Type Synthesis of 3-DOF Translational Parallel Manipulators Based on Atlas of DOF Characteristic Matrix

2006 ◽  
Author(s):  
Jingjun Yu ◽  
Jian S. Dai ◽  
Xin-Jun Liu ◽  
Shusheng Bi ◽  
Guanghua Zong
Keyword(s):  
System Theory ◽  
Lie Group ◽  
Synthesis Method ◽  
Parallel Manipulators ◽  
Complete Classification ◽  
Characteristic Matrix ◽  
Type Synthesis ◽  
Lie Group Theory ◽  
Low Degree ◽  
New Type

Low-degree-of-freedom (Low-DOF) parallel manipulators (PMs) have drawn extensive interest, particularly in type synthesis in which two main approaches were established in the reciprocal screw system theory and Lie group theory. This paper aims at proposing a new type synthesis method to complementing the above methods. For this purpose, the concept of the DOF characteristic matrix, originated from displacement subgroup and displacement submanifold, is proposed. A new but general approach based on the atlas of DOF Characteristic Matrix is addressed for both exhaustive classification and type synthesis of low-DOF PMs. Compared to the method based on Lie group, the proposed approach is prone to construct an orthogonal structure and easy to realize the complete classification and exhaustive enumeration of a class of low-DOF PM. In order to verify the effectiveness of the proposed method, type synthesis of Translational PMs (TPMs) particularly in ones with an orthogonal structure is performed, resulting in some novel orthogonal TPMs.

scholarly journals Type Synthesis of Two DOF Hybrid Translational Parallel Manipulators

2016 ◽  
Vol 836 ◽  
pp. 48-53 ◽  
Author(s):  
Latifah Nurahmi ◽  
Stéphane Caro
Keyword(s):  
Screw Theory ◽  
Synthesis Method ◽  
Parallel Manipulators ◽  
Degree Of Freedom ◽  
Type Synthesis ◽  
In Series ◽  
Actuation Scheme ◽  
Two Degree Of Freedom

This paper introduces a methodology for the type synthesis of two degree-of-freedom hybrid translational manipulators with identical legs. The type synthesis method is based upon the screw theory. Three types of two degree-of-freedom hybrid translational manipulators with identical legs are identified based upon their wrench decomposition. Each leg of the manipulators is composed of a proximal module and a distal module mounted in series. The assembly conditions and the validity of the actuation scheme are also defined. Eventually, some novel two degree-of-freedom hybrid translational manipulators are synthesized with the proposed procedure.

Topology synthesis of three-legged spherical parallel manipulators employing Lie group theory

2014 ◽  
Vol 229 (10) ◽  
pp. 1873-1886 ◽  
Author(s):  
Yang Qi ◽  
Tao Sun ◽  
Yimin Song ◽  
Yan Jin
Keyword(s):  
Group Theory ◽  
Lie Group ◽  
Degrees Of Freedom ◽  
Parallel Manipulators ◽  
Lie Group Theory ◽  
Finite Displacements ◽  
Rotational Degrees Of Freedom ◽  
Circular Track ◽  
Synthesis Procedure ◽  
Assembly Principles

Driven by the requirements of the bionic joint or tracking equipment for the spherical parallel manipulators (SPMs) with three rotational degrees-of-freedom (DoFs), this paper carries out the topology synthesis of a class of three-legged SPMs employing Lie group theory. In order to achieve the intersection of the displacement subgroups, the subgroup characteristics and operation principles are defined in this paper. Mainly drawing on the Lie group theory, the topology synthesis procedure of three-legged SPMs including four stages and two functional blocks is proposed, in which the assembly principles of three legs are defined. By introducing the circular track, a novel class of three-legged SPMs is synthesized, which is the important complement to the existing SPMs. Finally, four typical examples are given to demonstrate the finite displacements of the synthesized three-legged SPMs.

