Singularity and Sub-Branch Identification of Two-DOF Seven-Bar Parallel Manipulators

2009 ◽  
Author(s):  
Jun Wang ◽  
Kwun-Lon Ting ◽  
Changyu Xue ◽  
Kenneth R. Currie
Keyword(s):  
Parallel Manipulators ◽  
Singularity Analysis ◽  
Simple Explanation ◽  
Mobility Analysis ◽  
Joint Rotation ◽  
Computer Aided ◽  
Center Position ◽  
Planar Linkages ◽  
General Method ◽  
Unified Method

Mobility analysis of multi-DOF multiloop planar linkages is much more complicated than the single-DOF planar linkages and has been little explored. This paper offers a unified method to treat the singularity (dead center position) and sub-branch identification of the planar two-DOF seven-bar linkages regardless of the choice of the inputs or fixed links. This method can be extended for the singularity analysis of other multi-DOF multiloop linkages. Based on the concept of joint rotation space and N-bar rotatability laws, this paper presents a general method for the sub-branch identification of the seven-bar linkages. It offers simple explanation and geometric insights for the formation of branch, singularity and sub-branch of the two-DOF seven-bar linkages. The presented algorithm for sub-branch identification is suitable for automated computer-aided mobility identification. Examples are employed to demonstrate the proposed method.

Unified Mobility Identification and Rectification of Six-Bar Linkages

2009 ◽  
Author(s):  
Kwun-Lon Ting ◽  
Jun Wang ◽  
Changyu Xue
Keyword(s):  
Special Form ◽  
Simple Explanation ◽  
Input Output ◽  
Mobility Analysis ◽  
Joint Rotation ◽  
Input Condition ◽  
Computer Aided ◽  
Unified Method

This paper offers a unified method for a complete and unified treatment on the mobility identification and rectification of any planar and spherical six-bar linkages regardless the linkage type and the choice of the input, output, or fixed links. The method is based on how the joint rotation spaces of the four-bar loop and a five-bar loop in a Stephenson six-bar linkage interact each other. A Watt six-bar linkage is regarded as a special form of Stephenson six-bar linkage via the stretch and rotation of a four-bar loop. The paper offers simple explanation and geometric insights for the formation of branch (circuit), sub-branch, and order of motion of six-bar linkages. All typical mobility issues, including branch, sub-branch, and type of motion under any input condition can be identified and rectified with the proposed method. The method is suitable for automated computer-aided mobility identification. The applicability of the results to the mobility analysis of serially connected multiloop linkages is also discussed.

Singularity Analysis of Planar Multiple-DOF Linkages

2014 ◽  
Author(s):  
Jun Wang ◽  
Liangyi Nie ◽  
Quan Wang ◽  
Jinfeng Sun ◽  
Ying You ◽  
...  
Keyword(s):  
Singularity Analysis ◽  
General Concept ◽  
Degree Of Freedom ◽  
Simple Explanation ◽  
Constrained Motion ◽  
Singular Configurations ◽  
N Input ◽  
Center Position ◽  
Kinematic Loop ◽  
Planar Linkages

Singularity analysis of multi-DOF (multiple-degree-of-freedom) multiloop planar linkages is much more complicated than the single-DOF planar linkages. This paper offers a degeneration method to analyze the singularity (dead center position) of multi-DOF multiloop planar linkages. The proposed method is based on the singularity analysis results of single-DOF planar linkages and the less-DOF linkages. For an N-DOF (N>1) planar linkage, it generally requires N inputs for a constrained motion. By fixing M (M<N) input joints or links, the N-DOF planar linkage degenerates an (N-M)-DOF linkage. If any one of the degenerated linkages is at the dead center position, the whole N-DOF linkage must be also at the position of singularity. With the proposed method, one may find out that it is easy to obtain the singular configurations of a multiple-DOF multiloop linkage. The proposed method is a general concept in sense that it can be systematically applied to analyze the singularity for any multiple-DOF planar linkage regardless of the number of kinematic loop or the types of joints. The velocity method for singularity analysis is also used to verify the results. The proposed method offers simple explanation and straightforward geometric insights for the singularity identification of multiple-DOF multiloop planar linkages. Examples are also employed to demonstrate the proposed method.

