scholarly journals Type Synthesis of 2T1R Decoupled Parallel Mechanisms Based on Lie Groups and Screw Theory

2017 ◽  
Vol 2017 ◽  
pp. 1-11 ◽  
Author(s):  
Shuwei Qu ◽  
Ruiqin Li ◽  
Shaoping Bai
Keyword(s):  
Lie Groups ◽  
Lie Group ◽  
Screw Theory ◽  
New Method ◽  
Parallel Mechanisms ◽  
Type Synthesis ◽  
Compact Structure ◽  
Selection Of

Decoupled parallel mechanisms (DPMs) have the characteristics of compact structure and simple control with wide applications. This paper presents a new method of type synthesis for DPMs by virtue of Lie groups and screw theory. The method consists of synthesis at limb level and configuration level. At limb level, Lie group is used to synthesize the limbs with required DOFs. At configuration level, screw theory is adopted to determine configuration with synthesized limbs that satisfy the type synthesis criteria of DPMs. The type synthesis criteria including limb decoupling and selection of the driving pairs are presented. Upon the formulation, the procedure of type synthesis of DPMs is developed. Type synthesis is conducted with the proposed method, which leads to new spatial and planar fully decoupled 2T1R mechanisms.

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.

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.

Type synthesis of 2R2T parallel mechanisms based on motion equivalent chain method

2014 ◽  
Vol 228 (17) ◽  
pp. 3209-3217 ◽  
Author(s):  
Wei Ye ◽  
Yuefa Fang ◽  
Sheng Guo ◽  
Haibo Qu
Keyword(s):  
Parallel Mechanism ◽  
Screw Theory ◽  
Parallel Mechanisms ◽  
Motion Pattern ◽  
Type Synthesis ◽  
Constraint Force ◽  
Single Loop ◽  
Loop Chain ◽  
Serial Chains

In this paper, the motion equivalent chain method is proposed and then applied to the type synthesis of a class of 2R2T parallel mechanism. The equivalent serial chains are synthesized for a specific 2R2T motion pattern based on screw theory. Feasible limb structures that provide a constraint couple and a constraint force are enumerated according to the reciprocity of the twist and wrench systems. Several motion equivalent single loop chains are constructed with the equivalent serial chains. Using motion equivalent single loop chains to replace the equivalent serial chains, a class of 2R2T parallel mechanisms is obtained based on the foundation of motion equivalent single loop chain structures.

Compliance Analysis of Mechanisms with Spatial Continuous Compliance in the Context of Screw Theory and Lie Groups

2010 ◽  
Vol 224 (11) ◽  
pp. 2493-2504 ◽  
Author(s):  
X Ding ◽  
J S Dai
Keyword(s):  
Case Studies ◽  
Lie Groups ◽  
Screw Theory ◽  
Elastic Beam ◽  
Parallel Mechanisms ◽  
Finite Segment ◽  
Numerical Examples ◽  
Spatial Compliance ◽  
Eigenvectors And Eigenvalues

This paper investigates the compliance effect on both serial and parallel mechanisms based on study of deflections of a finite segment of elastic beam with spatial compliance and applies eigenvectors and eigenvalues to identify principal screws in the mechanisms and parallel devices with spatial continuous compliance. With the analysis, compliance characteristics of both serial mechanisms and parallel devices can be identified with effect of compliance. Case studies are presented with numerical examples.

Synthesis of 2T1R Decoupled Parallel Manipulators

2011 ◽  
Vol 308-310 ◽  
pp. 2025-2030 ◽  
Author(s):  
Wen Juan Lu ◽  
Li Jie Zhang ◽  
Da Xing Zeng ◽  
Ruo Song Wang
Keyword(s):  
Screw Theory ◽  
Control Design ◽  
Parallel Manipulators ◽  
Parallel Mechanisms ◽  
Type Synthesis ◽  
Precision Control ◽  
Kinematic Chains ◽  
Step Procedure ◽  
Nonlinear Relation ◽  
Three Degree Of Freedom

For the general parallel mechanisms(PMS), since the coupling between kinematic chains, the nonlinear relation between the input and output is presented, which have led to difficulty in the trajectory planning and precision control. Design of motion decoupled parallel mechanisms(DPMS) has become a good new topic in this area and has captured researcher's attention. In this work, the approach to a synthesis of three degree-of-freedom(3-DOF) DPMS is considered based on screw theory and motion synthesis ideas. Criterions for type synthesis of the branches for DPMS is established according to the twist screw system of the limbs, which assures the decoupling in each limb. Then a six-step procedure is presented for the type synthesis of 2T1R decoupled mechanisms.

Type synthesis of 4-DOF nonoverconstrained parallel mechanisms based on screw theory

Robotica ◽  
2011 ◽  
Vol 30 (1) ◽  
pp. 31-37 ◽  
Author(s):  
Sheng Guo ◽  
Yuefa Fang ◽  
Haibo Qu
Keyword(s):  
Parallel Mechanism ◽  
Screw Theory ◽  
Research Topic ◽  
Parallel Mechanisms ◽  
Type Synthesis ◽  
Systematic Method ◽  
Constraint System

SUMMARYA systematic method is developed for the type synthesis of 4-DOF nonoverconstrained parallel mechanisms with three translations and one rotation inspired by the design of H-4. First, the motion requirements of primary platform and secondary platform of the 4-DOF nonoverconstrained parallel mechanisms are analyzed, and the conflict between the number of actuators and the constraint system for nonoverconstrained parallel mechanism is solved. Then, the research topic of type synthesis of 4-DOF nonoverconstrained parallel mechanisms is transformed into the type synthesis of the secondary platform with three translational DOF linked by two chains. On the basis of the screw and reciprocal theory, all possible secondary limbs with 3-DOF, 4-DOF, and 5-DOF are synthesized, respectively. Finally, the configurations and spatial assembly conditions of all possible secondary limbs are provided and some typical mechanisms are sketched as examples.

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