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.

A New Method for Displacement Analysis of Multi-Loop Spatial Linkages Based on Ordered Simple-Opened-Chains

1996 ◽  
Author(s):  
Xian-Wen Kong ◽  
Ting-Li Yang
Keyword(s):  
Continuation Method ◽  
The Other ◽  
New Method ◽  
New Approach ◽  
Strongly Coupled ◽  
Displacement Analysis ◽  
Cpu Time ◽  
Base Points ◽  
Weakly Coupled ◽  
Spatial Linkages

Abstract This paper presents systematically a new method for the displacement analysis (DA) of multi-loop spatial linkages (MLSLs) based on ordered simple-opened-chains (SOCs). In performing DA, a MLSL is converted into not a set of base points, a set of isolated links or a tree with/without isolated links in common use, but a weakly coupled MLSL in this paper. The characteristics of the proposed method are: (a) The number of unknowns in the set of equations for displacement analysis (EDA) of a MLSL is reduced to the minimum; (b) All the possible configurations corresponding to a given set of inputs of a weakly coupled MLSL or a strongly coupled MLSL with the coupled degree k = 1 can be obtained quickly. As compared with the other two methods available to find all the solutions to the DA in the case of MLSL with k = 1, the proposed method is superior to the resultant method in that it is applicable to more complex MLSLs and superior to the continuation method in that it takes much less CPU time to find all the solutions; (c) The set of EDA can be formulated and solved automatically; and (d) The new approach makes it possible to perform the kinematic and kineto-static analyses in a unified and simplified way.

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.

A Double-Faced 6R Single-Loop Overconstrained Spatial Mechanism

2018 ◽  
Vol 10 (3) ◽  
Author(s):  
Xianwen Kong ◽  
Xiuyun He ◽  
Duanling Li
Keyword(s):  
Kinematic Analysis ◽  
Isosceles Triangle ◽  
The Other ◽  
Dual Quaternion ◽  
Single Loop ◽  
Plane Symmetric ◽  
Spatial Mechanism ◽  
Revolute Joints ◽  
Full Turn ◽  
Overconstrained Mechanisms

This paper deals with a 6R single-loop overconstrained spatial mechanism that has two pairs of revolute joints with intersecting axes and one pair of revolute joints with parallel axes. The 6R mechanism is first constructed from an isosceles triangle and a pair of identical circles. The kinematic analysis of the 6R mechanism is then dealt with using a dual quaternion approach. The analysis shows that the 6R mechanism usually has two solutions to the kinematic analysis for a given input and may have two circuits (closure modes or branches) with one or two pairs of full-turn revolute joints. In two configurations in each circuit of the 6R mechanism, the axes of four revolute joints are coplanar, and the axes of the other two revolute joints are perpendicular to the plane defined by the above four revolute joints. Considering that from one configuration of the 6R mechanism, one can obtain another configuration of the mechanism by simply renumbering the joints, the concept of two-faced mechanism is introduced. The formulas for the analysis of plane symmetric spatial triangle are also presented in this paper. These formulas will be useful for the design and analysis of multiloop overconstrained mechanisms involving plane symmetric spatial RRR triads.

A New Method for Overconstraint Analysis Based on Kinematic Compatibility of Single-Opened-Chains

2000 ◽  
Author(s):  
Qiong Jin ◽  
Lu-Bin Hang ◽  
Ting-Li Yang
Keyword(s):  
New Method ◽  
Input Output ◽  
Compatibility Conditions ◽  
The Difference ◽  
Overconstrained Mechanisms

Abstract A new method for analyzing overconstrained mechanisms is presented in this paper according to the kinematic compatibility criterion of single-opened-chains (SOCs). This criterion states that: if for any value of an active input, two SOCs have die same distances and angles between two ending axes of each SOC, and the difference of axis-lengths corresponding to each hand-side for two SOCs is kept constant, then the two SOCs can be combined together as one closure loop which is an overconstrained mechanism. This method is simple with four clear targets. It is quite different from other methods because the input-output relationships of variables can be obtained during overconstraint analysis. In order to find overconstrained mechanisms, we can begin with parts of compatibility conditions to obtain some kinematic relationships, so that the input-output law and the overconstraint conditions satisfying all compatibility relationships could be given. As examples, the 4R overconstrained mechanisms and a 4R2P overconstrained mechanism are proved using this method.

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.

