A Systematic Formulation of Overconstraint Conditions in Kinematic Chains by Displacement Groups

2005 ◽  
Author(s):  
Carlo Galletti ◽  
Pietro Fanghella ◽  
Elena Giannotti
Keyword(s):  
Dynamic Analysis ◽  
Systematic Approach ◽  
Computer Code ◽  
Computer Implementation ◽  
Mobility Analysis ◽  
Kinematic Synthesis ◽  
Single Loop ◽  
Kinematic Chains ◽  
Geometric Data ◽  
Systematic Formulation

The paper describes a systematic approach to define geometrical and dimensional overconstraint conditions for single-loop kinematic chains of both “banal” and “exceptional” types. The approach is an application of the theory of displacement groups. It presents several interesting features: it can be easily integrated with mobility analysis; it makes use of geometric data local to links and does not require a preliminary mechanism assembly nor a given initial congruent position; it is systematic and can be suitably implemented in a computer code; it suggests where geometrical and dimensional tolerances have to be located; it can be embedded in other group-based approaches, like kinematic synthesis or dynamic analysis. After a brief summary of the properties of displacement groups and their operations, the paper shows how they can be used to formulate systematically the overconstraint conditions in kinematic chains. A computer implementation of the approach is also outlined, and several examples with different complexities are given.

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.

Mobility of Single Loop Linkages: A Final Word?

2007 ◽  
Author(s):  
Jose´ Mari´a Rico ◽  
J. Jesu´s Cervantes ◽  
Juan Rocha ◽  
Jaime Gallardo ◽  
Luis Daniel Aguilera ◽  
...  
Keyword(s):  
Mobility Analysis ◽  
Additional Insight ◽  
Final Word ◽  
Single Loop ◽  
Kinematic Chains ◽  
Recent Developments ◽  
The Subject ◽  
Insight Into

Setting aside paradoxical linkages such as Bennett’s, Bricard’s or Goldberg’s, the mobility of single loop linkages seemed, with the developments on mobility analysis carried out in the last five years, a closed chapter in kinematic research. However, recent developments on the mobility of parallel platforms have shed additional insight into the problem. This contribution attempts to unify the results obtained in the last five years in the area of mobility of single-loop kinematic chains to state what appears to be a final word on the subject.

A Comparative Study on Some Modular Approaches for Analysis and Synthesis of Planar Linkages: Part II — Modular Dynamic Analysis, Modular Structural Synthesis and Modular Kinematic Synthesis

1998 ◽  
Author(s):  
Ting-Li Yang ◽  
Fang-Hua Yao ◽  
Ming Zhang
Keyword(s):  
Structural Analysis ◽  
Comparative Study ◽  
Dynamic Analysis ◽  
Structural Synthesis ◽  
Dynamical Equations ◽  
Kinematic Synthesis ◽  
Automated Generation ◽  
Kinematic Chains ◽  
Analysis And Synthesis ◽  
Planar Linkages

Abstract This paper presents a systematical comparative study of various modular methods based on the different module types: basic kinematic chains (BKCs), single opened chains (SOCs), loops (or a tree and co-tree), links-joints, etc. for analysis and synthesis of structure, kinematics and dynamics of planar linkages. The basic idea is that any linkage can be divided into (or built up by) some modular components in sequence, and based on the component constraints and network entirty constraints of the linkage, the unified modular approaches have been used for analysis and synthesis. In systematical comparative study, the main issues of a modular method have been discussed, such as: the topological characteristics revealed via different module types; the dimension of a set of kinematic equations; the automated generation and solution of kinematic equations; the dimension and automated generation of dynamical equations, and computation complexity for generating and solving dynamical equation; the automated generation of structural analysis and type synthesis; the generation of kinematic synthesis equations etc.. This paper gives a summary of the use of modular techniques for analyzing and synthesizing planar linkages in the recently thirty years. This comparative study includes two parts: Part I-modular structural analysis and modular kinematic analysis; Part II-modular dynamic analysis, modular structural synthesis and modular kinematic synthesis. This paper is the second part.

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.

Virtual Chain Approach for Mobility Analysis of Multiloop Deployable Mechanisms

2013 ◽  
Vol 135 (11) ◽  
Author(s):  
Hailin Huang ◽  
Zongquan Deng ◽  
Xiaozhi Qi ◽  
Bing Li
Keyword(s):  
Relative Motion ◽  
Twist Angle ◽  
Open Loop ◽  
Mobility Analysis ◽  
Link Length ◽  
Flexible Links ◽  
Single Loop ◽  
Kinematic Chains ◽  
In Series ◽  
Insight Into

In this paper, we present a virtual chain approach for the mobility analysis of multiloop deployable mechanisms. First, the relative motion of the links of single-loop units in multiloop mechanisms are analyzed using the equivalent motion of certain types of open-loop virtual kinematic chains; these kinematic chains comprise some types of joints connected in series by flexible links. This reveals that the links in these virtual chains are not rigid when the mechanism is moving. The parameters of these virtual kinematic chains (such as the link length, the twist angle of two adjacent revolute joint axes, and so on) are variable. By using this approach that involves equivalent kinematic chains, the multiloop mechanisms can be considered equivalent to single-loop mechanisms with flexible links; the closure equations of such multiloop mechanisms can also be derived. The analytical procedures are explained using examples of multiloop mechanisms in which Myard mechanisms as used as the basic single-loop units. A prototype is also fabricated to demonstrate the feasibility of the proposed multiloop mechanism. The proposed method yields a more intuitive and straightforward insight into the mobility of complicated multiloop mechanisms.

