Displacement Analysis of Spatial Five-Link Mechanisms Using (3×3) Matrices With Dual-Number Elements

1969 ◽  
Vol 91 (1) ◽  
pp. 152-156 ◽  
Author(s):  
A. T. Yang
Keyword(s):  
Closed Form ◽  
Algebraic Equation ◽  
Input Output ◽  
Fourth Degree ◽  
Displacement Analysis ◽  
Dual Number ◽  
Closure Equation

A closure equation, in terms of matrices with dual-number elements, for spatial five-link mechanisms, is presented in this paper. From the equation, a set of displacement equations for a RCRCR mechanism with general proportions is obtained; the input-output relationship is expressed as a fourth-degree algebraic equation and formulas to determine other linkage variables are expressed in closed form.

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.

Closed-Form Displacement Relations of a Five-Link R-R-C-C-R Spatial Mechanism

1971 ◽  
Vol 93 (1) ◽  
pp. 221-226 ◽  
Author(s):  
A. H. Soni ◽  
P. R. Pamidi
Keyword(s):  
Closed Form ◽  
Polynomial Equation ◽  
Input Output ◽  
Degree Polynomial ◽  
Spatial Mechanism ◽  
Dual Number ◽  
Numerical Example

Using (3 × 3) matrices with dual-number elements, closed form displacement relationships are derived for a spatial five-link R-R-C-C-R mechanism. The input-output closed form displacement relationship is an eighth degree polynomial equation. A numerical example is presented.

Polynomial Solutions to the Displacement Analysis of 10-Link 1-DOF Mechanisms

1998 ◽  
Author(s):  
A. K. Dhingra ◽  
A. N. Almadi ◽  
D. Kohli
Keyword(s):  
Closed Form ◽  
Solution Process ◽  
Input Output ◽  
Analysis Problem ◽  
Displacement Analysis ◽  
Kinematic Chains ◽  
Polynomial Solutions ◽  
Elimination Procedure ◽  
Half Angle ◽  
Univariate Polynomial

Abstract This paper presents closed-form polynomial solutions to the displacement analysis problem of planar 10-link mechanisms with 1 degree-of-freedom (DOF). Using the successive elimination procedure presented herein, the input-output (I/O) polynomials as well as the number of assembly configurations for five mechanisms resulting from two 10-link kinematic chains are presented. It is shown that the displacement analysis problems for all five mechanisms can be reduced to a univariate polynomial devoid of any extraneous roots. This univariate polynomial corresponds to the I/O polynomial of the mechanism. In addition, one of the examples also illustrates how trigonometric manipulations in conjunction with tangent half-angle substitutions can lead to non-trivial extraneous roots in the solution process. Theoretical conditions for identifying and eliminating these extraneous roots are also presented.

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.

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.

A Framework for Closed-Form Displacement Analysis of 10-Link 1-DOF Mechanisms

1998 ◽  
Author(s):  
A. K. Dhingra ◽  
A. N. Almadi ◽  
D. Kohli
Keyword(s):  
Closed Form ◽  
Input Output ◽  
Analysis Problem ◽  
Loop Closure ◽  
Displacement Analysis ◽  
Kinematic Chains ◽  
Solvable In Closed Form ◽  
Univariate Polynomial ◽  
Form Approach ◽  
Independent Loops

Abstract This paper presents a closed-form approach, based on the theory of resultants, to the displacement analysis problem of planar 10-link 1-DOF mechanisms. Since each 10-link mechanism has 4 independent loops, its displacement analysis problem can be written as a system of 4 reduced loop-closure equations in 4 unknowns. This system of 4 reduced loop closure equations, for all non-trivial mechanisms resulting from 230 10-link kinematic chains, can be classified into 22 distinct structures. Using the successive and repeated elimination procedures presented herein, it is shown how each of these structures can be reduced into a univariate polynomial devoid of any extraneous roots. This univariate polynomial corresponds to the input-output (I/O) polynomial of the mechanism. Based on the results presented, it can be seen that the displacement analysis problem for all 10-link 1-DOF mechanisms is completely solvable, in closed-form, devoid of any extraneous roots.

Closed-Form Displacement Analysis of 9-Link, 2-DOF and 10-Link, 3-DOF Mechanisms

1996 ◽  
Author(s):  
Abdulaziz N. Almadi ◽  
Anoop K. Dhingra ◽  
Dilip Kohli
Keyword(s):  
Closed Form ◽  
Degrees Of Freedom ◽  
Computational Procedure ◽  
Companion Paper ◽  
Input Output ◽  
Analysis Problem ◽  
Numerical Examples ◽  
Displacement Analysis ◽  
Kinematic Chains ◽  
Solvable In Closed Form

Abstract This paper addresses the closed-form displacement analysis problem of all mechanisms which can be derived from 9-link kinematic chains with 2-DOF, and 10-link kinematic chains with 3-DOF. The successive elimination procedure developed in the companion paper is used to solve the resulting displacement analysis problems. The input-output polynomial degrees as well as the number of assembly configurations for all mechanisms resulting from 40 9-link kinematic chains, and 74 10-link kinematic chains with non-fractionated degrees of freedom (DOF) are given. The computational procedure is illustrated through two numerical examples. The displacement analysis problem for all mechanisms resulting from these chains is completely solvable, in closed-form, devoid of any spurious roots.

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 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.

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.

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