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.

Mobility Analysis of Parallel Mechanisms Based on Screw Theory and the Concept of Equivalent Serial Kinematic Chain

2005 ◽  
Author(s):  
Xianwen Kong ◽  
Cle´ment M. Gosselin
Keyword(s):  
Systematic Approach ◽  
Screw Theory ◽  
Kinematic Chain ◽  
Second Step ◽  
Parallel Mechanisms ◽  
Mobility Analysis ◽  
Single Loop ◽  
Kinematic Chains ◽  
Serial Chain ◽  
Parallel Kinematic

This paper presents a systematic approach for the mobility analysis of parallel mechanisms. The method is based on screw theory and the concept of equivalent serial chain. An equivalent serial kinematic chain of a k-legged PKC (parallel kinematic chain) is defined as a serial kinematic chain which has the same twist system and the wrench system as the k-legged PKC. Using the proposed approach, the mobility analysis of a PKC is performed in two steps. The first step is the instantaneous mobility analysis, and the second step is the full-cycle mobility inspection. The first step is dealt with based on screw theory. The second step is performed with the aid of the concept of equivalent serial chain and the types of multi-DOF overconstrained single-loop kinematic chains. The proposed approach is illustrated with several examples.

Structure Synthesis of Rank-Degenerated Serial Mechanisms and Over-Constrained Single-Loop Kinematic Chains

2009 ◽  
Author(s):  
Ting-Li Yang ◽  
An-Xin Liu ◽  
Qiong Jin ◽  
Yu-Feng Luo ◽  
Hui-Ping Shen ◽  
...  
Keyword(s):  
Systematic Approach ◽  
Screw Theory ◽  
Degree Of Freedom ◽  
Parallel Mechanisms ◽  
Single Loop ◽  
Kinematic Chains ◽  
Structure Synthesis ◽  
Vector Algebra ◽  
Position And Orientation

Based on the Position and orientation characteristic (POC) equation of serial mechanisms proposed by the author, this paper presents a novel systematic approach for structure synthesis of rank-degenerated serial mechanisms and over-constrained single-loop kinematic chains (KCs) (excluding the Bennett mechanism etc). This approach is totally different from the approaches based on the screw theory and based on the displacement subgroup, and only simple mathematical tools (vector algebra, etc.) are used. Using this approach, the structure types of serial mechanisms with the specified ranks and the specified degree of freedom (DOF) are synthesized firstly. After that, using the structure types of the obtained serial mechanisms, structure types of over-constrained single-loop KCs with the specified ranks and the specified DOF can be generated in a straightforward way. The structure types of the obtained serial mechanisms can be used as branches of parallel mechanisms. The structure types and the ranks of the obtained over-constrained single-loop KCs can be used to calculate the DOF of multi-loop mechanisms. In fact, the systematic approach proposed in this paper is a key component of the systematic approach for structure synthesis of parallel mechanisms.

A General Formula of Degree of Freedom for Parallel Mechanisms

2008 ◽  
Author(s):  
Ting-Li Yang ◽  
Dun-Jin Sun
Keyword(s):  
General Formula ◽  
Screw Theory ◽  
Degree Of Freedom ◽  
Parallel Mechanisms ◽  
Characteristic Equations ◽  
Position And Orientation ◽  
Symbolic Operation ◽  
Selection Of

In this paper, a general formula of degree of freedom (DOF) for parallel mechanisms has been presented which could provide the full-cycle DOF. The key parameters in the formula can be determined via the position and orientation characteristic equations and their symbolic operations of serial and parallel mechanisms proposed by author and the symbolic operation is simple. It is totally different from the methods based on screw theory and based on displacement subgroup. The formula has been used for selection of driving pairs and determination of idle pairs. The formula may also be used for determining the DOF of other multi-loop mechanisms besides parallel mechanisms.

