Working Capability Analysis of Stewart Platforms

1996 ◽  
Vol 118 (2) ◽  
pp. 220-227 ◽  
Author(s):  
Chi-Mei Luh ◽  
F. A. Adkins ◽  
E. J. Haug ◽  
C. C. Qiu
Keyword(s):  
Numerical Methods ◽  
Motion Control ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Unilateral Constraints ◽  
Dimensional Solution ◽  
One Dimensional ◽  
Capability Analysis ◽  
Working Capability ◽  
Stewart Platforms

Working capability analysis of planar and spatial Stewart platforms with unilateral constraints on actuator length is carried out using numerical methods based on analytical criteria for the boundary of the accessible output set. Restrictions on achievable motion at singular configurations associated with points interior to the accessible output set are also analyzed. Since movement of the working point on a spatial Stewart platform occurs in three-dimensional space, the boundary of the accessible output set is a two-dimensional surface. Numerical methods used in this analysis map one-dimensional solution sets, permitting the boundary of the accessible output set to be characterized by a family of one dimensional generators. Motion control restrictions inside the accessible output set are similarly characterized by families of interior singular curves, and barriers to motion control across surfaces defined are analyzed.

Limits at $3 in a New Formulation for Path-Placement in the Workcells of Planar 3-R Robots

1995 ◽  
Vol 117 (3) ◽  
pp. 485-490 ◽  
Author(s):  
J. K. Davidson ◽  
N. A. Soman
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Solution Space ◽  
Graphical Form ◽  
Dimensional Solution ◽  
One Dimensional ◽  
Tool Paths ◽  
Planar Robot ◽  
New Formulation ◽  
Systematic Formulation

Excursion-limits at the third joint of a three-hinged planar robot are incorporated into a new systematic formulation for path-placement in which the three-dimensional solution-space is decomposed into a two-dimensional space of variables that strongly control the placement of the path and a one-dimensional space that is much less critical. The new formulation determines all acceptable positions for the first joint of the robot relative to the workpiece. All possible acceptable designs appear in a graphical form that can be readily visualized and be directly measured in a Cartesian frame of reference in the workcell. The method is extended to closed tool-paths, and the method is illustrated with practical examples.

Workspace Analysis of Closed Loop Mechanisms With Unilateral Constraints

1989 ◽  
Author(s):  
D.-Y. Jo ◽  
E. J. Haug
Keyword(s):  
Numerical Methods ◽  
Closed Loop ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Inequality Constraints ◽  
Stewart Platform ◽  
Unilateral Constraints ◽  
Higher Dimensional ◽  
Workspace Analysis ◽  
Slack Variable

Abstract Kinematics of mechanisms that contain elements with unilateral constraints such as stops are characterized by systems of equalities and inequalities. A slack variable formulation is introduced to convert inequality constraints to equalities, in a higher dimensional space of variables. The slack variable formulation permits use of manifold based theoretical and numerical methods for analysis of the boundaries of workspaces. The workspace of a simplified Stewart platform is analyzed, including rotatability of the top platform. Sets of reachable points of the top platform of a three dimensional Stewart platform, with fixed platform orientation, are analyzed.

scholarly journals Chaotic Attractor Generation via Space Function Controls

2011 ◽  
Vol 2011 ◽  
pp. 1-11
Author(s):  
Hong Shi ◽  
Guangming Xie ◽  
Desheng Liu
Keyword(s):  
Linear Systems ◽  
Chaotic Attractor ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Underlying Mechanism ◽  
Two Dimensional ◽  
One Dimensional ◽  
Suitable Space ◽  
Space Function ◽  
Three Dimensional Space

The analysis of chaotic attractor generation is given, and the generation of novel chaotic attractor is introduced in this paper. The underlying mechanism involves two simple linear systems with one-dimensional, two-dimensional, or three-dimensional space functions. Moreover, it is demonstrated by simulation that various attractor patterns are generated conveniently by adjusting suitable space functions' parameters and the statistic behavior is also discussed.

scholarly journals Synthetic Weyl Points of the Shear Horizontal Guided Waves in One-Dimensional Phononic Crystal Plates

2021 ◽  
Vol 12 (1) ◽  
pp. 167
Author(s):  
Hongbo Zhang ◽  
Shaobo Zhang ◽  
Jiang Liu ◽  
Bilong Liu
Keyword(s):  
Guided Waves ◽  
Dimensional Space ◽  
Phononic Crystal ◽  
Phase Interface ◽  
Three Dimensional ◽  
Interface States ◽  
Geometrical Parameters ◽  
One Dimensional ◽  
Higher Dimensional ◽  
Shear Horizontal

Weyl physics in acoustic and elastic systems has drawn extensive attention. In this paper, Weyl points of shear horizontal guided waves are realized by one-dimensional phononic crystal plates, in which one physical dimension plus two geometrical parameters constitute a synthetic three-dimensional space. Based on the finite element method, we have not only observed the synthetic Weyl points but also explored the Weyl interface states and the reflection phase vortices, which have further proved the topological phase interface states. As the first realization of three-dimensional topological phases through one-dimensional phononic crystal plates in the synthetic dimension, this research demonstrates the great potential of applicable one-dimensional plate structural systems in detecting higher-dimensional topological phenomena.

