Displacement Analysis of the General N-Bar, Single-Loop, Spatial Linkage—Part 2: Basic Displacement Equations in Matrix and Algebraic Form

1982 ◽  
Vol 104 (2) ◽  
pp. 520-525 ◽  
Author(s):  
H. Albala
Keyword(s):  
Matrix Form ◽  
General Analysis ◽  
Input Output ◽  
Algebraic Form ◽  
Displacement Analysis ◽  
Single Loop ◽  
Output Displacement ◽  
Spatial Mechanism ◽  
Displacement Equation

The displacement analysis of the single-loop, N-bar, spatial linkage is presented—first in matrix form and next in algebraic form. The latter is achieved by means of some novel mathematical tools. The intermediate rotation angles are elminated through various stages. Thus, the general analysis of any particular spatial mechanism, seeking to obtain the input-output displacement equation in closed algebraic form, may be started at the end of the stage suited to this objective.

Displacement Analysis of the RPRCRR Six-Link Spatial Mechanism

1971 ◽  
Vol 38 (4) ◽  
pp. 1029-1035 ◽  
Author(s):  
M. S. C. Yuan
Keyword(s):  
Algebraic Equation ◽  
Input Output ◽  
Variable Parameters ◽  
Displacement Analysis ◽  
Output Displacement ◽  
Spatial Mechanism ◽  
Numerical Example ◽  
Input And Output ◽  
Displacement Equation

Using the method of line coordinates, the input-output displacement equation of the RPRCRR six-link spatial mechanism is obtained as an algebraic equation of 16th order. For each set of the input and output angles obtained from the equation, all other variable parameters of the mechanism are also determined. A numerical example is presented.

Displacement Analysis of the RRCCR Five-Link Spatial Mechanism

1970 ◽  
Vol 37 (3) ◽  
pp. 689-696 ◽  
Author(s):  
M. S. C. Yuan
Keyword(s):  
Input Output ◽  
Eighth Order ◽  
Variable Parameters ◽  
Displacement Analysis ◽  
Output Displacement ◽  
Spatial Mechanism ◽  
Input And Output ◽  
Displacement Equation ◽  
Order Polynomial

By the method of line coordinates, the input-output displacement equation of the RRCCR five-link spatial mechanism is obtained as an eighth-order polynomial in the half tangent of the output angle. For each set of the input and output angles obtained from the polynomial, all other variable parameters of the mechanism are uniquely determined, and the accuracy of the numerical values of each set of solutions is verified.

Displacement Analysis of a Special Case of the 7R, Single-Loop, Spatial Mechanism

1983 ◽  
Vol 105 (1) ◽  
pp. 78-87
Author(s):  
Hiram Albala ◽  
David Pessen
Keyword(s):  
Input Output ◽  
Fourth Degree ◽  
Displacement Analysis ◽  
Single Loop ◽  
Spatial Mechanism ◽  
Rotation Axes ◽  
Successive Rotation ◽  
Special Case ◽  
Output Equation

Based on the displacement equations for the general n-bar, single-loop spatial linkage, obtained elsewhere, the displacement analysis for a special case of the 7R spatial mechanism is carried out. In this mechanism the successive rotation axes are perpendicular to each other, the distances between axes 3-4, 4-5, 5-6, are equal and the offsets along axes 4 and 5 are zero, when input axis is labeled axis 1. In this fashion, there still remain nine free linkage parameters. Input-output equation is of the eighth-degree in the tangent of half the output angle. A particular case of this one, where all the distances between axes are equal and all the offsets along axes are zero, leads to an input-output equation of the fourth-degree in the same quantity, with a maximum of four closures. This mechanism resulted to be a double-rocker.

Kinematic Structure Analysis and Classification of Single-Loop Spatial Linkage Mechanisms

1992 ◽  
Author(s):  
Y. B. Zhou ◽  
R. G. Fenton
Keyword(s):  
Kinematic Structure ◽  
Classification Criterion ◽  
Input Output ◽  
Linkage Mechanism ◽  
Symbolic System ◽  
Maximum Order ◽  
Single Loop ◽  
Output Displacement ◽  
Displacement Equation

Abstract This paper covers the following areas: all practical and typical kinematic input pairs used in a single-loop spatial linkage mechanism (SSLM) are classified using a new symbolic system; four basic groups of SSLMs are defined; and a new kinematic structure classification criterion is proposed, which provides a method to determine the maximum finite number of closures for the mechanism and the maximum order of the input-output displacement equation, free of extraneous roots, describing the kinematics of the SSLMs.

