Closure to “Discussions of ‘An Iterative Method for the Displacement Analysis of Spatial Mechanisms’” (1965, ASME J. Appl. Mech., 32, pp. 220–221)

1965 ◽  
Vol 32 (1) ◽  
pp. 221-221
Author(s):  
J. J. Uicker ◽  
J. Denavit ◽  
R. S. Hartenberg
Keyword(s):  
Iterative Method ◽  
Displacement Analysis ◽  
Spatial Mechanisms

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.

A Gröbner-Sylvester Hybrid Method for Closed-Form Displacement Analysis of Mechanisms

1998 ◽  
Author(s):  
A. K. Dhingra ◽  
A. N. Almadi ◽  
D. Kohli
Keyword(s):  
Gröbner Basis ◽  
Common Factor ◽  
Hybrid Approach ◽  
System Of Equations ◽  
Grobner Basis ◽  
Displacement Analysis ◽  
Spatial Mechanisms ◽  
Rational Procedure ◽  
Necessary And Sufficient ◽  
Term Ordering

Abstract The displacement analysis problem for planar and spatial mechanisms can be written as a system of multivariate polynomial equations. Elimination theory based on resultants and polynomial continuation are some of the methods which have been used to solve this problem. This paper presents a new approach to displacement analysis using the reduced Gröbner basis form of a system of equations under degree lexicographic (dlex) term ordering of its monomials and Sylvester’s Dialytic elimination method. Using the Gröbner-Sylvester hybrid approach, a finitely solvable system of equations F is transformed into its reduced Gröbner basis G using dlex term ordering. Next, using the entire or a subset of the set of generators in G, the Sylvester’s matrix is assembled. The vanishing of the resultant, given as the determinant of Sylvester’s matrix, yields the necessary and sufficient condition for the polynomials in G (as well as F) to have a common factor. The proposed approach appears to provide a systematic and rational procedure to the problem discussed by Roth (1994) dealing with the generation of (additional) equations for constructing the Sylvester’s matrix. Three examples illustrating the applicability of the proposed approach to displacement analysis of planar and spatial mechanisms are presented. The first and second examples deal with forward displacement analysis of the general 6-6 Stewart mechanism and the 6-6 Stewart platform, whereas the third example deals with the determination of the input-output polynomial of a 8-link 1-DOF mechanism which does not contain any 4-link loops.

Novel Methods in the Displacement Analysis of Spatial Mechanisms

1994 ◽  
Author(s):  
Ian S. Fischer
Keyword(s):  
Iterative Methods ◽  
Coordinate Transformation ◽  
Kinematic Analysis ◽  
Displacement Analysis ◽  
Dual Number ◽  
Transformation Matrices ◽  
Spatial Mechanisms ◽  
Novel Methods

Abstract An aspect of dual-number coordinate-transformation matrices is used to establish iterative methods for determining the rotational and translational displacements in the kinematic analysis of complex spatial mechanisms.

Displacement Analysis of Spatial Seven-Link 5R-2P Mechanisms

1977 ◽  
Vol 99 (3) ◽  
pp. 692-701 ◽  
Author(s):  
J. Duffy
Keyword(s):  
Significant Advance ◽  
Input Output ◽  
Spherical Torus ◽  
Numerical Examples ◽  
Displacement Analysis ◽  
Output Displacement ◽  
Spatial Mechanisms ◽  
Special Cases

Input-output displacement equations of eighth degree are derived for general spatial seven-link (RPPRRRR, RRRPPRR), (RPRRRPR, RPRRPRR), and (RPRPRRR) mechanisms. The results are verified by numerical examples. The solutions of these mechanisms constitute a significant advance in the theory of analysis of spatial mechanisms. They contain as special cases the solutions for spatial seven-link 4R-3P slider-crank mechanisms, the solutions for all five-link 3R-2C and six-link 4R-P-C mechanisms that have appeared in the literature, together with the solutions for a multitude of solved and unsolved mechanisms containing spherical, torus, and plane kinematic pairs.

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