Automatic Mobility Analysis of Parallel Mechanisms Based on Position and Orientation Characteristic Equation. Part II: Mobility analysis and Examples

2019 ◽  
pp. 2789-2798
Author(s):  
Xiaorong Zhu ◽  
Huiping Shen ◽  
Chengqi Wu ◽  
Tingli Yang
Keyword(s):  
Characteristic Equation ◽  
Parallel Mechanisms ◽  
Mobility Analysis ◽  
Position And Orientation

scholarly journals Automatic Mobility Analysis of Parallel Mechanisms: An Algorithm Approach Based on Position and Orientation Characteristic Equations

2019 ◽  
Author(s):  
Xiaorong Zhu ◽  
Huiping Shen ◽  
Chengqi Wu ◽  
Damien Chablat ◽  
Tingli Yang
Keyword(s):  
Systematic Approach ◽  
Fundamental Problem ◽  
Parallel Mechanisms ◽  
Mobility Analysis ◽  
Topological Structures ◽  
Design And Optimization ◽  
Logical Operations ◽  
Intelligent Analysis ◽  
Position And Orientation

Abstract The determination of the mobility of parallel mechanisms (PM) is a fundamental problem. An automatic and intelligent analysis software will be a significant tool for the design and optimization of mechanical systems. Based on the theory of position and orientation characteristics (POC) equations, a systematic approach to computer-aided mobility analysis of PMs is presented in this paper. First, a digital model for topological structures which has a mapping relationship with position and orientation characteristics of mechanism is proposed. It describes not only the dimension of the motion output, but also gives the mapping relationship between the output characteristic and the axis of the kinematic joints. Secondly, algorithmic rules are established that convert the union and intersection operations of POC into the binary logical operations and the automatic analysis of POC are realized. Then, the algorithm of the automatic mobility analysis of PMs and its implementation with VC++ are written. The mobility and its properties (POC) will also be analyzed and displayed automatically after introducing by users of the data of topological structures representation. Finally, typical examples are provided to show the effectiveness of the software platform.

A Systematical Approach for Structure Synthesis of Parallel Mechanisms Based on Single-Open-Chain Modules and Its Application

2009 ◽  
Author(s):  
Ting-Li Yang ◽  
An-Xin Liu ◽  
Qiong Jin ◽  
Yu-Feng Luo ◽  
Lu-Bin Hang ◽  
...  
Keyword(s):  
Parallel Mechanism ◽  
Systematic Approach ◽  
Screw Theory ◽  
Parallel Mechanisms ◽  
Type Synthesis ◽  
Open Chain ◽  
Structure Synthesis ◽  
Vector Algebra ◽  
Algebra Theory ◽  
Position And Orientation

Based on previous research results presented by authors, this paper proposes a novel systematic approach for structure synthesis of all parallel mechanisms (excluding Bennett mechanism etc), which is totally different from the approaches based on screw theory and based on displacement subgroup. Main characteristics of this approach are: (a) the synthesized mechanisms are non-instantaneous ones, and (b) only simple mathematical tools (vector algebra, theory of sets, etc.) are used. Main steps of this approach include: (1) Determining functional and structural requirements of the parallel mechanism to be synthesized, such as position and orientation characteristic (POC) matrix, degree of freedom (DOF), etc. (2) Type synthesis of branches. (3) Assembling of branches (determining the geometry constraint conditions among the branches attached between the moving platform and the frame, and checking the DOF). (4) Identifying the inactive joints. (5) Selecting the actuating joints. In order to illustrate the whole procedure, the type synthesis of spherical parallel mechanisms is studied using this approach.

Jacobian Derivation of 5-DOF 3R2T Parallel Mechanisms

2004 ◽  
Author(s):  
Qinchuan Li ◽  
Xudong Hu ◽  
Zhen Huang
Keyword(s):  
Degrees Of Freedom ◽  
Jacobian Matrix ◽  
Screw Theory ◽  
Kinematic Chain ◽  
Parallel Mechanisms ◽  
Mobility Analysis

This paper presents a method for the Jacobian derivation of 5-DOF 3R2T PMs (parallel mechanisms), where 3R denotes three rotational DOFs (degrees of freedom) and 2T denotes two translational DOFs. First the mobility analysis of such kind of parallel mechanisms is reviewed briefly. The Jacobian matrix of the single limb kinematic chain is obtained via screw theory, which is a 6 × 5 matrix. Then it is shown that the mobility analysis of such kind of PM is important when simplifying the 6 × 5 matrix into a 5 × 5 Jacobian matrix. After obtaining the 5 × 5 Jacobian matrix for each limb, a 5 × 5 Jacobian matrix for the whole mechanism can be established.

Position and Orientation Characteristic Equation for Topological Design of Parallel Mechanisms

2008 ◽  
Author(s):  
Ting-Li Yang ◽  
An-Xin Liu ◽  
Qiong Jin ◽  
Yu-Feng Luo ◽  
Hui-Ping Shen ◽  
...  
Keyword(s):  
Topological Structure ◽  
Parallel Mechanism ◽  
Screw Theory ◽  
Parallel Mechanisms ◽  
Output Link ◽  
Geometrical Meaning ◽  
Operation Rules ◽  
The Matrix ◽  
Position And Orientation ◽  
Symbolic Operation

This paper presents the explicit mapping relations between topological structure of parallel mechanism and position and orientation characteristic (in short, POC) of its motion output link. It deals with: (1) The symbolic representation and the invariant of topological structure of mechanism; (2) The matrix representation of POC of motion output link; (3) The POC equations of parallel mechanism and its symbolic operation rules. The symbolic operation involves simple mathematic tools and fewer operation rules, and has clear geometrical meaning. So, it is easy to use. The forward operation of the POC equations can be used for structural analysis; its inverse operation can be used for structural synthesis. The method proposed in this paper is totally different from the methods based on screw theory and based on displacement subgroup.