A Displacement Analysis of Spatial Six-Link 4-R-P-C Mechanisms—Part 2: Derivation of Input-Output Displacement Equation for RCRRPR Mechanism

1974 ◽  
Vol 96 (3) ◽  
pp. 713-717 ◽  
Author(s):  
J. Duffy ◽  
J. Rooney
Keyword(s):  
Angular Displacement ◽  
Input Output ◽  
Numerical Examples ◽  
Displacement Analysis ◽  
Output Displacement ◽  
Displacement Equation

The input-output displacement equation is expressed as a degree eight polynomial in the half-tangent of the output angular displacement. The equation can be used to generate input-output functions of spatial five-link RCRCR and RCRRC mechanisms. The results are illustrated by numerical examples.

Closed-Form Displacement Analysis of Five-Link R-C-R-C-P Spatial Mechanism

1973 ◽  
Vol 2 (4) ◽  
pp. 238-240
Author(s):  
R. V. Dukkipati
Keyword(s):  
Closed Form ◽  
Second Order ◽  
Input Output ◽  
Variable Parameters ◽  
Displacement Analysis ◽  
Output Displacement ◽  
Spatial Mechanism ◽  
Dual Number ◽  
Input And Output ◽  
Order Polynomial

Using (3 x 3) matrices with dual-number elements, closed-form displacement relationships are derived for a spatial five-link R-C-R-C-P 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. The derived input-output relationship can be used to synthesize an R-C-R-C-P function generating mechanism for a maximum of 15 precision conditions.

A Displacement Analysis of Spatial Six-Link 4R-P-C Mechanisms—Part 1: Analysis of RCRPRR Mechanism

1974 ◽  
Vol 96 (3) ◽  
pp. 705-712 ◽  
Author(s):  
J. Duffy ◽  
J. Rooney
Keyword(s):  
Angular Displacement ◽  
Physical Significance ◽  
Input Output ◽  
Numerical Examples ◽  
Displacement Analysis ◽  
Output Displacement ◽  
Spherical Mechanisms ◽  
Displacement Equation

The input-output displacement equation is expressed as a degree eight polynomial in the half-tangent of the output angular displacement. A procedure for determining uniquely all the linkage variables verifies the closures and in addition explains the physical significance of the closures of equivalent five-link R5 spherical mechanisms. The equation can be used to generate input-output functions of spatial five-link RCCRR and RCRCR mechanisms. The results are illustrated by numerical examples.

A Displacement Analysis of Spatial Six-Link 4R-P-C Mechanisms—Part 3: Derivation of Input-Output Displacement Equation for RRRPCR Mechanism

1974 ◽  
Vol 96 (3) ◽  
pp. 718-721 ◽  
Author(s):  
J. Duffy ◽  
J. Rooney
Keyword(s):  
Angular Displacement ◽  
Output Function ◽  
Input Output ◽  
Numerical Examples ◽  
Displacement Analysis ◽  
Output Displacement ◽  
Displacement Equation

The input-output displacement equation is expressed as a degree eight polynomial in the half-tangent of the output angular displacement. The equation can be used to generate the input-output function for the spatial five-link RRCCR mechanism. The results are illustrated by numerical examples.

Overconstrained Analysis of Five-Link Spatial Single Loops With Revolute and Prismatic Joints

2000 ◽  
Author(s):  
Qiong Jin ◽  
Lu-Bin Hang ◽  
Ming Zhang
Keyword(s):  
Theoretical Basis ◽  
The Other ◽  
New Method ◽  
Input Output ◽  
Displacement Analysis ◽  
Single Loop ◽  
Prismatic Joints ◽  
Existence Conditions ◽  
Closure Conditions ◽  
Overconstrained Mechanisms

Abstract A new method on determining the existence conditions of overconstrained mechanisms is presented in this paper, which is used for studying the spatial single loop generally possessing one configure. This method is very effective to distinguish finite and infinite solutions of displacement analysis, and can analytically deduce the input-output equations. It is elucidated that the existence conditions of overconstrained mechanism consist of the overconstrained conditions and the closure conditions, and that the independence of the closure conditions should be further discussed. On the other hand, the existence conditions of two known 5-link overconstrainded mechanisms are verified and corrected. This method also provides a theoretical basis for finding new oveconstrained 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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