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.

Equivalent Linkages and Dead Center Positions of Planar Single-DOF Complex Linkages

2013 ◽  
Author(s):  
Jun Wang ◽  
Kwun-Lon Ting ◽  
Daxing Zhao
Keyword(s):  
General Concept ◽  
First Order ◽  
Planar Complex ◽  
Center Position ◽  
Kinematic Loops ◽  
The Dead ◽  
Planar Linkages ◽  
Four Bar Linkage ◽  
First Time ◽  
Kinematic Properties

This paper proposes a simple and general approach for the identification of the dead center positions of single-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 basic idea behind this method is obvious and straightforward. The condition for the occurrence of a dead center position can be designed as when the three passive joints of the equivalent four-bar linkage become collinear. The proposed method is a general concept in the sense that it can be systematically applied to analyze the dead center positions for any type of 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 compare the results. The proposed method paves a novel and easy way to analyze the dead center positions for complex planar linkages. This concept is presented for the first time for the dead center analysis of planar complex linkages. Examples of complex linkages are employed to illustrate this concept in this paper.

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.

scholarly journals The Response of Nonlinear Single-Degree-of-Freedom Systems to Modulated High-Frequency Input

2006 ◽  
Vol 61 (10-11) ◽  
pp. 541-555
Author(s):  
Atef F. El-Bassiouny
Keyword(s):  
Carrier Frequency ◽  
Phase Modulation ◽  
Evolution Equations ◽  
Multiple Scales ◽  
Degree Of Freedom ◽  
Response Curves ◽  
Single Degree Of Freedom ◽  
First Order ◽  
Single Degree ◽  
Jump Phenomena

In this paper we study the response of single-degree-of-freedom with cubic, quartic and quintic nonlinearities to an amplitude-modulated excitation whose carrier frequency is much higher than the natural frequency of the system. The only restriction on the amplitude modulation is that it contains frequencies much lower than the carrier frequency of the excitation. The method of multiple scales is used to derive two coupled first-order ordinary differential equations that describe the evolution of the amplitude and phase with damping, nonlinearities and resonances. The evolution equations are used to determine the steady-state motions, while representative frequency-response curves are presented for each resonance. Stability analysis of the amplitude and phase modulation equations for both cases are performed. The bending of the response curves leads to multi-valued solutions and hence to jump phenomena.

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 An Energy Approach to the Design of Single Degree of Freedom Gravity Balancers With Compliant Joints

2011 ◽  
Author(s):  
Boaz L. Rijff ◽  
Just L. Herder ◽  
Giuseppe Radaelli
Keyword(s):  
Energy Efficient ◽  
Degree Of Freedom ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Compliant Joints ◽  
Constant Potential ◽  
Rigid Joints ◽  
Body Joints ◽  
First Time ◽  
Proof Of Principle

A gravity balancer is a mechanism that compensates the weight of a mass over a range of motion. When no friction is present, this gives an energy efficient mechanism and little effort is required to move an object. Conventional mechanisms have drawbacks due to the use of conventional rigid joints. Compliant joints do not have these disadvantages, can be made from fewer parts and can increase performance compared to rigid body joints. The goal of this paper is to develop a new method for the design of single degree of freedom gravity balancers where all the rigid joints are replaced with compliant joints. The method is based on connecting rigid links with compliant joints. With a constant potential energy as an objective, the method allows new gravity balancers to be designed. The second goal is to construct a demonstrator as proof of principle. It can be concluded that for the first time a gravity balancer has been constructed where all the rigid joints are replaced with compliant joints. The gravity balancer had a peak moment reduction of 93%. The presented method is extensible and allows others to understand and further develop gravity balancers with compliant joints for other applications.

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.

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.

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.

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