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.

Position and Orientation Characteristic Equation for Topological Design of Serial Mechanisms

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

This paper presents the explicit mapping relations between topological structure of mechanism and position and orientation characteristic (abbreviated as POC hereafter) 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 mechanism motion output; (3) The POC equation of serial 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 POC equation can be used for structural analysis and synthesis of serial and parallel mechanisms. The method proposed in this paper is totally different from the methods based on screw theory and based on displacement subgroup/sub-manifold.

Position and Orientation Characteristic Equation for Topological Design of Robot Mechanisms

2008 ◽  
Vol 131 (2) ◽  
Author(s):  
Ting-Li Yang ◽  
An-Xin Liu ◽  
Qiong Jin ◽  
Yu-Feng Luo ◽  
Hui-Ping Shen ◽  
...  
Keyword(s):  
Topological Structure ◽  
Kinematic Chain ◽  
Parallel Mechanisms ◽  
Structural Synthesis ◽  
Geometrical Meaning ◽  
Single Loop ◽  
Operation Rules ◽  
The Matrix ◽  
Position And Orientation ◽  
Symbolic Operation

This paper presents the explicit mapping relations between topological structure and position and orientation characteristic (POC) of mechanism motion output. It deals with (1) the symbolic representation and the invariant property of the topological structure of the mechanism, (2) the matrix representation of POC of mechanism motion output, and (3) the POC equations of serial and parallel mechanisms and the corresponding 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 POC equations cannot only be used for structural analysis of the mechanism (such as determining POC of the relative motion between any two links of a mechanism and the rank of single-loop kinematic chain and calculating the full-cycle DOF of a mechanism, etc.) but can be used for structural synthesis of the mechanism as well (e.g., structural synthesis of the rank-degenerated serial mechanism, the over constrained single-loop mechanism, and the rank-degenerated parallel mechanism, etc.).

On the Correctness and Strictness of the Position and Orientation Characteristic Equation for Topological Structure Design of Robot Mechanisms

2013 ◽  
Vol 5 (2) ◽  
Author(s):  
Ting-Li Yang ◽  
An-Xin Liu ◽  
Hui-Ping Shen ◽  
Yu-Feng Luo ◽  
Lu-Bin Hang ◽  
...  
Keyword(s):  
Topological Structure ◽  
Screw Theory ◽  
Structure Design ◽  
Parallel Mechanisms ◽  
Operation Rules ◽  
Structure Synthesis ◽  
Union Operation ◽  
Intersection Operation ◽  
Velocity Characteristic ◽  
Position And Orientation

Position and orientation characteristic (POC) equations for topological structure synthesis of serial and parallel mechanisms were proposed in a published paper by the authors. This paper will further prove the correctness and strictness of the theoretical foundation for POC equations and also be a reply to the reviewers of our follow-up papers. The main contents of this paper include: symbolic representation of mechanism topological structure and its invariance, velocity characteristic (VC) set and POC set of link and its invariance, one-to-one correspondence between elements of the VC set and POC set, POC equations for the serial mechanism and 10 corresponding “union” operation rules, and POC equations for the parallel mechanism and 14 corresponding “intersection” operation rules. In addition, the interrelations and differences among three methods (POC set based method, screw theory based method, and displacement subgroup based method) for mechanism topological structure design are concluded.

Rank and Mobility of Single Loop Kinematic Chains

2008 ◽  
Author(s):  
Ting-Li Yang ◽  
Dun-Jin Sun
Keyword(s):  
Screw Theory ◽  
Parallel Mechanisms ◽  
Geometrical Meaning ◽  
Single Loop ◽  
Kinematic Chains ◽  
Novel Method ◽  
Position And Orientation ◽  
Symbolic Operation ◽  
Serial Mechanism

This paper presents a novel method for determining rank and mobility of single loop kinematic chains which is totally different from the methods based on screw theory and based on displacement subgroup. The rank of single loop kinematic chains can be determined via the position and orientation characteristic (in short, POC) equation and its symbolic operation of serial mechanism presented by authors. The symbolic operation of the POC equation is simpler and has clear geometrical meaning. The method for determining the rank of single loop kinematic chains can be used for calculating DOF of parallel mechanisms.

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.

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.