Synthesis of 3-[P][S] Parallel Mechanism-Inspired Multimode Dexterous Hands With Parallel Finger Structure

2020 ◽  
Vol 142 (8) ◽  
Author(s):  
Xiaodong Jin ◽  
Yuefa Fang ◽  
Dan Zhang ◽  
Haiqiang Zhang
Keyword(s):  
Lie Group ◽  
Inverse Kinematics ◽  
Structural Characteristics ◽  
Synthesis Method ◽  
Parallel Mechanisms ◽  
Key Factors ◽  
End Effector ◽  
Lie Group Theory ◽  
Multimode Operation ◽  
Motion Types

Abstract Dexterous hands are an important end-effector of robots, but their relatively low carrying capacity, small workspace and poor task adaptability are the key factors that restrict their wide application. To overcome these shortcomings of dexterous hands, a novel Lie-group-based synthesis method that extends the 3-[P][S] parallel mechanisms (PMs) to dexterous hands is presented, and a class of three-finger dexterous hands with parallel finger structure is obtained. The multimode operation is proposed by designing a double-slider palm that provides the hands with a large workspace and high task adaptability. The operation types are presented, and the dexterous in-hand manipulations in all modes are analyzed by means of Lie group theory. In addition, the equivalent structural characteristics of pinching objects are classified to elucidate the motion types and the rotational properties of the pinched objects. The inverse kinematics of fingers is presented and is used to identify the input–output relationships. Finally, the workspaces of the fingers are determined according to the result of the inverse kinematics, and the relationships between the size and displacements of the pinched object are presented. The proposed dexterous hands overcome the problems of low carrying capability, small workspace, and weak in-hand manipulation ability that are encountered with the traditional dexterous hands, which are underactuated and are built with a series finger structure, and can be potentially applied to various application domains, such as services, industry, and rescue.

Type Synthesis for Remote Center of Motion Mechanisms Based on Coupled Motion of Two Degrees-of-Freedom

2016 ◽  
Vol 138 (12) ◽  
Author(s):  
Yucheng He ◽  
Peng Zhang ◽  
Haiyang Jin ◽  
Ying Hu ◽  
Jianwei Zhang
Keyword(s):  
Minimally Invasive Surgery ◽  
Degrees Of Freedom ◽  
Synthesis Method ◽  
Type Synthesis ◽  
End Effector ◽  
Coupled Motion ◽  
New Family ◽  
Robot Systems ◽  
New Type ◽  
Application Prospects

Robots play an increasingly important role in the development of minimally invasive surgery (MIS). In MIS assistant robot systems, the remote center of motion (RCM) mechanism is a key component, and is the primary choice as end-effector for such systems. In this paper, first, we propose a new type of synthesis method for RCM mechanisms, which is based on the coupled motion of two DOFs to obtain new virtual center of motion (VCM) mechanisms, and then, through different combinations and configurations of VCM mechanisms, a new family of RCM mechanisms is achieved. Second, one of the obtained RCM mechanisms, which is deemed to have potential application prospects in MIS assistant robot, is investigated in detail, and a prototype is designed and fabricated to verify its feasibility. Finally, preliminary experiments are carried out on the prototype; the results show that, compared with existing ones, the new RCM mechanism's volume can be adjusted according to its required workspace, and it will be more compact when the required workspace is small. It will be an applicable option of end-effector for an MIS assistant robot.

Equidimensional immersions of locally compact groups

1989 ◽  
Vol 105 (2) ◽  
pp. 253-261 ◽  
Author(s):  
K. H. Hofmann ◽  
T. S. Wu ◽  
J. S. Yang
Keyword(s):  
Exponential Function ◽  
Lie Group ◽  
Compact Groups ◽  
Locally Compact ◽  
Lie Group Theory ◽  
Group A ◽  
Image Position ◽  
Analytic Subgroup ◽  
Algebra Level ◽  
Connected Lie Group

Dense immersions occur frequently in Lie group theory. Suppose that exp: g → G denotes the exponential function of a Lie group and a is a Lie subalgebra of g. Then there is a unique Lie group ALie with exponential function exp:a → ALie and an immersion f:ALie→G whose induced morphism L(j) on the Lie algebra level is the inclusion a → g and which has as image an analytic subgroup A of G. The group Ā is a connected Lie group in which A is normal and dense and the corestrictionis a dense immersion. Unless A is closed, in which case f' is an isomorphism of Lie groups, dim a = dim ALie is strictly smaller than dim h = dim H.

scholarly journals Similarity solutions of the Konopelchenko–Dubrovsky system using Lie group theory

