Screw Theory Based Methodology for the Deterministic Type Synthesis of Flexure Mechanisms

2011 ◽  
Vol 3 (3) ◽  
Author(s):  
Jingjun Yu ◽  
Shouzhong Li ◽  
Hai-jun Su ◽  
M. L. Culpepper
Keyword(s):  
System Theory ◽  
Screw Theory ◽  
Building Blocks ◽  
Mathematical Tool ◽  
Geometric Form ◽  
Type Synthesis ◽  
Mechanism Synthesis ◽  
Flexure Mechanism ◽  
Synthesis Methodology ◽  
Set Operation

Flexure mechanism synthesis, however, is still a comparably difficult task. This paper aims at exploring a simple but systematic type synthesis methodology for general flexure mechanisms. The applied mathematical tool is reciprocal screw system theory in geometric form, and the proposed approach is an improvement of freedom and constraint topology (FACT), which is based on the FACT approach, combining with other methods including equivalent compliance mapping, set operation on building blocks, etc. As a result, it enables the type synthesis of flexure mechanisms simple, complete, and effective. What is more significant is that the proposed approach makes the unified type synthesis of both constraint-based and kinematics-based flexure mechanisms available. That is also the new contribution to the flexure de-sign.

scholarly journals Type Synthesis Principle and Practice of Flexure Systems in the Framework of Screw Theory: Part I—General Methodology

2010 ◽  
Author(s):  
J. J. Yu ◽  
S. Z. Li ◽  
X. Pei ◽  
Hai-jun Su ◽  
J. B. Hopkins ◽  
...  
Keyword(s):  
System Theory ◽  
Conceptual Design ◽  
Building Block ◽  
High Performance ◽  
Screw Theory ◽  
Physical Entity ◽  
Type Synthesis ◽  
General Methodology ◽  
Synthesis Procedure ◽  
Systematic Formulation

The systematic methodologies involved in type synthesis of flexure systems are no doubt helpful to generate one and more high-performance precision machine designs at the stage of conceptual design with a rapid and effective way. This paper provides a systematic formulation of the type synthesis of parallel, serial, and hybrid flexure systems via a mapping from a geometric concept to physical entity. The whole type synthesis principle is built upon screw system theory and the geometric Freedom and Constraint Topology (FACT) approach, also combining with other concepts and methods including equivalent compliance mapping, building block etc, which enables the type synthesis of flexure systems deterministic, simple and practical. After that, Type synthesis procedure for various flexure systems are elaborated with examples. As a result, as many specified-DOF (Degree of Freedom) flexure systems as possible can be found and therefore pave the way for obtaining an optimal configuration.

scholarly journals Type synthesis of freedom and constraint elements for design of flexure mechanisms

2013 ◽  
Vol 4 (2) ◽  
pp. 263-277 ◽  
Author(s):  
H.-J. Su ◽  
C. Yue
Keyword(s):  
Screw Theory ◽  
Building Blocks ◽  
Rigid Bodies ◽  
Hybrid Structures ◽  
Design Stage ◽  
Type Synthesis ◽  
Parallel Structures ◽  
Synthesis Procedure ◽  
Serial Chains ◽  
Basic Motion

Abstract. In this paper, we present the type synthesis of freedom and constraint elements for design of general flexure mechanisms. As an important step in the conceptual design stage, the goal of type synthesis is to qualitatively determine the topology or connectivity of flexure elements and rigid bodies in a mechanism. The synthesis procedure presented here is based on a recently emerging screw theory based approach for flexure mechanisms. We first categorize a list of commonly used atomic flexure primitives including blades, wires, notches and bellow springs etc. We then derive their twist and wrench matrices that mathematically represent their freedom and constraint spaces. The synthesis procedure rigorously follows screw algebra. Freedom elements including R-joints and P-joints are defined as basic motion elements that allow a single rotation or a single translation. By using parallel structures of these flexure primitives, eleven designs of R-joints and eight designs of P-joints are systematically synthesized. As a duality, constraint elements including P-constraints and R-constraints remove a single translation or rotation. In contract to freedom elements, we synthesized serial chains of flexure primitives and obtained six designs of P-constraints and three designs of R-constraints. These freedom and constraint elements form a catalogue of basic building blocks for designing more complex flexure mechanisms. At last we utilize four design examples to demonstrate how to synthesize hybrid structures with serial and parallel combination of these elements.

scholarly journals Type Synthesis Principle and Practice of Flexure Systems in the Framework of Screw Theory: Part III—Numerations and Synthesis of Flexure Mechanisms