Cubic Hybrid Mechanism Based on S[T] Output Base and P/R Input Base

2012 ◽  
Vol 430-432 ◽  
pp. 1725-1728
Author(s):  
Jian Guo Luo ◽  
Mao Yan He
Keyword(s):  
Parallel Mechanism ◽  
Dimensional Space ◽  
Three Dimensional ◽  
One Dimensional ◽  
Hybrid Mechanism ◽  
Hybrid Manipulator ◽  
New Type ◽  
The Stability ◽  
Serial Mechanism ◽  
Three Dimensional Space

Based on the flexibility of single couple of serial mechanism and the stability of multi couples of parallel mechanism, a new type of S[T] output base of hybrid mechanism presented, component of sphere joint run through the tiger joint, this component still the output one with the capability of rotate in three dimensional space. Add serial branch including three translation couple P or/and rotation couple R to the new type of S[T] output base, put these members on one cubic frame, twenty seven configurations obtained with 3-DOF(degree of freedom) allow of three dimensional rotation, twenty seven configurations belong to three conditions obtained with 4-DOF allow of three dimensional rotation and one dimensional translation, nine configurations belong to three conditions obtained with 5-DOF allow of three dimensional rotation and two dimensional translation, one configuration obtained with 6-DOF allow of three dimensional rotation and three dimensional translation, all those sixty four configurations have no more than six translation couple or rotation couple, and the sum of two kind of couple is equal to six. Developing new type of hybrid manipulator based on the hybrid cubic mechanism constructed with S[T] output base and P/R input base will be possible in theory and useful.

EFFECTIVE DIPOLE-RADIATION-FIELD THEORY I: ONE-DIMENSIONAL OSCILLATOR BEYOND STANDARD COUPLING

1994 ◽  
Vol 08 (17) ◽  
pp. 2307-2325 ◽  
Author(s):  
H. DEKKER
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Dipole Interaction ◽  
Quantum Mechanical ◽  
Renormalization Procedure ◽  
One Dimensional ◽  
Dipole Radiation ◽  
Consistent Treatment ◽  
Interaction Problem ◽  
Three Dimensional Space

A novel generalization is given of the standard dipole interaction between a charged particle and the electromagnetic field in the radiation gauge. The resulting nonlinear interaction problem is statistically linearized. The ensuing dynamics is solved exactly for a harmonically bound nonrelativistic electron in a finite region of three-dimensional space. The solution involves a generalized renormalization procedure and is free of runaway modes. The theory is particularly suited for a self-consistent treatment of the system's quantum mechanics. As a consequence of the generalized coupling an earlier noted ultraviolet quantum mechanical divergence is absent.

Analysis of Pulsed Thermography Methods for Defect Depth Prediction

2005 ◽  
Vol 128 (4) ◽  
pp. 329-338 ◽  
Author(s):  
J. G. Sun
Keyword(s):  
Test Specimen ◽  
Three Dimensional ◽  
Quantitative Prediction ◽  
Defect Depth ◽  
Effective Technique ◽  
Flat Bottom ◽  
Dimensional Solution ◽  
Pulsed Thermography ◽  
One Dimensional ◽  
Depth Prediction

Pulsed thermography is an effective technique for quantitative prediction of defect depth within a specimen. Several methods have been reported in the literature. In this paper, using an analysis based on a theoretical one-dimensional solution of pulsed thermography, we analyzed four representative methods. We show that all of the methods are accurate and converge to the theoretical solution under ideal conditions. Three methods can be directly used to predict defect depth. However, because defect features that appear on the surface during a pulsed thermography test are always affected by three-dimensional heat conduction within the test specimen, the performance and accuracy of these methods differs for defects of various sizes and depths. This difference is demonstrated and evaluated from a set of pulsed thermography data obtained from a specimen with several flat-bottom holes as simulated defects.

Three-Dimensional Deformations

1996 ◽  
Author(s):  
T. T. C. Ting
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Anisotropic Elasticity ◽  
Two Dimensional ◽  
Elastic Solids ◽  
Elastic Materials ◽  
Dimensional Solution ◽  
Line Integral ◽  
Isotropic Elasticity ◽  
Anisotropic Elastic

There appears to be very little study, if any, on the extension of Stroh's formalism to three-dimensional deformations of anisotropic elastic materials. In most three-dimensional problems the analyses employ approaches that are remotely related to Stroh's two-dimensional formalism. This is not unexpected, since this has been the situation between two-dimensional and three-dimensional isotropic elasticity. However it needs not be the case for three-dimensional anisotropic elasticity. Much can be gained if a connection to the Stroh formalism can be established. Barnett and Lothe (1975a) appeared to be the only ones who made a connection between a three-dimensional solution and Stroh's two-dimensional formalism. Earlier, several investigators obtained the Green's function for the infinite anisotropic medium in term of a line integral on an oblique plane in the three-dimensional space. That line integral, as we will see here, is one of Barnett-Lothe tensors on an oblique plane. We propose in this chapter extensions and applications of Stroh's two-dimensional formalism to certain three-dimensional deformations of anisotropic elastic solids.

scholarly journals A-topology for Minkowski space

1979 ◽  
Vol 21 (1) ◽  
pp. 53-64 ◽  
Author(s):  
Sribatsa Nanda
Keyword(s):  
Minkowski Space ◽  
Dimensional Space ◽  
Three Dimensional ◽  
One Dimensional ◽  
Group Of Homeomorphisms ◽  
Dimensional Space Time ◽  
The One ◽  
Induced Topology ◽  
Time Continuum ◽  
Inhomogeneous Lorentz Group

AbstractWe consider in this paper a topology (which we call the A-topology) on Minkowski space, the four-dimensional space–time continuum of special relativity and derive its group of homeomorphisms. We define the A-topology to be the finest topology on Minkowski space with respect to which the induced topology on time-like and light-like lines is one-dimensional Euclidean and the induced topology on space-like hyperplanes is three- dimensional Euclidean. It is then shown that the group of homeomorphisms of this topology is precisely the one generated by the inhomogeneous Lorentz group and the dilatations.

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