Rotatability of the Floating Link on Multi-Loop Planar Linkages

2020 ◽  
Vol 12 (6) ◽  
Author(s):  
Cody Leeheng Chan ◽  
Kwun-Lon Ting
Keyword(s):  
Rotation Angle ◽  
Parallel Manipulators ◽  
Orientation Error ◽  
Joint Rotation ◽  
Position Uncertainty ◽  
End Effector ◽  
Uncertainty Model ◽  
Branch Formation ◽  
Joint Clearances ◽  
Planar Linkages

Abstract This paper proposes a method to deal with the orientation uncertainty problem affected by joint clearances. To solve this problem, it is necessary to establish the theory of mobility of the floating link of multi-loop linkages. Since the theory of the mobility of floating link is yet complete, this paper provides a simple treatment to determine the rotatability between any two links, adjoined or not, in planar multi-loop linkages. The rotation angle of the floating link with respect to the reference link is defined so that there is no ambiguity in analyzing the rotation range of the floating link. Based on the joint rotation space (JRS) method, one may identify not only the branch formation but also the rotatability between any two links on each of the branches. It is a visualized method that reveals the rotation characteristic of multi-loop linkages. This paper demonstrates the rotation range of the floating link with respect to the reference link on six-bar Stephenson linkages, 2-degree-of-freedom (DOF). 7-bar linkages, and 3-DOF. Eight-bar parallel manipulators. This might be the first paper to deal with the rotatability of 3-DOF planar multi-loop linkages. This paper uses the method to predict the clearance-induced angle uncertainty of the 8-bar parallel manipulators, which determines the worst orientation error of the end-effector and fills up the void of the joint clearance uncertainty model proposed by Ting et al. (2017, “Clearance-Induced Position Uncertainty of Planar Linkages and Parallel Manipulators,” J. Mech. Rob., 9, p. 061001).

Branch Identification of Planar Two-DOF Seven-Bar Linkages

2009 ◽  
Author(s):  
Jun Wang ◽  
Kwun-Lon Ting ◽  
Changyu Xue
Keyword(s):  
Degrees Of Freedom ◽  
Robot Navigation ◽  
Parallel Manipulators ◽  
Companion Paper ◽  
Physical Experiment ◽  
Analysis Method ◽  
Mobility Analysis ◽  
Joint Rotation ◽  
Multiple Degrees Of Freedom ◽  
Linkage Synthesis

Mobility identification mainly refers to the problems with the motion continuity and smoothness of a potential design or plan. In any linkage synthesis or robot navigation, it is highly desirable that the ability of any of the numerous design candidates to reach the desired positions in a favorable manner can be determined in a single decisive step automatically rather than through a blind trial or even a physical experiment. Mobility of complex linkages has been one of the most troublesome problems in linkage synthesis and programming and the problem is further complicated with multiple degrees-of-freedom. For multiloop parallel manipulators this paper may represent the first mobility analysis method that can not only decisively and unambiguously rectify motion continuity between discrete positions but also provide clear geometric insight or interpretation regarding the formation of discontinuity. The treatment is based on the principle that the mobility of a multiloop linkage is affected by the mobility of each individual loop as well as the interaction between loops. Since the N-bar rotatability laws govern the mobility of an individual loop, the main mobility issue for multiloop linkages is how the mobility of these loops affects each other. One may find that the concept of joint rotation space (JRS) offers simple and intuitive explanation on how the mobility is affected by the combination of loops. The treatment is very suitable for an automated computer-aided mobility analysis. Examples are employed to demonstrate the proposed method. Continuity is a pivotal issue in linkage mobility analysis. Once the continuity can be rectified, problems with smoothness or singularity, which are discussed in the companion paper [28], can be resolved.

Equivalent Five-Bar Linkages for the Singularity Analysis of Two-DOF Seven-Bar Linkages

2017 ◽  
Author(s):  
Jun Wang ◽  
Liangyi Nie ◽  
Daxing Zhao ◽  
Jun Ren ◽  
Quan Wang ◽  
...  
Keyword(s):  
Singularity Analysis ◽  
Center Position ◽  
Planar Linkages ◽  
Four Bar Linkage ◽  
First Time

Equivalent four-bar linkage has been proved to be a simple and general approach for the identification of the singularity (dead center position) of single-DOF complex planar linkages. Based on the concept of equivalent four-bar linkage, this paper proposes the concept of equivalent five-bar linkage and extend this concept to analyze the singularity (dead center position) of three different topologies of two-DOF seven-bar planar linkages for the first time. The five links chosen from the two-DOF seven-bar linkage compose one equivalent five-bar linkage. A singular position may happen when the three passive joints of one equivalent five-bar linkage become collinear. When the equivalent five-bar linkage is at the singular position, the whole two-DOF seven-bar planar linkage must be also at the position of singularity. The propose method offers another geometric insights for the singularity analysis of two-DOF seven-bar planar linkages and other multiple-DOF planar linkages.