2010 ◽  
Author(s):  
S. Z. Li ◽  
J. J. Yu ◽  
X. Pei ◽  
Hai-jun Su ◽  
J. B. Hopkins ◽  
...  
Keyword(s):  
High Precision ◽  
Screw Theory ◽  
Degree Of Freedom ◽  
Type Synthesis ◽  
General Design ◽  
Flexure Mechanism ◽  
Design Philosophy ◽  
Large Motion ◽  
Application Requirements ◽  
Made In

In recent years, the increasing of application requirements call for development of a variety of flexure mechanisms with high precision or large motion and both. Therefore, in Part III of this series of papers we demonstrate how to use the methodology addressed in Part I to synthesize concepts for two kinds of flexure mechanisms, i.e. kinematics-type flexure mechanisms (KFMs) and constraint-type flexure mechanisms (CFMs) with the specified-DOF (Degree of Freedom) characteristics. Although most of them utilize parallel configurations and flexure elements, there is a clear difference in the behavior of flexures between KFMs and CFMs, The resultant type synthesis approaches fall into two distinct categories i.e. freedom-based and constraint-based one, both of which have presented in Part I. In order to derive useful flexure mechanism concepts available for different applications, a general design philosophy and rules are summarized firstly. As the main content of this part, the classifications, numerations, and synthesis for KFMs and CFMs are made in a systematic way. As a result, a majority of new precision flexure mechanisms are developed. In addition, qualitative comparisons are provided to demonstrate the performance and application differences between kinematic-type and constraint-type flexure mechanisms with the same DOF.

Design of Reconfigurable Machine Tools

2002 ◽  
Vol 124 (2) ◽  
pp. 480-483 ◽  
Author(s):  
Yong-Mo Moon , ◽  
Sridhar Kota,
Keyword(s):  
Machine Tools ◽  
Screw Theory ◽  
Building Blocks ◽  
Mathematical Framework ◽  
Functional Requirements ◽  
Matrix Representations ◽  
Graph Theoretic ◽  
Structural Configurations ◽  
Synthesis Methodology ◽  
The Given

In this paper, we present a systematic methodology for designing Reconfigurable Machine Tools (RMTs). The synthesis methodology takes as input a set of functional requirements—a set of process plans and generates a set of kinematically viable reconfigurable machine tools that meet the given design specifications. We present a mathematical framework for synthesis of machine tools using a library of building blocks. The framework is rooted in (a) graph theoretic methods of enumeration of alternate structural configurations and (b) screw theory that enables us to manipulate matrix representations of motions to identify appropriate kinematic building blocks.

Synthesis of Reconfigurable Machine Tools With Screw Theory

2000 ◽  
Author(s):  
Yong-Mo Moon ◽  
Sridhar Kota
Keyword(s):  
Machine Tool ◽  
Machine Tools ◽  
Screw Theory ◽  
Dynamic Stiffness ◽  
Building Blocks ◽  
Mathematical Framework ◽  
Functional Requirements ◽  
Structural Configurations ◽  
Synthesis Methodology ◽  
Reconfigurable Machine Tool

Abstract In this paper, we present a systematic methodology for designing Reconfigurable Machine Tools (RMTs). The synthesis methodology takes as input a set of functional requirements — a set of process plans and outputs a set of kinematically-viable reconfigurable machine tools that meet the given design specifications. We present a mathematical framework for synthesis of machine tools using a library of building blocks. The framework is rooted in (a) graph theoretic methods of enumeration of alternate structural configurations and (b) screw theory that enables us to manipulate matrix representations of motions to identify appropriate kinematic building blocks. The methodology described in this paper provides a mathematical framework to address dynamic stiffness, and accuracy prediction of the kinematically-viable designs that are generated by the synthesis procedure. This methodology has been implemented in a program, called PREMADE (PRogram for REconfigurable MAchine tool DEsign), and the results are validated against commercial machine tool designs.

scholarly journals A New Method for Type Synthesis of 2R1T and 2T1R 3-DOF Redundant Actuated Parallel Mechanisms with Closed Loop Units

2020 ◽  
Vol 33 (1) ◽  
Author(s):  
Yongquan Li ◽  
Yang Zhang ◽  
Lijie Zhang
Keyword(s):  
Closed Loop ◽  
Screw Theory ◽  
Line Graph ◽  
Degree Of Freedom ◽  
Parallel Mechanisms ◽  
Type Synthesis ◽  
Allocation Criteria ◽  
Grassmann Line Geometry ◽  
Moving Platform ◽  
Atlas Method

