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.

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.

General Characteristics of the Motion of Multiple-Pode Joints

1984 ◽  
Vol 51 (1) ◽  
pp. 171-178 ◽  
Author(s):  
T. W. Lee ◽  
E. Akbil
Keyword(s):  
Functional Analysis ◽  
Analytical Method ◽  
Input Output ◽  
Displacement Analysis ◽  
General Displacement ◽  
Motion Parameters ◽  
The Creation ◽  
Motion Characteristics ◽  
And Behavior ◽  
Output Equation

This paper presents an analytical method on the investigation of the motion characteristics of a class of spatial mechanical components involving the ball-and-trunnion type of joint, namely, the multiple-pode joint. Algebraic derivations of the input-output equation and explicit relations for motion parameters are presented for these joints as well as their shaft couplings. From this general displacement analysis, some insights into the basic nature and behavior of the multiple-pode joint are observed and interpreted. The creation of shaft couplings using these joints and their functional analysis are also illustrated in several cases.

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 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.

Displacement Analysis of the Generalized Clemens Coupling, The R-R-S-R-R Spatial Linkage

1975 ◽  
Vol 97 (2) ◽  
pp. 575-580 ◽  
Author(s):  
D. M. Wallace ◽  
F. Freudenstein
Keyword(s):  
Fourth Order ◽  
Constant Velocity ◽  
Degrees Of Freedom ◽  
Input Output ◽  
Closed Form Solutions ◽  
Input And Output ◽  
Order Polynomial ◽  
Special Case ◽  
Output Equation ◽  
Fourth Order Polynomial

The Clemens Coupling is a constant-velocity, universal-type joint for nonparallel intersecting shafts. This mechanism is a spatial linkage with five links connected by four revolute pairs, R, and one spherical pair (ball-and-socket joint), S, which is located symmetrically with respect to the input and output shafts. The Clemens Coupling is a special case of the R-R-S-R-R spatial linkage with general proportions, which will, therefore, be called the Generalized Clemens Coupling. This paper gives the algebraic derivation of the input-output equation for the general R-R-S-R-R linkage and demonstrates that it is a fourth-order polynomial in the half tangents of the crank angles. The effect of housing-error tolerances on the displacements of the Clemens Coupling has also been considered. The results demonstrate feasibility of closed-form solutions for five-link mechanisms with kinematic pairs having more than two degrees of freedom.

The Displacement Analysis of the Generalized Tracta Coupling

1970 ◽  
Vol 37 (3) ◽  
pp. 713-719 ◽  
Author(s):  
D. M. Wallace ◽  
F. Freudenstein
Keyword(s):  
Constant Velocity ◽  
General Mechanism ◽  
Universal Joint ◽  
Displacement Analysis ◽  
Spatial Mechanism ◽  
Input And Output ◽  
Previous Solution ◽  
The Subject ◽  
Algebraic Solutions ◽  
Special Case

The displacement analysis of spatial linkages has been the subject of a number of recent investigations, using a variety of mathematical approaches. Algebraic solutions have been developed principally, in cases in which the number of links, n, is less than or equal to 4. When n > 4, the complexity of the displacement analysis appears to increase by one or more orders of magnitude. In this paper we describe a method, which we call the geometric-configuration method, which we have used when n > 4. The method is illustrated with respect to the algebraic displacement analysis of a five-link spatial mechanism, which includes the Tracta joint as a special case. The Tracta joint is a spatial linkage of symmetrical proportions functioning as a constant-velocity universal joint for nonparallel, intersecting shafts (Myard, 1933). It has four turning or revolute pairs (R) and one plane pair (E), which is located symmetrically with respect to the input and output shafts. The generalization of this linkage, which we call the generalized Tracta coupling, is the R-R-E-R-R spatial linkage with general proportions. The displacement analysis of the general mechanism, for which we know of no previous solution, has been derived. An analysis of the effect of tolerances in the Tracta joint has been included.

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 a Spatial 7R Mechanism—A Generalized Lobster’s Arm

1979 ◽  
Vol 101 (2) ◽  
pp. 224-231 ◽  
Author(s):  
J. Duffy ◽  
S. Derby
Keyword(s):  
Mathematical Model ◽  
Kinematic Analysis ◽  
Input Output ◽  
Major Step ◽  
Displacement Analysis ◽  
The Mathematical Model ◽  
Output Equation

An input-output equation of degree 24 is derived for a spatial 7R mechanism with consecutive pair axes intersecting. This mechanism is essentially the mathematical model for the kinematic analysis of a lobster’s arm which is an open 6R chain with mutually perpendicular consecutive pair axes, the geometry of which was first described by Willis [4] in 1841. The analysis of this special 7R mechanism constitutes a major step towards the solution of the general 7R mechanism with seven axes arbitrarily oriented in space.

Displacement Analysis of Spatial Six-Link, 5R-C Mechanisms: A General Solution

1985 ◽  
Vol 107 (3) ◽  
pp. 353-357 ◽  
Author(s):  
Xu Li Ju ◽  
J. Duffy
Keyword(s):  
General Solution ◽  
Angular Displacement ◽  
Problem Formulation ◽  
Input Output ◽  
Displacement Analysis ◽  
Numerical Example ◽  
Single Operation ◽  
Half Angle ◽  
Output Equation

Four angular displacement equations are derived for the spatial 5R-C hexagon from which an input-output equation of 16th degree in the tan-half-angle of the output angular displacement for each of the RCRRRR, RRCRRR mechanisms and the yet unsolved RRRRRC2 mechanism can be obtained by the elimination of two unwanted variables in a single operation. This novel problem formulation is a general solution for all 5R-C mechanisms. Results are verified by a numerical example.

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.

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