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.

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.

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 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.

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.

scholarly journals Inverse kinematic analysis for triple-octahedron variable-geometry truss manipulators

2001 ◽  
Vol 215 (2) ◽  
pp. 247-251 ◽  
Author(s):  
L J Xu ◽  
G Y Tian ◽  
Y Duan ◽  
S X Yang
Keyword(s):  
Solution Procedure ◽  
Inverse Kinematic ◽  
Variable Geometry ◽  
Input Output ◽  
Output Variable ◽  
Output Displacement ◽  
Displacement Equation ◽  
Inverse Kinematic Analysis ◽  
Variable Geometry Truss Manipulator ◽  
Variable Geometry Truss

In this paper, a new triple-octahedron variable-geometry truss manipulator is presented. Its inverse kinematic solutions in closed form are studied. An input-output displacement equation in one output variable is derived. The solution procedure is given in detail. A numerical example is illustrated.

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.

scholarly journals CLASSIFICATION OF ACTUAL COMPOSITIONS DEPENDING ON THE ORDER OF ACCUMULATION OF ELEMENTS

2021 ◽  
Vol 7 (73) (1) ◽  
pp. 349-354
Author(s):  
E. Yu. Tsukanova
Keyword(s):  
Limited Time ◽  
Classification Criterion ◽  
Active Behavior ◽  
Modern Level ◽  
Structural Principles ◽  
Theory Of Law ◽  
Subjective Rights ◽  
Different Order ◽  
Legal Consequences

This article analyzes the order of accumulation of elements of the actual composition as a classification criterion for their division into types. Depending on this, the following compositions are distinguished: 1) with the sequential accumulation of their elements; 2) with independent accumulation of elements; 3) built using various structural principles. A logical explanation of the different order of construction of legal facts using the theory of absolute and relative legal relations is given. The relevance of this issue for the modern level of the theory of law is indicated. The conclusion is formulated that relative subjective rights are not, as it were, self-sufficient. They are not able to serve as a means of satisfying interest indefinitely. This right exists only for a limited time and is aimed at achieving such a legal state in which the interest will be ensured through one’s own active behavior. As a result, the temporary order of development of actual circumstances in some situations may have legal significance, and in others — be completely indifferent to future legal consequences.

Analysis and Synthesis of Overconstrained Mechanism

1994 ◽  
Author(s):  
Constantinos Mavroidis ◽  
Bernard Roth
Keyword(s):  
Input Output ◽  
Systematic Method ◽  
Numerical Examples ◽  
Single Loop ◽  
Analysis And Synthesis ◽  
Overconstrained Mechanisms

Abstract This paper presents a new systematic method for dealing with overconstrained mechanisms, and describes how the method was used to discover new overconstrained mechanisms and correct errors in several previously published overconstraint conditions. With this one method we are able to verify all previously known overconstrained mechanisms. In addition, this method yields the input-output equations of any single-loop overconstrained mechanism. For all new and corrected overconstrained mechanisms, numerical examples of input-output curves are 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.

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