Abstract The current type synthesis of the redundant actuated parallel mechanisms is adding active-actuated kinematic branches on the basis of the traditional parallel mechanisms, or using screw theory to perform multiple getting intersection and union to complete type synthesis. The number of redundant parallel mechanisms obtained by these two methods is limited. In this paper, based on Grassmann line geometry and Atlas method, a novel and effective method for type synthesis of redundant actuated parallel mechanisms (PMs) with closed-loop units is proposed. Firstly, the degree of freedom (DOF) and constraint line graph of the moving platform are determined successively, and redundant lines are added in constraint line graph to obtain the redundant constraint line graph and their equivalent line graph, and a branch constraint allocation scheme is formulated based on the allocation criteria. Secondly, a scheme is selected and redundant lines are added in the branch chains DOF graph to construct the redundant actuated branch chains with closed-loop units. Finally, the branch chains that meet the requirements of branch chains configuration criteria and F&C (degree of freedom & constraint) line graph are assembled. In this paper, two types of 2 rotational and 1 translational (2R1T) redundant actuated parallel mechanisms and one type of 2 translational and 1 rotational (2T1R) redundant actuated parallel mechanisms with few branches and closed-loop units were taken as examples, and 238, 92 and 15 new configurations were synthesized. All the mechanisms contain closed-loop units, and the mechanisms and the actuators both have good symmetry. Therefore, all the mechanisms have excellent comprehensive performance, in which the two rotational DOFs of the moving platform of 2R1T redundant actuated parallel mechanism can be independently controlled. The instantaneous analysis shows that all mechanisms are not instantaneous, which proves the feasibility and practicability of the method.

Type Synthesis of Compliant Mechanisms Employing a Simplified Approach to Segment Type

1994 ◽  
Author(s):  
Morgan D. Murphy ◽  
Ashok Midha ◽  
Larry L. Howell
Keyword(s):  
Rigid Body ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Type Synthesis ◽  
Simplified Approach ◽  
Design Procedures ◽  
Synthesis Techniques ◽  
Design Solutions ◽  
Synthesis Methodology

Abstract The formulation of design procedures for rigid-body mechanisms has benefited from the application of type-synthesis techniques. Therefore, with modifications to allow for inclusions of compliance, type synthesis is seen as a useful tool in the design of compliant mechanisms. Previous efforts have developed methods that result in a large number of possible design solutions to a given problem. This paper deals primarily with the development of a simplified compliant-mechanism type-synthesis methodology that limits the number of design solutions considered. The techniques are derived by modifying existing compliant mechanism type-synthesis techniques to yield a simpler model with greater pragmatic value.

scholarly journals A Screw Theory Approach for the Type Synthesis of Compliant Mechanisms With Flexures

2009 ◽  
Author(s):  
Hai-Jun Su ◽  
Denis V. Dorozhkin ◽  
Judy M. Vance
Keyword(s):  
Compliant Mechanisms ◽  
Screw Theory ◽  
Compliant Mechanism ◽  
Computational Techniques ◽  
Theory Approach ◽  
Type Synthesis ◽  
Precision Engineering ◽  
Pattern Design ◽  
Design Constraint ◽  
Systematic Formulation

This paper presents a screw theory based approach for the type synthesis of compliant mechanisms with flexures. We provide a systematic formulation of the constraint-based approach which has been mainly developed by precision engineering experts in designing precision machines. The two fundamental concepts in the constraint-based approach, constraint and freedom, can be represented mathematically by a wrench and a twist in screw theory. For example, an ideal wire flexure applies a translational constraint which can be described a wrench of pure force. As a result, the design rules of the constraint-based approach can be systematically formulated in the format of screws and screw systems. Two major problems in compliant mechanism design, constraint pattern analysis and constraint pattern design are discussed with examples in details. This innovative method paves the way for introducing computational techniques into the constraint-based approach for the synthesis and analysis of compliant 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.

Type Synthesis of 3-DOF Spherical Parallel Manipulators Based on Screw Theory1

2004 ◽  
Vol 126 (1) ◽  
pp. 101-108 ◽  
Author(s):  
Xianwen Kong ◽  
Cle´ment M. Gosselin
Keyword(s):  
Parallel Manipulator ◽  
Screw Theory ◽  
General Procedure ◽  
Kinematic Chain ◽  
Parallel Manipulators ◽  
Type Synthesis ◽  
Validity Condition ◽  
First Time ◽  
Spherical Parallel Manipulator ◽  
Selection Of

A spherical parallel manipulator (SPM) refers to a 3-DOF (degree-of-freedom) parallel manipulator generating 3-DOF spherical motion. A method is proposed for the type synthesis of SPMs based on screw theory. The wrench systems of a spherical parallel kinematic chain (SPKC) and its legs are first analyzed. A general procedure is then proposed for the type synthesis of SPMs. The type synthesis of legs for SPKCs, the type synthesis of SPKCs, as well as the selection of inputs of SPMs are dealt with in sequence. An input validity condition of SPMs is proposed. SPKCs with and without inactive joints are synthesized. The number of overconstraints of each SPKC is also given. The phenomenon of dependent joint groups in an SPKC is revealed for the first time.

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