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2018 | Buch

Topology Design of Robot Mechanisms

verfasst von: Ting-Li Yang, Anxin Liu, Huiping Shen, LuBin Hang, Yufeng Luo, Qiong Jin

Verlag: Springer Singapore

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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Über dieses Buch

This book focuses on the topology theory of mechanisms developed by the authors and provides a systematic method for the topology design of parallel mechanisms (PMs).

The main original theoretical contributions of this book include:

(1) Three basic concepts

(a) The “geometrical constraint type”, kinematic pair and connection of links are three structural elements. As such, the symbolic expression of these mechanisms’ structures is an invariance.

(b) The position and orientation characteristic (POC) set describes the POC of relative motion between any two links and is an invariance.

(c) In turn, the simple open chain (SOC) unit is used to develop four basic equations of mechanism topology (see Chapters 4 to 6).

(2) Mechanism composition principle

The book proposes a mechanism composition principle based on the SOC unit and establishes a systematic theory for the unified modeling of the topology, kinematics, and dynamics of mechanisms (see Chapter 7).

(3) Four basic equations

(a) A POC equation of serial mechanisms and its 10 operation rules (see Chapter 4).

(b) A POC equation of PMs and its 14 operation rules (see Chapter 5).

(see Chapter 6).

(d) The coupling degree formula for the Assur kinematic chain (see Chapter 7).

(4) One systematic method for the topology design of parallel mechanisms (see Chapters 8-10)

Drawing on these three basic concepts and four basic equations, the book puts forward a systematic method for the topology design of PMs, one that is fundamentally different from existing methods. Its main characteristics are as follows:

(a) The design process includes two stages: the first is structure synthesis, which allows many structure types to be obtained; the second involves the performance analysis, classification and optimization of structure types.

(b) The design operation is independent of the motion position and selection of fixed coordinate system.

As such, the proposed method is essentially geometrical. This ensures that full-cycle DOF and the generality of geometric conditions of mechanism existence apply.

(c) Each individual design step follows an explicit formula or the guidelines for design criteria, making the operation simple, feasible and reproducible. In addition, the topology design of the SCARA PM is studied in detail, providing an example to illustrate the proposed method (see Chapter 10).

Inhaltsverzeichnis

Frontmatter

Chapter 1. Introduction

Abstract

The theory and method for topology design of robot mechanisms are briefly introduced in this chapter. The content deals with: (1) The systematic theory and method for topological structure design of mechanisms is called mechanism topology and the topological structure design of mechanisms is abbreviated as mechanism topology design. (2) Four categories of PM topology design methods and their main features. (3) Four types of mechanism composition principles and their corresponding mechanism theory systems. (4) Some original work of this book, including: (a) Three new basic concepts (geometric constraint type of axes, POC set and SOC unit) are proposed (refer to Chaps. 2 and 3). (b) Four basic equations for mechanism topology (POC equation for serial mechanisms, POC equation for PMs, full cycle DOF formula, coupling degree formula of AKC) are established (refer to Chaps. 4–7). (c) 12 topological characteristics of PMs are derived. These topological characteristics can be used in topological performance analysis, classification and optimization of PM structure types (refer to Chap. 9). (d) A systematic method for topology design of PMs is established. The design process includes two stages. The first stage covers the structure synthesis in which many structure types can be obtained. The second stage contains topological performance analysis, classification and optimization of structure types based on the topological characteristics (refer to Chaps. 8–10). This method is independent of the motion position and the fixed coordinate system (i.e. it is not necessary to establish the fixed coordinate system). Thus, the full-cycle DOF mechanisms are obtained and the geometry conditions of mechanism existence have generality. Therefore, this method is a geometrical method, which is totally different from the other three methods. (e) The mechanism composition principle based on SOC unit is proposed. This composition principle provides a theoretical basis for unified modeling of mechanism topology, kinematics and dynamics based on SOC unit (refer to Chap. 7).