Overconstrained Mechanisms Derived From RPRP Loops

2018 ◽  
Vol 140 (6) ◽  
Author(s):  
Kuan-Lun Hsu ◽  
Kwun-Lon Ting
Keyword(s):  
Computer Aided Design ◽  
Random Search ◽  
Modular Approach ◽  
Input Output ◽  
Assembly Strategy ◽  
Revolute Joints ◽  
Prismatic Joints ◽  
Overconstrained Mechanisms ◽  
Aided Design ◽  
Four Bar Linkage

This paper addresses the assembly strategy capable of deriving a family of overconstrained mechanisms systematically. The modular approach is proposed. It treats the topological synthesis of overconstrained mechanisms as a systematical derivation rather than a random search. The result indicates that a family of overconstrained mechanisms can be constructed by combining legitimate modules. A spatial four-bar linkage containing two revolute joints (R) and two prismatic joints (P) is selected as the source-module for the purpose of demonstration. All mechanisms discovered in this paper were modeled and animated with computer-aided design (CAD) software and their mobility were validated with input–output equations as well as computer simulations. The assembly strategy can serve as a self-contained library of overconstrained mechanisms.

Analysis of Overconstrained Mechanisms

1995 ◽  
Vol 117 (1) ◽  
pp. 69-74 ◽  
Author(s):  
C. Mavroidis ◽  
B. Roth
Keyword(s):  
Input Output ◽  
Systematic Method ◽  
Numerical Examples ◽  
Single Loop ◽  
Overconstrained Mechanisms

This paper presents a new systematic method for dealing with overconstrained mechanisms. 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. Two numerical examples and one set of input-output curves are presented.

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.

Planning with Semi-input-output Method with Empirical Application to Nigeria. By Arie Kuyvenhoven. Leiden: Martinus Nijhoff Social Sciences Division. 1978. xi + 266 pp.

1980 ◽  
Vol 19 (3) ◽  
pp. 247-249
Author(s):  
A. R. Kemal
Keyword(s):  
Social Sciences ◽  
Developing Countries ◽  
Final Demand ◽  
The Other ◽  
Production Structure ◽  
Input Output ◽  
Output Analysis ◽  
Input Output Analysis ◽  
Comparative Cost ◽  
Planning Models

Input -output analysis is being widely used in developing countries for planning purposes. For a given level of final demand, input-output analysis allows us to project the required level of gross output to ensure consistency of plan. These projections are made on the assumption that the existing production structure is optimal and it implies that an increase in demand will be met through the expansion of domestic output even when it can be satisfied through an increase in imports. On the other hand, according to the semi-input-output method, we do not have to increase the output of international sectors in order to meet the increase in demand because the level and composition of these activities should be determined by comparative- cost considerations. These are the only national sectors in which output must increase in order to avoid shortage. The semi-input -output method has been such a useful and important contribution, yet, regrettably, its influence on the planning models had been rather limited.

The Problem of the Typology of Rationality in Muslim Culture

2019 ◽  
Vol 62 (6) ◽  
pp. 88-99
Author(s):  
Andrey A. Lukashev
Keyword(s):  
Modern Philosophy ◽  
Theoretical Basis ◽  
Theoretical Models ◽  
The Other ◽  
Common Denominator ◽  
Islamic Culture ◽  
The Common ◽  
Per Se ◽  
The One ◽  
Muslim Culture

The typology of rationality is one of major issues of modern philosophy. In an attempt to provide a typology to Oriental materials, a researcher faces additional problems. The diversity of the Orient as such poses a major challenge. When we say “Oriental,” we mean several cultures for which we cannot find a common denominator. The concept of “Orient” involves Arabic, Indian, Chinese, Turkish and other cultures, and the only thing they share is that they are “non-Western.” Moreover, even if we focus just on Islamic culture and look into rationality in this context, we have to deal with a conglomerate of various trends, which does not let us define, with full confidence, a common theoretical basis and treat them as a unity. Nevertheless, we have to go on trying to find common directions in thought development, so as to draw conclusions about types of rationality possible in Islamic culture. A basis for such a typology of rationality in the context of the Islamic world was recently suggested in A.V. Smirnov’s logic of sense theory. However, actual empiric material cannot always fit theoretical models, and the cases that do not fit the common scheme are interesting per se. On the one hand, examination of such cases gives an opportunity to specify certain provisions of the theory and, on the other hand, to define the limits of its applicability.

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