Synthesis of Deployable/Foldable Single Loop Mechanisms With Revolute Joints

2011 ◽  
Vol 3 (3) ◽  
Author(s):  
Zongquan Deng ◽  
Hailin Huang ◽  
Bing Li ◽  
Rongqiang Liu
Keyword(s):  
Computer Aided Design ◽  
Geometric Approach ◽  
Mobility Analysis ◽  
Design Models ◽  
Single Loop ◽  
Kinematic Chains ◽  
Design And Synthesis ◽  
Revolute Joints ◽  
Computer Aided ◽  
Aided Design

This paper presents a geometric approach for design and synthesis of deployable/foldable single loop mechanisms with pure revolute joints. The basic kinematic chains with symmetric mobility are first synthesized, and an intuitive geometric method is proposed for the mobility analysis of these kinematic chains. The deployable/foldable single loop mechanisms can be regarded as a combination of the basic kinematic chains with nontrivial mobility intersection, under this approach, the 5R to 8R single loop mechanisms with symmetric mobility are synthesized systematically. The method for determining the positions of the joint axes on polyhedral links is also proposed, so that the mechanism can be fully deployed or fully folded without suffering from physical interference. Under this framework, a class of novel deployable/foldable single loop mechanisms is developed. The computer-aided design models for typical examples are built to illustrate their feasibility.

A Hexagonal Prism Folding for Membrane Packaging Based on Concepts of Finite Rigid Motion and Kinematic Synthesis

2016 ◽  
Author(s):  
Kassim Abdul-Sater
Keyword(s):  
Spatial Configuration ◽  
Rigid Motion ◽  
Building Blocks ◽  
Computational Procedure ◽  
Hexagonal Prism ◽  
Linkage Mechanism ◽  
Space Applications ◽  
Kinematic Synthesis ◽  
Kinematic Chains ◽  
Position Synthesis

This paper discusses the use of concepts of finite rigid body kinematics as well as kinematic synthesis in non-rigid, engineering folding problems. The exemplary task consists in designing a folding pattern, which allows to fold a circular sheet from a flat unfolded state into a prescribed compact spatial configuration that forms a hexagonal prism. Other two-configuration design problems may be found for instance in space applications where membranes in tensegrity reflector antennas need to be stowed in a spacecraft. The folding motion could be actuated using an appropriately designed linkage mechanism attached to the membrane, which, however, is not considered in this paper. The specific result of this work is a creative but systematic and computational procedure for crease pattern design. The approach is essentially based on the relative kinematics equations of serial kinematic chains and the finite position synthesis of linkage building blocks. These techniques sucessively combine to segment a flat bounded surface, such that it can reach the prescribed spatial configuration.

A Novel Method for Constructing Multi-Mode Deployable Polyhedron Mechanisms Using Symmetric Spatial RRR Compositional Units

2018 ◽  
Author(s):  
Jieyu Wang ◽  
Xianwen Kong
Keyword(s):  
Kinematic Chain ◽  
Degree Of Freedom ◽  
Single Loop ◽  
Kinematic Chains ◽  
The Third ◽  
Motion Modes ◽  
3D Printed ◽  
Novel Method ◽  
Multi Mode ◽  
Motion Mode

A novel construction method is proposed to construct multimode deployable polyhedron mechanisms (DPMs) using symmetric spatial RRR compositional units, a serial kinematic chain in which the axes of the first and the third revolute (R) joints are perpendicular to the axis of the second R joint. Single-loop deployable linkages are first constructed using RRR units and are further assembled into polyhedron mechanisms by connecting single-loop kinematic chains using RRR units. The proposed mechanisms are over-constrained and can be deployed through two approaches. The prism mechanism constructed using two Bricard linkages and six RRR limbs has one degree-of-freedom (DOF). When removing three of the RRR limbs, the mechanism obtains one additional 1-DOF motion mode. The DPMs based on 8R and 10R linkages also have multiple modes, and several mechanisms are variable-DOF mechanisms. The DPMs can switch among different motion modes through transition positions. Prototypes are 3D-printed to verify the feasibility of the mechanisms.

Protein Molecules as Natural Nano Bio Devices: Mobility Analysis

2010 ◽  
Author(s):  
Zahra Shahbazi ◽  
Horea T. Ilies¸ ◽  
Kazem Kazerounian
Keyword(s):  
Degrees Of Freedom ◽  
Conformational Transitions ◽  
Living Cells ◽  
Mobility Analysis ◽  
Folding Process ◽  
Kinematic Chains ◽  
Protein Molecules ◽  
Kinematic Models ◽  
Lower Mobility ◽  
Molecular Components

Proteins are nature’s nano-robots in the form of functional molecular components of living cells. The function of these natural nano-robots often requires conformational transitions between two or more native conformations that are made possible by the intrinsic mobility of the proteins. Understanding these transitions is essential to the understanding of how proteins function, as well as to the ability to design and manipulate protein-based nano-mechanical systems [1]. Modeling protein molecules as kinematic chains provides the foundation for developing powerful approaches to the design, manipulation and fabrication of peptide based molecules and devices. Nevertheless, these models possess a high number of degrees of freedom (DOF) with considerable computational implications. On the other hand, real protein molecules appear to exhibits a much lower mobility during the folding process than what is suggested by existing kinematic models. The key contributor to the lower mobility of real proteins is the formation of Hydrogen bonds during the folding process.

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