Displacement Analysis of Spatial Six-Link, 5R-C Mechanisms

1974 ◽  
Vol 41 (3) ◽  
pp. 759-766 ◽  
Author(s):  
J. Duffy ◽  
J. Rooney
Keyword(s):  
Physical Model ◽  
Numerical Results ◽  
Input Output ◽  
Displacement Analysis ◽  
Output Displacement ◽  
Spatial Mechanisms ◽  
Special Cases

Input-output displacement equations of degree 16 are derived for spatial six-link RRRRCR and RRCRRR2 mechanisms. The derivation of these equations provides the solution to one of the most formidable problems in the theory of analysis of spatial mechanisms. The subsequent displacement analysis is derived by extending Be´zout’s reduction (1764) of the degree of a pair of equations in a single unknown, to equations with two unknowns. Numerical results were verified using a physical model. The input-output equations contain as special cases eighth-degree polynomials for spatial six-link 4R-P-C slider-crank 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.

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.

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.

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.

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.

Displacement Analysis of the R0-2R-2C Spatial Linkage Mechanisms

1994 ◽  
Author(s):  
Y. B. Zhou ◽  
R. O. Buchal ◽  
R. G. Fenton
Keyword(s):  
Closed Form ◽  
Algebraic Method ◽  
Input Output ◽  
Displacement Analysis ◽  
Output Displacement

Abstract Closed form input-output displacement equations are derived for the R0-2R-2C mechanisms using the vector algebraic method. As compared to previous works, the proposed method is characterized by its standardized analysis steps, compact expressions and simplicity.

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.

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