An Algorithm for Analytically Calculating the Positions of the Secondary Instant Centers of Indeterminate Linkages

2008 ◽  
Vol 130 (4) ◽  
Author(s):  
Raffaele Di Gregorio
Keyword(s):  
Analytical Method ◽  
Direct Application ◽  
Degree Of Freedom ◽  
Single Degree Of Freedom ◽  
Planar Mechanism ◽  
Single Degree ◽  
Planar Linkages

In a planar mechanism, the position of the instant centers reveals important pieces of information about its static and kinematic behaviors. Such pieces of information are useful for designing the mechanism. Unfortunately, when the mechanism architecture becomes complex, common methods to locate the instant centers, which are based on the direct application of the Aronold–Kennedy theorem, fail. Indeterminate linkages are single-degree-of-freedom (single-dof) planar linkages where the secondary instant centers cannot be found by direct application of the Aronold–Kennedy theorem. This paper presents an analytical method to locate all the instant centers of any single-dof planar mechanism, which, in particular, succeeds in determining the instant centers of indeterminate linkages. In order to illustrate the proposed method, it will be applied to locate the secondary instant centers of the double butterfly linkage and of the single flier eight-bar linkage.

Analytical method for the singularity analysis and exhaustive enumeration of the singularity conditions in single-degree-of-freedom spherical mechanisms

2012 ◽  
Vol 227 (8) ◽  
pp. 1830-1840 ◽  
Author(s):  
Raffaele Di Gregorio
Keyword(s):  
Analytical Method ◽  
Singularity Analysis ◽  
Degree Of Freedom ◽  
Systems Of Equations ◽  
Single Degree Of Freedom ◽  
Planar Mechanism ◽  
Single Degree ◽  
Geometric Conditions ◽  
Spherical Mechanisms ◽  
Spherical Mechanism

In spherical-mechanism kinematics, instantaneous pole axes play the same role as, in planar-mechanism kinematics, instant centres. Their locations only depend on the mechanism configuration when spherical single-degree-of-freedom mechanisms are considered. Such a property makes them a tool to visualize and/or to analyse the instantaneous kinematics of those mechanisms. This article addresses the singularity analysis of single-degree-of-freedom spherical mechanisms by exploiting the properties of instantaneous pole axes. An exhaustive enumeration of the geometric conditions which occur for all the singularity types is given, and a general analytical method based on this enumeration is proposed for implementing the singularity analysis. The proposed analytical method can be used to generate systems of equations useful either for finding the singularities of a given mechanism or to synthesize mechanisms that have to match specific requirements about the singularities.

Study of Dead-Centre Positions of Single-Degree-of-Freedom Planar Linkages Using Assur Kinematic Chains

2006 ◽  
Vol 220 (7) ◽  
pp. 1057-1074 ◽  
Author(s):  
G R Pennock ◽  
G M Kamthe
Keyword(s):  
Direct Application ◽  
Degree Of Freedom ◽  
Special Structure ◽  
Single Degree Of Freedom ◽  
Kinematic Chains ◽  
Single Degree ◽  
Original Technique ◽  
Stationary Configuration ◽  
Planar Linkages ◽  
Dead Centre

The article presents an original technique, using the concept of Assur kinematic chains (AKCs), to determine whether a single-degree-of-freedom planar linkage is in a dead-centre position, i.e. a position where the input link is instantaneously stationary. An AKC is a special structure with mobility zero from which it is not possible to obtain a simpler substructure of the same mobility by removing one or more links. The article presents the concept of modularization of planar linkages into AKC based on the choice of the input link. Then, the article presents the constraints on the locations of the instantaneous centres of zero velocity (or instant centres) for a single-degree-of-freedom planar linkage to be in a stationary configuration, i.e. a configuration where one, or more, of the links is instantaneously stationary. The article shows that constraints on the locations of the instant centres for a stationary configuration are satisfied if an AKC, as part of the linkage, gains a degree of freedom. As the modularization of a planar linkage is based on the choice of the input link, the stationary configurations, determined by this method, are in fact dead-centre positions. Finally, this method is applied to indeterminate linkages, i.e. a class of single-degree-of-freedom planar linkages for which it is not possible to locate all the secondary (or unknown) instant centres by the direct application of the Aronhold—Kennedy theorem.

