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.

Kinematics of the Generalized Slider-Crank Mechanism

1993 ◽  
Author(s):  
Ian S. Fischer ◽  
Sahidur Rahman
Keyword(s):  
Coordinate Transformation ◽  
Kinematics And Dynamics ◽  
Cylinder Axis ◽  
Dual Number ◽  
Transformation Matrices ◽  
Manufacturing Tolerances ◽  
Newton Raphson ◽  
Raphson Method ◽  
Crank Mechanism

Abstract Dual-number techniques are used to analyze the kinematics and dynamics of the slider crank mechanism generalized to consider the effects of the cylinder axis being offset and non-perpendicular to the crankshaft axis, conditions which result in reciprocating machinery such as engines and compressors from manufacturing tolerances. The kinematics of the mechanism are evaluated with a Newton-Raphson method using dual-number coordinate-transformation matrices which in this work is extended to include mechanisms with spherical joints. Results for various cases are shown and are ready to be used in a study of the dynamics of the generalized slider-crank.

Modeling the Plane Joint

1999 ◽  
Vol 121 (3) ◽  
pp. 383-386 ◽  
Author(s):  
I. S. Fischer
Keyword(s):  
Coordinate Transformation ◽  
Degrees Of Freedom ◽  
Flat Surfaces ◽  
Dual Number ◽  
Transformation Matrices ◽  
Swash Plate ◽  
Plane Joint ◽  
Three Degrees Of Freedom

The plane joint, often referred to as the “E” joint is modeled using dual-number coordinate-transformation matrices. The joint consists of two flat surfaces held in contact so that three degrees of freedom are allowed, two translations and a rotation. The swash-plate mechanism is used as an example of a mechanism featuring the plane joint.

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.

Kinematic Analysis of Spatial Mechanisms by Means of Screw Coordinates. Part 2—Analysis of Spatial Mechanisms

1971 ◽  
Vol 93 (1) ◽  
pp. 67-73 ◽  
Author(s):  
M. S. C. Yuan ◽  
F. Freudenstein ◽  
L. S. Woo
Keyword(s):  
Computer Program ◽  
Kinematic Analysis ◽  
Static Force ◽  
Single Degree Of Freedom ◽  
Numerical Examples ◽  
Spatial Mechanism ◽  
Single Degree ◽  
Spatial Mechanisms ◽  
Torque Analysis ◽  
Basic Concepts

The basic concepts of screw coordinates described in Part I are applied to the numerical kinematic analysis of spatial mechanisms. The techniques are illustrated with reference to the displacement, velocity, and static-force-and-torque analysis of a general, single-degree-of-freedom spatial mechanism: a seven-link mechanism with screw pairs (H)7. By specialization the associated computer program is capable of analyzing many other single-loop spatial mechanisms. Numerical examples illustrate the results.

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.

An Automated Inversion Apporach to Closed-Form Kinematic Analysis of Planar Mechanisms

1992 ◽  
Author(s):  
Arunava Biswas ◽  
Gary L. Kinzel
Keyword(s):  
Closed Form ◽  
Iterative Methods ◽  
Kinematic Analysis ◽  
Equation Approach ◽  
Planar Mechanisms ◽  
Loop Equation ◽  
Closed Form Solutions

Abstract In this paper an inversion approach is developed for the analysis of planar mechanisms using closed-form equations. The vector loop equation approach is used, and the occurrence matrices of the variables in the position equations are obtained. After the loop equations are formed, dependency checking of the unknowns is performed to determine if it is possible to solve for any two equations in two unknowns. For the cases where the closed-form solutions cannot be implemented directly, possible inversions of the mechanism are studied. If the vector loop equations for an inversion can be solved in closed-form, they are identified and solved, and the solutions are transformed back to the original linkage. The method developed in this paper eliminates the uncertainties involved, and the large number of computations required in solving the equations by iterative methods.

Kinematic Analysis of Spatial Six-Link 3R-2P-C Mechanisms

1976 ◽  
Vol 4 (2) ◽  
pp. 71-76
Author(s):  
M.O.M. Osman ◽  
R. V. Dukkipati
Keyword(s):  
Closed Form ◽  
Kinematic Analysis ◽  
Input Output ◽  
Variable Parameters ◽  
Output Displacement ◽  
Loop Equation ◽  
Dual Number ◽  
Input And Output ◽  
Order Polynomial ◽  
Output Equation

Using (3 x 3) matrices with dual-number elements, closed-form displacement relationships are derived for a spatial six-link R-C-P-R-P-R mechanism. The input-output closed form displacement relationship is obtained as a second order polynomial in the output displacement. For each set of the input and output displacements obtained from the equation, all other variable parameters of the mechanism are uniquely determined. A numerical illustrative example is presented. Using the dual-matrix loop equation, with proper arrangement of terms and following a procedure similar to that presented, the closed-form displacement relationships for other types of six-link 3R + 2P + 1C mechanisms can be obtained. The input-output equation derived may also be used to generate the input-output functions for five-link 2R + 2C + 1P mechanisms and four-link mechanisms with one revolute and three cylinder pairs.

Configuration Design and Displacement Analysis of a Novel Decoupled 3T2R Parallel Robot

2011 ◽  
Vol 308-310 ◽  
pp. 2037-2041
Author(s):  
Zhi Xin Shi ◽  
Mei Yan Ye
Keyword(s):  
Kinematic Analysis ◽  
Topological Structure ◽  
Theoretical Basis ◽  
Parallel Robot ◽  
Configuration Design ◽  
Displacement Analysis ◽  
Position And Orientation

Based on the control decoupled principle and approach of Position and Orientation Characteristic (in short, POC) set, a novel decoupled parallel robot with 3-Translation and 2-Rotation (in short, 3T2R) outputs has been presented in the paper. And the topological structure of this new mechanism is fully decoupled, which have the advantages of easily control, simple kinematic analysis, and so on. Then the structure and displacement analysis of this novel parallel robot have been accomplished. The research provides theoretical basis for design and practical applicability of this novel parallel robot.

Kinematic analysis of multi-loop spatial mechanisms: The five-loop case

Meccanica ◽  
1991 ◽  
Vol 26 (2-3) ◽  
pp. 101-110 ◽  
Author(s):  
R. Garziera ◽  
E. T. Hajiyev ◽  
R. Riva
Keyword(s):  
Kinematic Analysis ◽  
Spatial Mechanisms
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