Ting-Li Yang, Anxin Liu, Huiping Shen, Lubin Hang, Yufeng Luo, Qiong Jin

Chapter 2. Topological Structure of Mechanisms and Its Symbolic Representation

Abstract

Topological structure of mechanisms and the symbolic representation are introduced in this chapter. The content deals with: (1) A new element for describing topological structure - geometric constraint type (the type of geometrical constraints to pair axes imposed by links, is proposed. This new element and the other two traditional elements (type of kinematic pair, connection relation between links) formed the three basic elements of topological structure. (2) The mechanism topological structure described using these three basic elements and the corresponding symbolic representation are independent of motion position of the mechanism and the fixed coordinate system. This feature is called the topological structure invariance during motion process. (3) The symbolic representation of topological structure and the topological structure invariance could be used for establishing the position and orientation characteristics (POC) equation for serial mechanisms, the POC equation for parallel mechanisms (PMs) and their operation rules (refer to Chaps. 4–5). (4) Any serial mechanisms or multi-loop spatial mechanisms can be generated by connecting single-open-chain (SOC) in parallels or in series. The SOC unit is a new structure unit of mechanisms proposed by authors, which could be used for establishing the POC equation for serial mechanisms (refer to Chap. 4), the POC equation for PMs (refer to Chap. 5), the DOF formula (refer to Chap. 6) and the coupling degree formula (refer to Chap. 7).

Ting-Li Yang, Anxin Liu, Huiping Shen, Lubin Hang, Yufeng Luo, Qiong Jin

Chapter 3. Position and Orientation Characteristics Set

Abstract

The position and orientation characteristics (POC) set is proposed by authors in this chapter, which is used for describing the POCs of the mechanism. The content deals with: (1) Based on the velocity analysis and the unit vector set of velocity of kinematic pairs, this unit vector set can be rewritten into the form of velocity characteristic (VC). Hence, the VC set are defined, which is used to express the velocity characteristic of the kinematic pairs. Subsequently, based on the topological structure invariance, the POC set are defined, which is used to describe the POCs of the kinematic pairs. (2) Based on the velocity analysis, the unit vector set of velocity of mechanism link is used for describing its velocity characteristics. Since this unit vector set can be rewritten into the form of velocity characteristic, the VC set is defined. Subsequently, based on one-to-one correspondence between elements of the POC set and elements of the VC set, the POC set of the mechanism is defined. Both VC set and POC set depend only on topological structure of the mechanism. (3) The dimension of the POC set is not greater than the DOF of a mechanism. There are only 15 basic types of the POC sets containing only independent elements. (4) The POC set could be used for establishing the POC equation for serial mechanisms (refer to Chap. 4) and the POC equation for PMs (refer to Chap. 5).

Ting-Li Yang, Anxin Liu, Huiping Shen, Lubin Hang, Yufeng Luo, Qiong Jin

Chapter 4. Position and Orientation Characteristics Equation for Serial Mechanisms

Abstract

Position and orientation characteristics (POC) equation for serial mechanisms is introduced in this chapter. The content deals with: (1) Based on velocity analysis and topological structure invariance of serial mechanisms (Chap. 2), the unit vector set of the end link velocity is “union” of unit vector sets of each pair, which depends only on the topological structure (excluding singular positions) of a mechanism (Chap. 3). (2) Since the unit vector set of velocity could be rewritten into the form of velocity characteristic (Chap. 3), the velocity characteristics (VC) equation and its operation rules for serial mechanisms are derived. (3) Based on one-to-one correspondence between elements of the POC set and elements of the VC set (excluding singular positions), the POC equation for serial mechanisms and the “union” operation rules of POC sets (eight linear rules and two nonlinear criteria) are obtained. This POC equation is independent of motion position and it is not necessary to establish the fixed coordinate system. (4) This POC equation could be used for determining POC set of a serial mechanism when its topological structure is known (Chap.4) and topological structure of a serial mechanism when its POC set and DOF are known (refer to Chap. 8). (5) This POC equation will be used for building POC equation for parallel mechanisms (refer to Chap. 5) and general DOF formula for spatial mechanisms (refer to Chap. 6).

