scholarly journals Instant Center Identification of Single-Loop Multi-DOF Planar Linkage Using Virtual Link

2021 ◽  
Vol 11 (10) ◽  
pp. 4463
Author(s):  
Liangyi Nie ◽  
Huafeng Ding ◽  
Kwun-Lon Ting ◽  
Andrés Kecskeméthy
Keyword(s):  
Singularity Analysis ◽  
Kinematic Characteristic ◽  
Virtual Link ◽  
Dynamics Modeling ◽  
Single Loop ◽  
Straightforward Method ◽  
Prismatic Joints ◽  
Configuration Synthesis ◽  
Definition Of ◽  
Planar Linkages

Instant center is an important kinematic characteristic which can be used for velocity and singularity analysis, configuration synthesis and dynamics modeling of multi-degree of freedom (multi-DOF) planar linkage. The Aronhold–Kennedy theorem is famous for locating instant centers of four-bar planar linkage, but for single-loop multi-DOF linkages, it fails. Increasing with the number of the links of single-loop multi-DOF planar linkages, the lack of link relationship makes the identification of instant center become a recognized difficulty. This paper proposes a virtual link method to identify instant centers of single-loop multi-DOF planar linkage. First, three types of instant centers are redefined and the instant center identification process graph is introduced. Then, based on coupled loop chain characteristic and definition of instant center, two criteria are presented to convert single-loop multi-DOF planar linkage into a two-loop virtual linkage by adding the virtual links. Subsequently, the unchanged instant centers are identified in the virtual linkage and used to acquire all the instant centers of original single-loop multi-DOF planar linkage. As a result, the instant centers of single-loop five-bar, six-bar planar linkage with several prismatic joints are systematically researched for the first time. Finally, the validity of the proposed method is demonstrated using loop equations. It is a graphical and straightforward method and the application is wide up to single-loop multi-DOF N-bar (N ≥ 5) planar linkage.

Mobility of Single-Loop N-Bar Linkage With Active/Passive Prismatic Joints

2005 ◽  
Vol 128 (6) ◽  
pp. 1261-1271 ◽  
Author(s):  
W. Z. Guo ◽  
R. Du
Keyword(s):  
Open Loop ◽  
Class Iii ◽  
Active Joint ◽  
Revolute Joint ◽  
Single Loop ◽  
Prismatic Joint ◽  
Passive Joint ◽  
Offset Distance ◽  
Prismatic Joints ◽  
Planar Linkages

Single-loop N-bar linkages that contain one prismatic joint are common in engineering. This type of mechanism often requires complicated control and, hence, understanding its mobility is very important. This paper presents a systematic study on the mobility of this type of mechanism by introducing the concept of virtual link. It is found that this type of mechanism can be divided into three categories: Class I, Class II, and Class III. For each category, the slide reachable range is cut into different regions: Grashof region, non-Grashof region, and change-point region. In each region, the rotation range of the revolute joint or rotatability of the linkage can be determined based on Ting’s criteria. The characteristics charts are given to describe the rotatability condition. Furthermore, if the prismatic joint is an active joint, the revolvability of the input revolute joint is dependent in non-Grashof region but independent in other regions. If the prismatic joint is a passive joint, the revolvability of the input revolute joint is dependent on the offset distance of the prismatic joint. Two examples are given to demonstrate the presented method. The new method is able to cover all the cases of N-bar planar linkages with one or a set of adjoined prismatic joints. It can also be used to study N-bar open-loop planar robotic mechanisms.

Mass Flow and Derivative Moment of Inertia Flow in Planar (Geared) Linkages

1992 ◽  
Author(s):  
Zhonghe Ye ◽  
M. R. Smith
Keyword(s):  
Mass Flow ◽  
Kinematic Analysis ◽  
Moment Of Inertia ◽  
Force Balance ◽  
New Concepts ◽  
Prismatic Joints ◽  
Planar Linkages ◽  
First Time ◽  
Shaking Moment

Abstract The paper describes a method for the determination of the conditions for the complete shaking force and shaking moment balancing of planar linkages, including geared linkages, with revolute and prismatic joints. The conditions may be written down without the need for any kinematic analysis of the linkage by the application of two new concepts. These are the concept of mass flow for complete shaking force balance and the concept of derivative moment of inertia flow for complete shaking moment balance, the second of which is described here for the first time. A number of examples demonstrate the power of the method.

A Proposed Categorization Method and Category Domain Inequality Development Procedure for Ground Joints of Five Bar Linkages

1998 ◽  
Author(s):  
Chuen-Sen Lin ◽  
Terry Lee ◽  
Bao-Ping Jia
Keyword(s):  
Computer Program ◽  
Single Loop ◽  
Loop Equation ◽  
Development Procedure ◽  
Five Dimension ◽  
Simple Logic ◽  
Logic Operations ◽  
Definition Of ◽  
Dimension Space ◽  
The Given

Abstract This paper presents a method for the development of sets of symbolic inequalities in terms of link lengths for the prediction of the rotation capabilities of ground joints of single-loop five-bar linkages. The inequalities are obtained from the combination of the loop equation of a five-bar linkage and its derivatives and the application of simple logic operations. The rotation capabilities of ground joints are divided into three categories: the incomplete-rotation ground joints, the conditioned complete-rotation ground joints, and the unconditioned complete-rotation ground joints. The derived sets of inequalities define the domain, in a five-dimension space of the five link lengths, for each of the rotation categories. In this paper, the definition of each category is clearly described and the derivations of sets of inequalities are explained in details. A computer program was constructed to examine the completeness and correctness of the categorization method and to analyze the given five-bar linkages to determine the appropriate categories for their ground joints.