Mobility Identification of a Group of Single Degree-of-Freedom Eight-Bar Linkages

2010 ◽  
Author(s):  
Jun Wang ◽  
Kwun-Lon Ting
Keyword(s):  
Linkage Analysis ◽  
Range Of Motion ◽  
Configuration Space ◽  
Mobility Analysis ◽  
Joint Rotation ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Computer Aided ◽  
Analysis And Synthesis ◽  
First Time

This paper presents the first complete and automated mobility identification method for a group of single-DOF planar eight-bar linkages and thus represents a breakthrough on the recognition and understanding of complex linkage mobility. The mobility identification in this paper refers to the configuration space, the range of motion, and configuration recognition. It is a troublesome problem encountered in any linkage analysis and synthesis. The problem becomes extremely confusing with complex multiloop linkages. The proposed approach is simple and straightforward. It recognizes that the loop equations are the mathematical fundamentals for the formation of branches, sub-branches, and other mobility issues of the entire linkage. The mobility information is then extracted through the discriminant method. The paper presents complete answers to all typical mobility issues, offers the mathematical insight as well as explanation on the effects of multiple loops via joint rotation space, and casts light for treating the mobility problems of other complex linkages. The merits of the discriminant method for mobility identification are clarified and examples are employed to showcase the proposed method. The computer-aided automated mobility analysis of eight-bar linkages is made possible for the first time.

Determination of the Workspace of a Three-Degrees-of-Freedom Parallel Manipulator Using a Three-Dimensional Computer-Aided-Design Software Package and the Concept of Virtual Chains1

2015 ◽  
Vol 8 (2) ◽  
Author(s):  
Andrew Johnson ◽  
Xianwen Kong ◽  
James Ritchie
Keyword(s):  
Computer Aided Design ◽  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Graphical Representation ◽  
Three Dimensional ◽  
Parallel Manipulators ◽  
Workspace Analysis ◽  
Computer Aided ◽  
Aided Design

The determination of workspace is an essential step in the development of parallel manipulators. By extending the virtual-chain (VC) approach to the type synthesis of parallel manipulators, this technical brief proposes a VC approach to the workspace analysis of parallel manipulators. This method is first outlined before being illustrated by the production of a three-dimensional (3D) computer-aided-design (CAD) model of a 3-RPS parallel manipulator and evaluating it for the workspace of the manipulator. Here, R, P and S denote revolute, prismatic and spherical joints respectively. The VC represents the motion capability of moving platform of a manipulator and is shown to be very useful in the production of a graphical representation of the workspace. Using this approach, the link interferences and certain transmission indices can be easily taken into consideration in determining the workspace of a parallel manipulator.

The Methods to Study the Influence of the Clearance in the Case of Great Speeds and Small Speeds

2013 ◽  
Vol 837 ◽  
pp. 88-92
Author(s):  
Jan Cristian Grigore
Keyword(s):  
Dynamic Behavior ◽  
Reaction Force ◽  
Accurate Method ◽  
Angular Speed ◽  
Connecting Rod ◽  
Lagrange Equations ◽  
Joint Rotation ◽  
First Case ◽  
Multi Body ◽  
General Method

In kinematic couplings, clearances are inevitable for their operation. The size of these clearances but as a consequence of use, causes a malfunction of the mechanism to which it belongs. The law of motion of driveline changes, big clearances, non-technological system causes vibration, leading to discomfort, uncertainty, and thus reach its degradation. In the paper we shall make a few of geometric and mechanical type considerations about the clearances in the linkages, linkages planes with joint rotation links. Based on mathematical algorithm developed and applied crank mechanism, the model presented in [1], this paper scientifically developed mathematical model, proposing mathematical models to study the influence of the size of the clearance in general dynamic calculation mechanisms. Mechanism considered is crank connecting rod mechanism with clearance cinematic coupling between rod and crank rotation. The paper makes a study of the influence on the dynamic behavior of the crank rod mechanism at high speeds, but also general method algorithm is developed and accurate method to assess the dynamic behavior of multi-body mechanism. The first case is considered a constant angular speed motor and thus determine the elemental expressions that establish the mechanism position, velocity and acceleration expressions in the two directions heads elements. Finally we obtain the expression of the normal reaction force, as well as position expression that defines its angle. With reaction force can specify phase (contact, flight, impact) [1], the behavior of the journal. For the case of general method - the method multi-body - the exact method are established liaison relationships between the parameters , write matrices , inertia matrix. Use Lagrange equations, if non-holonomic constraints. Matrix differential equation of motion is written and it can be solved numerically using Runge-Kutta method of order four. Of the iterative method, we obtain the parameters used in calculating the reaction force expression that can be evaluated accurately in journal bearings behaviour. Any would be their source of appearance, they usually produce unwished effects during the mechanisms functioning.

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