Ting-Li Yang, Anxin Liu, Huiping Shen, Lubin Hang, Yufeng Luo, Qiong Jin

Chapter 5. Position and Orientation Characteristics Equation for Parallel Mechanisms

Abstract

Position and orientation characteristics (POC) equation for parallel mechanisms (PMs) is introduced in this chapter. The content deals with: (1) Based on velocity composition principle and topological structure invariance of PMs (Chap. 2), the unit vector set of moving platform velocity is “intersection” of unit vector sets of the end link velocity of its each branch, which depends only on the topological structure (excluding singular positions) of a mechanism (Chap. 3). (2) Since the unit vector set of velocity could be rewritten as the form of velocity characteristic (Chap. 3), the velocity characteristics (VC) equation and its operation rules for PMs are derived. (3) Based on one-to-one correspondence between elements of the POC set and elements of the VC set (excluding singular positions), the POC equation for PMs and the “intersection” operation rules of POC sets (twelve linear rules and two nonlinear criteria) are obtained. However, determination of the POC set always involves DOF calculation and inactive pair judgment (refer to Chap. 6). (4) The POC equation is independent of motion position (excluding singular positions), and it is not necessary to establish the fixed coordinate system. (5) Complex branches can be replaced by their topologically equivalent SOC branches in order to simplify POC set calculation of PMs. (6) This POC equation could be used for determining POC set of PMs when its topological structure is known (Sect. 5.5) , and can be used in structure synthesis, i.e. determining topological structure of a PM when its POC set and DOF are known (refer to Chap. 9). (7) This POC equation will be used for building general DOF formula for spatial mechanisms (refer to Chap. 6).

Ting-Li Yang, Anxin Liu, Huiping Shen, Lubin Hang, Yufeng Luo, Qiong Jin

Chapter 6. General Formula of Degrees of Freedom for Spatial Mechanisms

Abstract

The general DOF formula which is of great importance to mechanism topology, kinematics and dynamics is introduced in this chapter. The content deals with: (1) The general DOF formula for PMs is proposed based on the topologically equivalent principle, POC equation of serial mechanisms in Chap. 4 and POC equation of PMs in Chap. 5. This DOF formula is independent of motion position of a PM and it is not necessary to establish the fixed coordinate system. Hence, it can guarantee that full-cycle DOF is obtained. (2) Based on the DOF formula, the criteria for determination of inactive pairs and the criteria for selection of driving pairs are proposed. (3) With replacement method for topological equivalent kinematic chains, DOF of general multi-loop spatial mechanisms can be calculated with this DOF formula very easily. (4) This DOF formula can be used for calculating DOF of PMs whose POC set contains non-independent element. (5) Based on the DOF formula, formulas for determining number of independent displacement equations, number of over-constraints and redundancy of mechanisms are derived. In brief , this DOF formula reveals the internal relations among topological structure, DOF and POC set of spatial mechanisms and will be used for topology design of PMs (refer to Chap. 9).

Ting-Li Yang, Anxin Liu, Huiping Shen, Lubin Hang, Yufeng Luo, Qiong Jin

Chapter 7. Mechanism Composition Principle Based on Single-Open-Chain Unit

Abstract

The mechanism composition principle based on Single-Open-Chain (SOC) unit is introduced in this chapter. The content deals with: (1) The mechanism composition principle based on SOC unit is proposed. Constraint degree of SOC is defined, which is used to describe constraint features of SOC unit to DOF of the mechanism. (2) A general method for decomposing an AKC into ordered SOCs is proposed. The coupling degree of an AKC is defined and is used to represent complexity of the AKC. (3) A general method for decomposing mechanism into ordered SOCs is proposed. Criteria for AKC determination is defined and is used to determine AKCs contained in the mechanism. (4) A general method for determination of DOF types is proposed based on the AKCs in the mechanism. And a general method for motion decoupling design based on partial DOF is proposed. (5) This mechanism composition principle could be used to establish a systematic theory for unified modeling of mechanism topology, kinematics and dynamics based on SOC unit (refer to Sect. 7.7).

Ting-Li Yang, Anxin Liu, Huiping Shen, Lubin Hang, Yufeng Luo, Qiong Jin

Chapter 8. General Method for Structure Synthesis of Serial Mechanisms

Abstract

Structure synthesis of serial mechanisms is introduced in this chapter. The content deals with: (1) A easy-to-use method for structure synthesis of serial mechanisms is proposed based on POC equation for serial mechanisms and sub-SOCs of geometric constraint types of axes in Chap. 4. And 28 structure types of serial mechanisms containing only R and P pairs with DOF= dim{POC set} and 15 structure types of serial mechanisms containing only R and P pairs with DOF= dim{POC set}+1 are obtained. (2) An simple method for structure synthesis of general over-constrained single-loop mechanisms (SLC) is proposed. And 15 types of general over-constrained SLCs with DOF=1 and only R and P pairs are obtained. (3) The method for structure synthesis of serial mechanisms is independent of motion position of mechanisms and it is not necessary to establish the fixed coordinate system. In brief, contents in this chapter will be used for structure synthesis of simple and complex branches of parallel mechanisms (refer to Chaps. 9-10).