A Computer Implementation of the Position Solution of Planar Linkages Using Vector Loop Decomposition

1998 ◽  
Author(s):  
Clint A. Kahler ◽  
J. Keith Nisbett ◽  
Clement R. Goodin
Keyword(s):  
Closed Form ◽  
Computer Software ◽  
Computer Implementation ◽  
Software Application ◽  
Prismatic Joints ◽  
Position Solution ◽  
Planar Linkages ◽  
Form Approach ◽  
Independent Loops

Abstract A general closed-form approach to the solution of loop equations of planar n-bar linkages is presented. Each loop of a set of canonical independent loops is decomposed to a set of vectors. Several common combinations of revolute and prismatic joints are defined. By evaluating the types of joints at each end of a vector, the magnitude and direction of the vector are determined to be known constants or unknown variables. This leads to an identification of the number of unknowns and the distribution of unknowns in the loop. This identification allows the unknowns to be found by matching the situation to one of the unique, closed-form cases for a solvable loop. A computer software application has been developed and is analyzed for efficiency.

INDEX POLYNOMIAL INVARIANTS OF TWISTED LINKS

2013 ◽  
Vol 22 (04) ◽  
pp. 1340005 ◽  
Author(s):  
NAOKO KAMADA
Keyword(s):  
Virtual Link ◽  
Alternative Definition ◽  
Polynomial Invariant ◽  
Polynomial Invariants ◽  
Intersection Index ◽  
Definition Of

Bourgoin defined the notion of a twisted link. In a sense, it is a non-orientable version of a virtual link. Im, Lee and Lee defined a polynomial invariant of a virtual link by using the virtual intersection index. In this paper, we give an alternative definition of index polynomial by using indices of real crossings and extend it to a twisted links.

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.

Assembly Configurations of Spatial Single-Loop Mechanisms With Revolute, Cylindric, and Prismatic Joints

1998 ◽  
Author(s):  
David E. Foster ◽  
Raymond J. Cipra
Keyword(s):  
Single Loop ◽  
Spatial Mechanisms ◽  
Prismatic Joints ◽  
Spherical Mechanism

Abstract This paper examines the problem of identifying the assembly configurations (ACs), also called circuits, of certain spatial single-loop mechanisms. First, the spherical mechanism is considered; it is believed that such a mechanism has one AC if every pair of adjacent links can line up; otherwise, it has 2 ACs. Next, general spatial mechanisms with revolute, cylindric, and prismatic points are considered. If the mechanism has three or more sliding (cylindric or prismatic) joints, it is possible to find an equivalent spherical mechanism which has the same angular motions. However, it is also possible that at certain positions, some of the links may have to slide an infinite distance, which is not possible. Therefore, the mechanism may have more ACs than the equivalent spherical mechanism. Several examples are given, and some general conclusions are drawn.

Topological invariant and definition method for detecting isomorphism in planar kinematic chains

2020 ◽  
pp. 095440622096078
Author(s):  
Rongjiang Cui ◽  
Zhizheng Ye ◽  
Liang Sun ◽  
Chuanyu Wu
Keyword(s):  
Planetary Gear ◽  
Topological Invariant ◽  
Detection Methods ◽  
Kinematic Chains ◽  
Essential Step ◽  
Planetary Gear Trains ◽  
Gear Trains ◽  
Configuration Synthesis ◽  
Definition Of ◽  
Isomorphism Identification

Isomorphism identification is an essential step in mechanism configuration synthesis. Although various detection methods have been proposed, some of them can only effectively identify kinematic chains (KCs) within 10 links or complex programs that are needed to identify multilink KCs. In this study, a new isomorphism identification method is proposed based on the distance concept of graphs and the graph theory definition of isomorphism. In addition to two complex 21- and 28-link planar simple-joint KCs (PSKCs), the proposed algorithm is tested on the complete atlas of 8-link 1-DOF, 9-link 2-DOF, 10-link 1-DOF, 12-link 1-DOF, and 13-link 2-DOF PSKCs. The algorithm is also tested on 6-link 1-DOF and 7-link 1-DOF planetary gear trains (PGTs) to detect isomorphism. All results are in agreement with those of the existing literature. The method is fully automated via a computer program and has been verified to be reliable and efficient.

THE SYNTHESIS OF THE PLANAR LINKAGES WITH SYMMETRICAL CONFIGURATIONS

2016 ◽  
Vol 40 (5) ◽  
pp. 971-979
Author(s):  
Chia-Chun Chu ◽  
Deng-Maw Lu
Keyword(s):  
Structure Synthesis ◽  
Systematic Methodology ◽  
Configuration Synthesis ◽  
Planar Linkages ◽  
Four Bar Linkage ◽  
Linkage Synthesis

The mechanisms that employ symmetrical configurations can be found in the steering mechanisms, double open refrigerator, roof boxes, and double open windows, among others. They are useful for some special applications with kinematic symmetry. There have been studies about the linkage synthesis, especially in the research of planar closed chains, from as early as 1960s. However, no study has focused on the symmetry of planar linkages. Thus, the purpose of this paper is to present a methodology to synthesize the configurations of planar linkages. The systematic methodology can be divided into structure synthesis, configuration synthesis and results produced from three major processes. Finally, four suitable results of up to six-bar linkages can be obtained, for example. The four results include one four-bar linkage and three six-bar linkages.

Sign in / Sign up

Export Citation Format

Share Document