2016 ◽  
Vol 71 (10) ◽  
pp. 2051-2059 ◽  
Author(s):  
Mukesh Kumar ◽  
Anshu Kumar ◽  
Raj Kumar
Keyword(s):  
Group Theory ◽  
Lie Group ◽  
Similarity Solutions ◽  
Lie Group Theory

scholarly journals Correction: Çakmak, A. New Type Direction Curves in 3-Dimensional Compact Lie Group Symmetry 2019, 11, 387

Symmetry ◽  
2020 ◽  
Vol 12 (2) ◽  
pp. 284
Author(s):  
Ali Çakmak
Keyword(s):  
Lie Group ◽  
Group Symmetry ◽  
Compact Lie Group ◽  
3 Dimensional ◽  
New Type ◽  
Lie Group Symmetry

The authors wish to make the following corrections to their paper [...]

Allee’s Effect Bifurcation in Generalized Logistic Maps

2019 ◽  
Vol 29 (03) ◽  
pp. 1950039
Author(s):  
J. Leonel Rocha ◽  
Abdel-Kaddous Taha
Keyword(s):  
Allee Effect ◽  
Dynamical Behavior ◽  
Complete Classification ◽  
Unimodal Maps ◽  
New Class ◽  
New Type ◽  
Local And Global Bifurcations ◽  
One Dimensional Maps ◽  
Necessary And Sufficient

This paper concerns the study of the Allee effect on the dynamical behavior of a new class of generalized logistic maps. The fundamentals of the dynamics of this 4-parameter family of one-dimensional maps are presented. A complete classification of the nature and stability of its fixed points is provided. The main results relate to the Allee effect bifurcation: a new type of bifurcation introduced for this class of unimodal maps. A necessary and sufficient condition so that the Allee fixed point is a snap-back repeller is established. In addition, in the parameters space is defined an Allee’s effect region, which determines the existence of an essential extinction for the generalized logistic maps. Local and global bifurcations of generalized logistic maps are investigated.

scholarly journals Uracil-Containing Heterodimers of a New Type: Synthesis and Study of Their Anti-Viral Properties

Molecules ◽  
2020 ◽  
Vol 25 (15) ◽  
pp. 3350
Author(s):  
Anna A. Maslova ◽  
Elena S. Matyugina ◽  
Robert Snoeck ◽  
Graciela Andrei ◽  
Sergey N. Kochetkov ◽  
...  
Keyword(s):  
Hiv Infection ◽  
Reverse Transcriptase ◽  
Viral Infections ◽  
Virus Infections ◽  
Healthy Individuals ◽  
Type Synthesis ◽  
Hiv Reverse Transcriptase ◽  
Reverse Transcriptase Inhibitors ◽  
New Type ◽  
Nucleoside Inhibitors

Widespread latent herpes viral infections within a population can lead to the development of co-infections in HIV-infected patients. These infections are not particularly dangerous for healthy individuals and often occur with minimal symptoms, but for those who are immunocompromised, these infections can accelerate the acute phase of HIV infection and AIDS. Thus, the idea of designing compounds that could combine activity against HIV and co-infections would seem promising. In that regard, eleven compounds were synthesized that represent conjugates of non-nucleoside HIV reverse transcriptase inhibitors and nucleoside inhibitors of the herpes family viruses with the hope that these novel heterodimers will result in dual activity against HIV and concomitant herpes virus infections.

scholarly journals Unitary spherical representations of Drinfeld doubles

2018 ◽  
Vol 2018 (742) ◽  
pp. 157-186 ◽  
Author(s):  
Yuki Arano
Keyword(s):  
Quantum Group ◽  
Lie Group ◽  
Complete Classification ◽  
Unitary Representations ◽  
Compact Lie Group ◽  
Drinfeld Double ◽  
Quantum Analogue ◽  
Property T ◽  
Simply Connected

Abstract We study irreducible spherical unitary representations of the Drinfeld double of the q-deformation of a connected simply connected compact Lie group, which can be considered as a quantum analogue of the complexification of the Lie group. In the case of \mathrm{SU}_{q}(3) , we give a complete classification of such representations. As an application, we show the Drinfeld double of the quantum group \mathrm{SU}_{q}(2n+1) has property (T), which also implies central property (T) of the dual of \mathrm{SU}_{q}(2n+1) .

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