Ting-Li Yang, Anxin Liu, Huiping Shen, Lubin Hang, Yufeng Luo, Qiong Jin

Chapter 9. General Method for Topology Design of Parallel Mechanisms

Abstract

Based on four equations of mechanism topology (POC equation for serial mechanisms in Chap. 4, POC equation for PMs in Chap. 5, DOF formula in Chap. 6 and coupling degree formula in Chap. 7, an systematic method for topology design of PMs is established. Its core content include: (a) Structure synthesis of simple branches based on the POC equation for serial mechanisms. (b) Structure synthesis of complex branches based on the topological equivalence principle. (c) Arranging schemes of branch combinations based on the POC equation for PMs. (d) The formulas for determining the geometric conditions for assembling branches are derived based on the POC equation for PMs and DOF formula. (e) Performance analysis and classification for structure types based on twelve topological characteristics. Main features of this design method are as follows: (1) The design process covers two stages: the first is structure synthesis for obtaining many topological structure types, and the second is performance analysis, classification and optimization of the obtained structure types. (2) Since each step in the design procedure has explicit formula or criteria, it is easy to understand and easy to use. (3) Since this method is independent of motion position and it is not necessary to establish the fixed coordinate system, it can obtain the full-cycle DOF PMs and the geometry conditions of PM existence have generality. Therefore, this method could be called a geometrical method, which is totally different from the other methods (such as, based on screw theory, based on subgroup/submanifold, based on linear transformations). The complete process for topology design of the (3T-1R) PMs will be discussed in detail as an example to illustrate the proposed method in Chap. 10.

Ting-Li Yang, Anxin Liu, Huiping Shen, Lubin Hang, Yufeng Luo, Qiong Jin

Chapter 10. Topology Design of (3T-1R) Parallel Mechanisms

Abstract

Topology design of (3T-1R) parallel mechanism (PM) based on POC equations is discussed in detail as an example to illustrate the systematic method for topology design of PMs proposed in Chap. 9. The design process includes two stages. The first stage involves traditional structure synthesis, which results in 18 structure types of (3R-1R) PMs that contain no P pairs. The second stage includes topological performance analysis and classification of the obtained PM structure types which may help designer to select the most suitable structure type. Its core contents include: (1) Key steps of topology design for (3R-1R) PMs include: (a) Determine structure types of the SOC branch containing only R and P pairs according to the method for structure synthesis of SOC branch described in Chap.8. Then obtain corresponding HSOC branches through topologically equivalent principle in Chap.9. (b) Determine the geometrical condition for assembling branches between two platforms according to corresponding basic formulas in Chap. 9. Then determine different assembling schemes for the same geometrical condition. (c) Performance analysis and classification of the obtained PM structures are conducted based on topological characteristics of PMs in Chap. 9. The result can be used for assessment and optimization of (3R-1R) PM structure types. (2) 18 types of (3T-1R) PM structures containing no P pair are obtained, two of which have already been used in existing SCARA parallel robots. The other structure types may potentially be used in new SCARA parallel robots. (3) These 18 structure types of (3R-1R) PMs are classified into four types: Type-1 include four PMs containing only SOC branches; Type-2 include six PMs containing only HSOC branches; Type-3 include seven PMs containing both HSOC and SOC branches; Type-4 include three PMs with partial motion decoupling property. (4) According to topological performance analysis and classification of these PMs based on topological characteristics, the type-3 PM has a higher rigidity than a type-1 PM and a larger workspace than a type-2 PM. So, special attentions shall be paid to type-3 PMs.

Ting-Li Yang, Anxin Liu, Huiping Shen, Lubin Hang, Yufeng Luo, Qiong Jin

Titel: Topology Design of Robot Mechanisms
verfasst von: Ting-Li Yang
Anxin Liu
Huiping Shen
LuBin Hang
Yufeng Luo
Qiong Jin
Verlag: Springer Singapore
Electronic ISBN: 978-981-10-5532-4
Print ISBN: 978-981-10-5531-7
DOI: https://doi.org/10.1007/978-981-10-5532-4

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