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.

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.

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.

Comparison Study on Three Approaches for Type Synthesis of Robot Mechanisms

2009 ◽  
Author(s):  
Ting-Li Yang ◽  
An-xin Liu ◽  
Yu-Feng Luo ◽  
Li-Ping Zhang ◽  
Hui-Ping Shen ◽  
...  
Keyword(s):  
Screw Theory ◽  
Mathematical Representation ◽  
Parallel Mechanisms ◽  
Comparison Study ◽  
Type Synthesis ◽  
Basic Principles ◽  
Operation Rules ◽  
Structure Synthesis ◽  
Vector Algebra ◽  
Basic Equations

Basic principles and main characteristics of three approaches for structure synthesis of robot mechanisms (the screw theory-based approach, the displacement subgroup-based approach and the approach based on position and orientation characteristic (in short, POC) ) are studied and compared in this paper. The comparison deals with the mathematical tools, the symbolic representation of mechanism topological structure, the mathematical representation of POC of the output motion link with respect to the frame link, the basic equations for structure synthesis of serial and parallel mechanisms and relevant operation rules, and the characteristics of their synthesized mechanisms, etc. This comparative study shows that the POC-based approach is totally different from the other two approaches: (1) the POC-based approach requires only simple mathematical tools (such as vector algebra, set theory, etc), (2) the POC-based approach is conceptually simpler and therefore easier to understand and to use, and (3) the POC-based approach is more general.

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.).

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.

Design and kinematics of a novel double-ring truss deployable antenna mechanism

2021 ◽  
pp. 1-14
Author(s):  
Wen-ao Cao ◽  
Sheng Xi ◽  
Huafeng Ding ◽  
Ziming Chen
Keyword(s):  
Topological Structure ◽  
Screw Theory ◽  
Structural Characteristics ◽  
Kinematic Model ◽  
Structure Design ◽  
Structural Symmetry ◽  
Double Ring ◽  
Joint Axis ◽  
Structure Decomposition ◽  
Topological Scheme

Abstract This paper aims to present the topological structure design and kinematic analysis of a novel double-ring truss deployable satellite antenna mechanism. First, a new topological scheme and a new rectangular prism deployable linkage unit are proposed for constructing the kind of antenna mechanisms. Second, the degree-of-freedom (DOF) of the deployable unit and the antenna mechanism are analyzed based on structure decomposition and screw theory. Third, the kinematic model of the double-ring truss deployable antenna mechanism is established based on its structural characteristics. Finally, a typical numerical example is used to illustrate the effectiveness of the designed mechanism and the established kinematic model. The new double-ring truss deployable antenna mechanism consists of the units with the better structural symmetry, and has simpler joint axis layouts, comparing with the same type of most existing mechanisms.

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.

Topological Structure Synthesis of 3-Translation Parallel Mechanisms

2012 ◽  
pp. 269-284
Author(s):  
Huiping Shen ◽  
Tongzhu Yu ◽  
Jiaming Deng ◽  
Zheng Wang ◽  
Tingli Yang
Keyword(s):  
Topological Structure ◽  
Parallel Mechanisms ◽  
Structure Synthesis

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.

Sign in / Sign up

Export Citation Format

Share Document