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 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.

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 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 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.

The RCRRC Five-Link Space Mechanism—Displacement Analysis, Force and Torque Analysis and Its Transmission Criteria

1975 ◽  
Vol 97 (2) ◽  
pp. 581-594 ◽  
Author(s):  
Ing-Ping Jack Lee ◽  
Cemil Bagci
Keyword(s):  
Angular Displacement ◽  
Unified Theory ◽  
Eighth Order ◽  
Joint Force ◽  
Output Displacement ◽  
Displacement Equation ◽  
The Matrix ◽  
Torque Analysis ◽  
Force Components ◽  
Inertia Forces

Displacement, and force and torque analyses of the RCRRC five-link space mechanism are performed using 3 × 3 screw matrix and dual vectors. Expressions for all the displacements in the mechanism are given. Input-output displacement equation is obtained in both eighth order and 16th order polynomials in half-tangents of the angular displacement. The solution of the 16th order displacement equation shows that the RCRRC mechanism may have 16 geometric inversions for a set of dimensions. The eighth order displacement equation, which conforms with that obtained by the Unified Theory which uses dual spherical trigonometry, is an incomplete relationship and it only gives the displacements of half of the existing geometric inversions. Numerical examples and photographs of the geometric inversions are given. The force and torque analysis of the RCRRC five-link space mechanism is performed by joint force analysis. Dual inertia forces are neglected, and the motion of the mechanism is known. Explicit expressions for the dual force components at the pair locations are given, as well as the matrix solution. Transmissivities of the mechanism are defined. Force and torque analysis of one of the geometric inversions is performed in a numerical example.

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.

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 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.

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