Equivalent Linkages and Dead Center Positions of Planar Single-Degree-of-Freedom Complex Linkages

2015 ◽  
Vol 7 (4) ◽  
Author(s):  
Jun Wang ◽  
Kwun-Lon Ting ◽  
Daxing Zhao
Keyword(s):  
General Concept ◽  
Degree Of Freedom ◽  
Single Degree Of Freedom ◽  
First Order ◽  
Single Degree ◽  
Kinematic Loops ◽  
The Dead ◽  
Planar Linkages ◽  
Four Bar Linkage ◽  
First Time

This paper proposes a simple and general approach for the identification of the dead center positions of single-degree-of-freedom (DOF) complex planar linkages. This approach is implemented through the first order equivalent four-bar linkages. The first order kinematic properties of a complex planar linkage can be represented by their instant centers. The condition for the occurrence of a dead center position of a single-DOF planar linkage can be designated as when the three passive instantaneous joints of any equivalent four-bar linkage become collinear. By this way, the condition for the complex linkage at the dead center positions can be easily obtained. The proposed method is a general concept and can be systematically applied to analyze the dead center positions for more complex single-DOF planar linkages regardless of the number of kinematic loops or the type of the kinematic pairs involved. The velocity method for the dead center analysis is also used to verify the results. The proposed method extends the application of equivalent linkage and is presented for the first time. It paves a novel and straightforward way to analyze the dead center positions for single-DOF complex planar linkages. Examples of some complex planar linkages are employed to illustrate this method in this paper.

scholarly journals Application of Distance Geometry to Tracing Coupler Curves of Pin-Jointed Linkages1

2013 ◽  
Vol 5 (2) ◽  
Author(s):  
Nicolás Rojas ◽  
Federico Thomas
Keyword(s):  
Configuration Space ◽  
Distance Geometry ◽  
High Order ◽  
Degree Of Freedom ◽  
Step Method ◽  
Simple Method ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Planar Linkages ◽  
Predictor Corrector

In general, high-order coupler curves of single-degree-of-freedom plane linkages cannot be properly traced by standard predictor–corrector algorithms due to drifting problems and the presence of singularities. Instead of focusing on finding better algorithms for tracing curves, a simple method that first traces the configuration space of planar linkages in a distance space and then maps it onto the mechanism workspace, to obtained the desired coupler curves, is proposed. Tracing the configuration space of a linkage in the proposed distance space is simple because the equation that implicitly defines this space can be straightforwardly obtained from a sequence of bilaterations, and the configuration space embedded in this distance space naturally decomposes into components corresponding to different combinations of signs for the oriented areas of the triangles involved in the bilaterations. The advantages of this two-step method are exemplified by tracing the coupler curves of a double butterfly linkage.

Circuits and Branches of Single-Degree-of-Freedom Planar Linkages

1993 ◽  
Vol 115 (2) ◽  
pp. 223-230 ◽  
Author(s):  
T. R. Chase ◽  
J. A. Mirth
Keyword(s):  
Degree Of Freedom ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Planar Linkages

Improved definitions for circuits and branches of mechanisms are proposed and discussed in application to planar linkages. The difficulty of circuit and branch identification of multi-loop planar linkages is introduced. The nomenclature used by various authors is correlated with the definitions proposed here. The danger of confusing circuits with branches is illustrated by demonstrating that mechanisms satisfying published “branch” criteria may actually require disassembly to reach all desired positions, rendering them useless in practice. Furthermore, a change of branch within a circuit is shown to be irrelevant to some applications.

Singularity Traces of Single Degree-of-Freedom Planar Linkages That Include Prismatic and Revolute Joints

2016 ◽  
Vol 8 (5) ◽  
Author(s):  
Saleh M. Almestiri ◽  
Andrew P. Murray ◽  
David H. Myszka ◽  
Charles W. Wampler
Keyword(s):  
Design Parameter ◽  
Closed Loop ◽  
Degree Of Freedom ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Revolute Joints ◽  
Prismatic Joints ◽  
Motion Characteristics ◽  
Planar Linkages ◽  
General Method

This paper extends the general method to construct a singularity trace for single degree-of-freedom (DOF), closed-loop linkages to include prismatic along with revolute joints. The singularity trace has been introduced in the literature as a plot that reveals the gross motion characteristics of a linkage relative to a designated input joint and a design parameter. The motion characteristics identified on the plot include a number of possible geometric inversions (GIs), circuits, and singularities at any given value for the input link and the design parameter. An inverted slider–crank and an Assur IV/3 linkage are utilized to illustrate the adaptation of the general method to include prismatic joints.

scholarly journals Design of Anti-Parallelogram Loop Assemblies

2019 ◽  
Vol 60 (3) ◽  
pp. 232-240
Author(s):  
Şebnem Gür ◽  
Koray Korkmaz ◽  
Gökhan Kiper
Keyword(s):  
Degree Of Freedom ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Assembly Method ◽  
Design Alternatives ◽  
Alternative Approach ◽  
The Subject ◽  
Planar Linkages ◽  
Symmetry Operations ◽  
Selection Of

