An Iterative Method for the Displacement Analysis of Spatial Mechanisms

1964 ◽  
Vol 31 (2) ◽  
pp. 309-314 ◽  
Author(s):  
J. J. Uicker ◽  
J. Denavit ◽  
R. S. Hartenberg
Keyword(s):  
Iterative Method ◽  
Complete Solution ◽  
Algebraic Method ◽  
Matrix Equations ◽  
Displacement Analysis ◽  
Spatial Mechanisms ◽  
Symbolic Notation ◽  
The Matrix ◽  
The Subject ◽  
Computer Operation

An algebraic method for the displacement analysis of linkages has been the subject of earlier publications [1, 2]. This method, based on the use of a symbolic notation, allows the application of matrix algebra to the study of displacements in linkages, and permits formulation of all the kinematic relations of a linkage in terms of matrix equations. Based on this earlier work, the present paper develops an iterative method for the solution of the matrix equations required in displacement analysis. A complete solution is given for simple-closed linkages consisting of revolute and prismatic pairs (and their combinations). A brief indication of how higher pairs and multiple-closed chains may be handled is also given. Particularly useful in spatial problems, since it does not depend on visualization, this approach is developed in a manner intended for digital-computer operation.

A Dual Iterative Method for Displacement Analysis of Spatial Mechanisms

1994 ◽  
Author(s):  
Sean Thompson ◽  
Harry H. Cheng
Keyword(s):  
Iterative Method ◽  
Programming Language ◽  
Displacement Analysis ◽  
Spatial Mechanism ◽  
Dual Transformation ◽  
Transformation Matrices ◽  
Spatial Mechanisms

Abstract A dual iterative method for displacement analysis of a spatial mechanism is presented in this paper. The algorithm and formulation based upon 3 × 3 dual transformation matrices are succinct. They can be easily implemented in the CH programming language. The algorithm has been numerically verified by dual iterative displacement analysis of an RCCC four-link spatial mechanism.

DISPLACEMENT ANALYSIS OF Ro-R-R-CP SPATIAL MECHANISMS WITH VECTOR ALGEBRAIC METHOD

1999 ◽  
Vol 23 (1A) ◽  
pp. 95-112
Author(s):  
C.M. Wong ◽  
K.C. Chan ◽  
Y.B. Zhou
Keyword(s):  
Closed Form ◽  
Algebraic Method ◽  
Input Output ◽  
Displacement Analysis ◽  
Output Displacement ◽  
Spatial Mechanisms ◽  
Kinematic Loop

This paper presents the displacement analysis of the three variants of a spatial kinematic loop containing 3R and 1CP joints using vector algebraic method. The closed-form input-output displacement equations of this mechanism are derived as forth-order polynomials. Analytical steps and expressions are laid out uniformly and simply.

Microdiffraction analysis of precipitate crystallography and morphology in Al alloys

1990 ◽  
Vol 48 (4) ◽  
pp. 954-955
Author(s):  
B.C. Muddle ◽  
G.R. Hugo
Keyword(s):  
Point Group ◽  
Hexagonal Lattice ◽  
Intersection Point ◽  
Saed Pattern ◽  
Point Symmetry ◽  
Hexagonal Symmetry ◽  
Precipitate Crystal ◽  
The Matrix ◽  
The Subject ◽  
Electron Microdiffraction

Electron microdiffraction has been used to determine the crystallography of precipitation in Al-Cu-Mg-Ag and Al-Ge alloys for individual precipitates with dimensions down to 10 nm. The crystallography has been related to the morphology of the precipitates using an analysis based on the intersection point symmetry. This analysis requires that the precipitate form be consistent with the intersection point group, defined as those point symmetry elements common to precipitate and matrix crystals when the precipitate crystal is in its observed orientation relationship with the matrix.In Al-Cu-Mg-Ag alloys with high Cu:Mg ratios and containing trace amounts of silver, a phase designated Ω readily precipitates as thin, hexagonal-shaped plates on matrix {111}α planes. Examples of these precipitates are shown in Fig. 1. The structure of this phase has been the subject of some controversy. An SAED pattern, Fig. 2, recorded from matrix and precipitates parallel to a <11l>α axis is suggestive of hexagonal symmetry and a hexagonal lattice has been proposed on the basis of such patterns.

scholarly journals A New Iterative Algorithm for Solving a Class of Matrix Nearness Problem

2012 ◽  
Vol 2012 ◽  
pp. 1-6
Author(s):  
Xuefeng Duan ◽  
Chunmei Li
Keyword(s):  
Iterative Algorithm ◽  
Projection Algorithm ◽  
Frobenius Norm ◽  
Matrix Equations ◽  
Von Neumann ◽  
Numerical Examples ◽  
Matrix Nearness Problem ◽  
Least Frobenius Norm Solution ◽  
Alternating Projection ◽  
The Matrix

Based on the alternating projection algorithm, which was proposed by Von Neumann to treat the problem of finding the projection of a given point onto the intersection of two closed subspaces, we propose a new iterative algorithm to solve the matrix nearness problem associated with the matrix equations AXB=E, CXD=F, which arises frequently in experimental design. If we choose the initial iterative matrix X0=0, the least Frobenius norm solution of these matrix equations is obtained. Numerical examples show that the new algorithm is feasible and effective.

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