systems
- Vol. 18 (3), 135-146
- https://doi.org/10.1002/rob.1011
Abstract
This article presents a new method for the synthesis of an arbitrary spatial elastic behavior with an elastic mechanism. The mechanisms considered are parallel and serial mechanisms with concurrent axes. We show that any full‐rank spatial stiffness matrix can be realized using a parallel mechanism with all spring axes intersecting at a unique point. It is shown that this intersection point must be the center of stiffness. We also show that any full‐rank spatial compliance matrix can be realized using a serial mechanism with all joint axes intersecting at a unique point. This point is shown to be the center of compliance. Synthesis procedures for mechanisms with these properties are provided. The realizations are shown to be minimal in the sense that both the number of screw components and the total number of components are minimum. © 2001 John Wiley & Sons, Inc.Keywords
This publication has 15 references indexed in Scilit:
- Conservative Congruence Transformation for Joint and Cartesian Stiffness Matrices of Robotic Hands and FingersThe International Journal of Robotics Research, 2000
- Modeling of Elastically Coupled Bodies: Part II—Exponential and Generalized Coordinate MethodsJournal of Dynamic Systems, Measurement, and Control, 1998
- Modeling of Elastically Coupled Bodies: Part I—General Theory and Geometric Potential Function MethodJournal of Dynamic Systems, Measurement, and Control, 1998
- Achieving an Arbitrary Spatial Stiffness with Springs Connected in ParallelJournal of Mechanical Design, 1998
- The bounds and realization of spatial stiffnesses achieved with simple springs connected in parallelIEEE Transactions on Robotics and Automation, 1998
- On the 6 × 6 cartesian stiffness matrix for three-dimensional motionsMechanism and Machine Theory, 1998
- Structure of Robot ComplianceJournal of Mechanical Design, 1993
- Global stiffness modeling of a class of simple compliant couplingsMechanism and Machine Theory, 1993
- Kinestatic Control: A Novel Theory for Simultaneously Regulating Force and DisplacementJournal of Mechanical Design, 1991
- Normal forms of stiffness and compliance matricesIEEE Journal on Robotics and Automation, 1987