A General Degree of Freedom Formula for Parallel Mechanisms and Multiloop Spatial Mechanisms

2012 ◽  
Vol 4 (1) ◽  
Author(s):  
Ting-Li Yang ◽  
Dong-Jin Sun
Keyword(s):  
Screw Theory ◽  
Degree Of Freedom ◽  
Parallel Mechanisms ◽  
Spatial Mechanisms ◽  
Vector Algebra ◽  
Algebra Theory ◽  
Position And Orientation ◽  
Displacement Group ◽  
Selection Of

Based on the position and orientation characteristic (POC) set and the POC equations for serial mechanisms and parallel mechanisms proposed by authors, this paper presents a novel general degree of freedom (DOF) formula which is totally different from approaches based on the screw theory and the displacement group. It can be used to determine the full-cycle DOF of parallel mechanisms (PMs) and multiloop spatial mechanisms using symbolic “union” and “intersection” operations for POC sets. These operations involve only several rules and only simple mathematical tools (vector algebra, theory of sets, etc.) are used. Furthermore, criteria for determination of the inactive joints and selection of the actuating joints are proposed. The presented approach is illustrated with several examples.

Analytic Determination of Wrench Closure Workspace of Spatial Cable Driven Parallel Mechanisms

2015 ◽  
Author(s):  
Zhiyu Sheng ◽  
Joon-Hyuk Park ◽  
Paul Stegall ◽  
Sunil K. Agrawal
Keyword(s):  
Simulation Study ◽  
Null Space ◽  
Boundary Surface ◽  
Parallel Mechanisms ◽  
Analytic Determination ◽  
Structure Matrix ◽  
Feasible Solutions

This paper proposes an efficient way of determining analytically the Wrench Closure Workspace (WCW) of spatial redundant cable-driven parallel mechanisms (CDPM). The method builds upon the boundary surface equations obtained from the null space of the structure matrix of CDPM. The set of feasible solutions is obtained that satisfies positive tension in the cables. This method was applied to characterize the WCW of spatial CDPM which has redundancy of 1 or 2. A simulation study was carried out to validate the accuracy and efficiency of the method. Several advantages over conventional approaches for determining the WCW were identified through simulation.

Determination of Singularity-Free Zones in the Workspace of Planar 3-P̱RR Parallel Mechanisms

2006 ◽  
Vol 129 (6) ◽  
pp. 649-652 ◽  
Author(s):  
Mehdi Tale Masouleh ◽  
Clément Gosselin
Keyword(s):  
Parallel Mechanisms ◽  
Numerical Examples ◽  
Mathematical Derivation

This paper presents an algorithm for the determination of singularity-free zones in the workspace of the planar 3-P̱RR mechanism. The mathematical derivation of the algorithm is first given. Numerical examples are then included to demonstrate the application of the proposed approach.

A novel numerical approach for workspace determination of parallel mechanisms

2017 ◽  
Vol 31 (6) ◽  
pp. 3005-3015 ◽  
Author(s):  
Yiqun Zhou ◽  
Junchuan Niu ◽  
Zhihui Liu ◽  
Fuliang Zhang
Keyword(s):  
Numerical Approach ◽  
Parallel Mechanisms

Construction, Mobility Analysis and Synthesis of Polyhedra With Articulated Faces

2013 ◽  
Vol 6 (1) ◽  
Author(s):  
Thierry Laliberté ◽  
Clément Gosselin
Keyword(s):  
Physical Models ◽  
Single Type ◽  
Mobility Analysis ◽  
Analysis And Synthesis ◽  
Articulated Mechanisms ◽  
Mechanical Arrangement

The concept of polyhedra with articulated faces is investigated in this paper. Polyhedra with articulated faces can be described as polyhedral frameworks, whose faces are constrained to remain planar. A mechanical arrangement based on a single type of component is proposed for the construction of the polyhedra. Then, the determination of their infinitesimal and full-cycle mobility is addressed. In some cases, they are rigid structures while in others they are articulated mechanisms. Finally, examples are given, using simulation and physical models, and several new families of articulated polyhedra are synthesized.

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