Lie Group Based Method for Type Synthesis of Parallel Mechanisms

2019 ◽  
pp. 55-71
Author(s):  
Qinchuan Li ◽  
Jacques M. Hervé ◽  
Wei Ye
Keyword(s):  
Lie Group ◽  
Parallel Mechanisms ◽  
Type Synthesis

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 Type Synthesis of 1T2R Parallel Mechanisms Using Structure Coupling-Reducing Method

2019 ◽  
Vol 32 (1) ◽  
Author(s):  
Haitao Liu ◽  
Ke Xu ◽  
Huiping Shen ◽  
Xianlei Shan ◽  
Tingli Yang
Keyword(s):  
Explicit Form ◽  
Parallel Mechanism ◽  
Analytic Solutions ◽  
Forward Kinematics ◽  
Parallel Mechanisms ◽  
Type Synthesis ◽  
Real Time Control ◽  
Time Control ◽  
Topological Characteristics ◽  
Zero Coupling

Abstract Direct kinematics with analytic solutions is critical to the real-time control of parallel mechanisms. Therefore, the type synthesis of a mechanism having explicit form of forward kinematics has become a topic of interest. Based on this purpose, this paper deals with the type synthesis of 1T2R parallel mechanisms by investigating the topological structure coupling-reducing of the 3UPS&UP parallel mechanism. With the aid of the theory of mechanism topology, the analysis of the topological characteristics of the 3UPS&UP parallel mechanism is presented, which shows that there are highly coupled motions and constraints amongst the limbs of the mechanism. Three methods for structure coupling-reducing of the 3UPS&UP parallel mechanism are proposed, resulting in eight new types of 1T2R parallel mechanisms with one or zero coupling degree. One obtained parallel mechanism is taken as an example to demonstrate that a mechanism with zero coupling degree has an explicit form for forward kinematics. The process of type synthesis is in the order of permutation and combination; therefore, there are no omissions. This method is also applicable to other configurations, and novel topological structures having simple forward kinematics can be obtained from an original mechanism via this method.

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.

scholarly journals Type Synthesis of Parallel Mechanisms with the First Class GF Sets and Two-Dimensional Rotations

10.5772/50645 ◽  
2012 ◽  
Vol 9 (3) ◽  
pp. 61 ◽  
Author(s):  
Jialun Yang ◽  
Feng Gao ◽  
Kuanjun Zhu ◽  
Bin Liu
Keyword(s):  
Two Dimensional ◽  
Parallel Mechanisms ◽  
Type Synthesis

scholarly journals Type Synthesis of Fully-Decoupled Three-Rotational and One-Translational Parallel Mechanisms

10.5772/62684 ◽  
2016 ◽  
Vol 13 (2) ◽  
pp. 79 ◽  
Author(s):  
Yi Cao ◽  
Hai Chen ◽  
Youlei Qin ◽  
Kai Liu ◽  
Shuyi Ge ◽  
...  
Keyword(s):  
Parallel Mechanisms ◽  
Type Synthesis

Type Synthesis of Binary Actuated Parallel Mechanisms

2012 ◽  
pp. 131-138
Author(s):  
D. Schütz ◽  
R. J. Ellwood ◽  
A. Raatz ◽  
J. Hesselbach
Keyword(s):  
Parallel Mechanisms ◽  
Type Synthesis
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