Mobility analysis and structural synthesis of a class of spatial mechanisms with coupling chains

Robotica ◽  
2015 ◽  
Vol 34 (11) ◽  
pp. 2467-2485 ◽  
Author(s):  
Wen-ao Cao ◽  
Huafeng Ding ◽  
Ziming Chen ◽  
Shipei Zhao
Keyword(s):  
Structural Analysis ◽  
Parallel Mechanisms ◽  
Mobility Analysis ◽  
Structural Synthesis ◽  
Systematic Method ◽  
General Methodology ◽  
Spatial Mechanisms ◽  
Analysis And Synthesis

SUMMARYThis paper presents a systematic method for dealing with mobility analysis and structural synthesis of a class of important spatial mechanisms with coupling chains, which involve more complex coupling relations than spatial parallel mechanisms. First, an approach to the establishment of the motion screw equation of the class of mechanisms is derived. Then, a general methodology for mobility analysis along with detection of rigid substructures is proposed based on the motion screw equation. Third, the principle of structural synthesis of the class of mechanisms is established on the basis of the method of mobility analysis. Finally, some novel spatial mechanisms with coupling chains are synthesized, illustrating the effectiveness of the method. The study of the paper will benefit structural analysis and synthesis of more complex spatial mechanisms with coupling chains.

Mobility Change in Two Types of Metamorphic Parallel Mechanisms

2009 ◽  
Vol 1 (4) ◽  
Author(s):  
Dongming Gan ◽  
Jian S. Dai ◽  
Qizheng Liao
Keyword(s):  
Parallel Mechanism ◽  
Type A ◽  
Parallel Mechanisms ◽  
Mobility Analysis ◽  
Topological Change ◽  
Mobility Factor ◽  
Local Mobility

This paper presents a new joint coined as the rT joint and proposes two types of metamorphic parallel mechanisms assembled with this rT joint. In the first type, the mechanism changes its topology by turning the rT joints in all limbs into different configurations. This change in mobility is completed by two cases illustrated by a 3(rT)PS metamorphic parallel mechanism having variable mobility from 3 to 6 and a 3(rT)P(rT) parallel mechanism having various configurations including pure translations, pure rotations, and mobility 4. In the second type, a central strut with the rT joint is added in a parallel mechanism. The variable mobility of the mechanism results from the topological change of the central (rT)P(rT) strut. This is illustrated in a 3SPS-1(rT)P(rT) metamorphic parallel mechanism, which changes its mobility from 4 to 5. It is demonstrated in mobility analysis that the change in local mobility of each limb results in the change in the platform mobility that a metamorphic process can be achieved. This particular analysis leads to advancement of improved Grübler–Kutzbach criterion by introducing the local mobility factor in the mobility analysis.

A Simple Method for Mobility Analysis Using Reciprocal Screws

2006 ◽  
Author(s):  
Z. Huang ◽  
Q. J. Ge
Keyword(s):  
Coordinate System ◽  
Scalar Product ◽  
Simple Procedure ◽  
Parallel Manipulators ◽  
Simple Expression ◽  
Parallel Mechanisms ◽  
Complex Mechanism ◽  
Mobility Analysis ◽  
Simple Method ◽  
Analysis Process

The goal of this paper is to demonstrate that the Modified Gru¨bler-Kutzbach Criterion when combined with a simple procedure for determining the reciprocal screws offers a direct and simple method for analysing highly complex mechanisms including the over-constrained parallel manipulators. Since the scalar product of screws is not dependent on the choice of the origin, one can quickly obtain a simple expression of screws by selecting an appropriate coordinate system. In such simple expression, the coordinates of a screw would include 0 or 1, and thus greatly simplifies the procedure for determine the number of constraints in a mechanism. Seven rules have been presented to help simplify the analysis process. The advocated approach makes it possible to determine, within minutes, the mobility of a highly complex mechanism by using a pencil and a paper. Many over-constrained mechanisms, including three parallel mechanisms, are presented as examples.

scholarly journals Mobility analysis of parallel mechanisms based on screw theory and mechanism topology

2015 ◽  
Vol 7 (11) ◽  
pp. 168781401561046 ◽  
Author(s):  
Liping Wang ◽  
Huayang Xu ◽  
Liwen Guan
Keyword(s):  
Screw Theory ◽  
Parallel Mechanisms ◽  
Mobility Analysis

Structure Synthesis of Two-Translation and Two-Rotation Parallel Mechanisms Based on the POC-Based Approach

2011 ◽  
Vol 52-54 ◽  
pp. 759-767
Author(s):  
Yang Yan ◽  
Yu Feng Luo ◽  
Zhi Xin Shi ◽  
Wei Ke Yao ◽  
Ting Li Yang
Keyword(s):  
Parallel Mechanism ◽  
Parallel Manipulator ◽  
Parallel Mechanisms ◽  
Structure Synthesis ◽  
Position And Orientation ◽  
Detailed Application

A systematically approach for structure synthesis of parallel manipulator is based on position and orientation characteristic (POC) matrix, by which a detailed application is focused on the synthesis of 2-translation and 2-rotation parallel mechanisms. The result synthesized involves not only part known mechanisms, but also some novel mechanisms. This paper synthesizes SOC branches which include 2-translation and 2-rotation output, classifies synthesized parallel mechanisms based on SOC branches types, analyses and research this kind parallel mechanism.

Sign in / Sign up

Export Citation Format

Share Document