Type synthesis of 2R2T parallel mechanisms based on motion equivalent chain method

2014 ◽  
Vol 228 (17) ◽  
pp. 3209-3217 ◽  
Author(s):  
Wei Ye ◽  
Yuefa Fang ◽  
Sheng Guo ◽  
Haibo Qu
Keyword(s):  
Parallel Mechanism ◽  
Screw Theory ◽  
Parallel Mechanisms ◽  
Motion Pattern ◽  
Type Synthesis ◽  
Constraint Force ◽  
Single Loop ◽  
Loop Chain ◽  
Serial Chains

In this paper, the motion equivalent chain method is proposed and then applied to the type synthesis of a class of 2R2T parallel mechanism. The equivalent serial chains are synthesized for a specific 2R2T motion pattern based on screw theory. Feasible limb structures that provide a constraint couple and a constraint force are enumerated according to the reciprocity of the twist and wrench systems. Several motion equivalent single loop chains are constructed with the equivalent serial chains. Using motion equivalent single loop chains to replace the equivalent serial chains, a class of 2R2T parallel mechanisms is obtained based on the foundation of motion equivalent single loop chain structures.

Analysis and Design of Lower-Mobility Parallel Mechanism of Non-Symmetrical Based on Variable Topology Theory

2011 ◽  
Vol 201-203 ◽  
pp. 1907-1912
Author(s):  
Rong Jiang Cui ◽  
Zong He Guo ◽  
Zi Xun Yin ◽  
Song Song Zhu
Keyword(s):  
Parallel Mechanism ◽  
Screw Theory ◽  
Parallel Mechanisms ◽  
Basic Variable ◽  
Analysis And Design ◽  
And Topology ◽  
Variable Topology ◽  
Lower Mobility ◽  
Branched Chain ◽  
Mechanism Theory

First, the branched-chain of parallel mechanism was Classified according to reciprocal screw theory. Then, the introduction of variable topology mechanism theory, with the characteristics of parallel mechanisms themselves, the definition and basic variable topology means of variable topology parallel mechanism were given. With evolutionary theory, the method to design lower-mobility parallel mechanisms of non-asymmetric was proposed based on variable topology mechanism theory .Taking 3-RPS as ideal mechanism and topology synthesis was carried out, besides 2-RPS mechanism were analyzed. The introduction of variable topology mechanism theory provided a theoretical basis and innovative approaches for the synthesis configuration of Lower-mobility parallel mechanisms of non-asymmetric.

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.

scholarly journals Type Synthesis of 3-Translational Redundant Actuated Parallel Mechanisms With Closed-Loop Branch Chains Based On Graphical Approach

2021 ◽  
Author(s):  
Yongquan Li ◽  
Hong-Sheng Jiang ◽  
Tian-Yu Zheng ◽  
Ke-Long Xi ◽  
Han Jing ◽  
...  
Keyword(s):  
Bearing Capacity ◽  
Parallel Mechanism ◽  
Large Scale ◽  
Vibration Isolation ◽  
Closed Loop ◽  
Screw Theory ◽  
Simple Calculation ◽  
Parallel Mechanisms ◽  
Logistics Industry ◽  
Graphical Approach

Abstract The 3-translational parallel mechanism is widely used in industrial, medical, and military fields, among others. With the development of the national logistics industry, a pressing need for a kind of 3-translational parallel mechanism emerged. Such mechanisms have high stiffness and high bearing capacity and are used for cargo handling and sorting. A novel method based on the graphical approach was proposed for the synthesis of 3-translational redundancy actuated parallel mechanism with closed-loop branch chains. The new mechanism has four symmetrically arranged branch chains, which eases subsequent kinematics and dynamics analyses while providing good mechanical properties. Based on the graphical approach theory, according to the constraint number contained in the branch chain, two types of redundant driven branch chains with closed-loop structures were constructed. The first type includes rotation constraint in one direction, while the second type includes the rotation constraint in two directions. Based on various combinations of two branch chain types, their allocation schemes can be divided into two types. Moreover, said these two allocation schemes can be integrated into at least 500 and 400 types of 3-translational redundant actuated parallel mechanisms with closed-loop branch chains. Then, the degree of freedom properties of representative mechanisms were tested using the screw theory. A large number of novel mechanisms were integrated assessed using this method, and branch chains such mechanisms were symmetrically distributed. They have a strong bearing capacity, simple calculation, and control, and can be applied to the handling and sorting of goods, large-scale precision machine tools, and large construction machinery vibration isolation systems, among others.

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