Scissor mechanisms are frequently used for deployable structures and many studies have been conducted on the subject. Most of the studies consider scissor units as modules in the design process. An alternative approach is to utilize loops as the modules for design. In this paper, the design alternatives of single degree-of-freedom planar linkages comprising anti-parallelogram loops using the loop assembly method is presented. First, scissor mechanisms are reviewed. Next, the types of four-bar loops and the resulting linkages in the literature are introduced and those which are yet to be explored, anti-parallelogram being one of them, are identified. Then the loop assembly method and the examples in the literature are reviewed. As a method to form as many alternatives as possible, symmetry operations are proposed. Suitable frieze symmetry groups utilized for obtaining the assemblies are explained and the anti-parallelogram loop patterns are derived. Next, the single degree-of-freedom linkages are obtained from the loop assemblies. Finally, a selection of the resulting linkages with novel properties are presented. This study shows that loop assemblies are efficient in systematic type synthesis of scissor linkages, some types of which could not be foreseen by using units as modules.

scholarly journals GEOMETRICAL METHODS TO LOCATE SECONDARY INSTANTANEOUS POLES OF SINGLE-DOF INDETERMINATE SPHERICAL MECHANISMS

2011 ◽  
Vol 41 (2) ◽  
pp. 80-88 ◽  
Author(s):  
Soheil Zarkandi
Keyword(s):  
Great Circle ◽  
Direct Application ◽  
Degree Of Freedom ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Spherical Mechanisms ◽  
Geometric Methods ◽  
Point Of Intersection ◽  
Spherical Mechanism ◽  
Work Done

A single-degree-of-freedom (DOF) indeterminate spherical mechanism is defined as a mechanism for which it is not possible to find all the instantaneous poles by direct application of the Aronhold-Kennedy theorem. This paper shows that a secondary instantaneous pole of a two DOFs spherical mechanism lies on a unique great circle instantaneously. Using this property, two geometric methods are presented to locate secondary instantaneous poles of indeterminate single DOF spherical mechanisms. Common approach of the methods is to convert a single DOF indeterminate spherical mechanism into a two DOFs mechanism and then to find two great circles that the unknown instantaneous pole lies on the point of intersection of them. The presented methods are directly deduced from a work done for indeterminate single DOF planar mechanisms.DOI: http://dx.doi.org/10.3329/jme.v41i2.7471

General Order Criteria for the Precision Position Synthesis of Single Degree-of-Freedom Planar Linkages

1994 ◽  
Author(s):  
John A. Mirth
Keyword(s):  
Order Conditions ◽  
Degree Of Freedom ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Complete Order ◽  
Continuous Rotation ◽  
General Order ◽  
Planar Linkages ◽  
Position Synthesis

Abstract The order in which a single degree-of-freedom planar linkage passes through a series of design positions depends on both the relative orientations of a designated input link and the branch characteristics of that same link. The input link must have a continuous rotation as it passes through all design positions that lie on the same branch. The continuous rotation criteria does not apply to design positions on different branches of the linkage. Complete order conditions are presented for linkages with four design positions that lie on one to four separate branches.

Analysis of Maximum Elasto-Plastic Response of Multi-Degree-of-Freedom Oscillators Based on a Modal Combination of Equivalently Linearized Response of Each Mode

2016 ◽  
Author(s):  
Tomoyo Taniguchi ◽  
Hiroki Nishiraku ◽  
Yusuke Ono
Keyword(s):  
Analytical Method ◽  
Degree Of Freedom ◽  
Base Excitation ◽  
Plastic Response ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Linearized System ◽  
Plastic Displacement ◽  
Relationship Of ◽  
Force Displacement

This study develops a new analytical method for evaluating maximum elasto-plastic displacement of multi-degree-of-freedom (MDOF) oscillators under the action of base excitation based on a modal combination. The essence is that modal frequencies, shapes and damping during yielding of any member of the MDOF oscillators are readily specified by the modal analysis with the secondary stiffness of the members being yielded. In addition, assuming that a bilinear hysteresis may describe the force-displacement relationship of each mode, an equivalently linearized system consisting of a single-degree-of-freedom (SDOF) oscillator is introduced to approximate maximum elsato-plastic displacement of each mode. Employing the SRSS-rule, the maximum elasto-plastic displacement of the MDOF oscillator subjected to Kobe-NS accelerogram is calculated and compared with that computed by the commercial software. Applicability of the proposed method to evaluating maximum elasto-plastic displacement of the MDOF oscillator is thoroughly discussed.

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