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.

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.

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.

Exact Displacement Analysis of Four-Link Spatial Mechanisms by the Direction Cosine Matrix Method

1984 ◽  
Vol 51 (4) ◽  
pp. 921-928 ◽  
Author(s):  
T. C. Huang ◽  
Y. Youm
Keyword(s):  
Local Coordinate System ◽  
Direction Cosine ◽  
Displacement Analysis ◽  
Spatial Mechanism ◽  
Spatial Mechanisms ◽  
Local Coordinates ◽  
Development Direction ◽  
Direction Cosine Matrix ◽  
Direction Cosines ◽  
Unit Vectors

A method of displacement analysis of the four-link spatial mechanism is developed. The results through this analysis will be exact solutions that can be obtained without resorting to numerical or iteration schemes. In the analysis, the position of a link in a mechanism can be fully defined if its direction and length are known. Therefore, this analysis involves the calculation of the unknown direction cosines and length of each link for a given configuration of the mechanism. In finding the direction cosines of the unknown unit vectors involved for each link and rotating axis, two types of coordinates, the global and the local, are generally used. Then, a direction cosine matrix between each local coordinate system and the global coordinates is established. Thus, the unknown direction cosines of the local coordinates, the links, and the rotating axes are obtained in global coordinates. In this development, direction cosine matrices are used throughout the analysis. As an illustration, the application of this method to the study of four-link spatial mechanisms, RGGR, RGCR, RRGG, and RRGC will be presented.

Computer-Aided Displacement Analysis of Spatial Mechanisms

1994 ◽  
Author(s):  
Sean Thompson ◽  
Harry H. Cheng
Keyword(s):  
Programming Languages ◽  
Design Automation ◽  
Data Type ◽  
Complex Numbers ◽  
Dual Numbers ◽  
Displacement Analysis ◽  
Spatial Mechanism ◽  
Programming Paradigm ◽  
Spatial Mechanisms ◽  
Programming Techniques

Abstract Recently, Cheng (1993) introduced the CH programming language. CH is designed to be a superset of ANSI C with all programming features of FORTRAN. Many programming features in CH are specifically designed and implemented for design automation. Handling dual number as a basic built-in data type in the language is one example. Formulas with dual numbers can be translated into CH programming statements as easily as formulas with real and complex numbers. In this paper we will show that both formulation and programming with dual numbers are remarkably simple for analysis of complicated spatial mechanisms within the programming paradigm of CH. With computational capabilities for dual formulas in mind, formulas for analysis of spatial mechanisms are derived differently from those intended for implementation in computer programming languages without dual data type. We will demonstrate some formulation and programming techniques in the programming paradigm of CH through a displacement analysis of the RCRCR five-link spatial mechanism. A CH program that can obtain both numerical and graphical results for complete displacement analysis of the RCRCR mechanism will be presented.

Sign in / Sign up

Export Citation Format

Share Document