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Research Papers

The Design of Looped-Synchronous Mechanism With Duplicated Spatial Assur-Groups

[+] Author and Article Information
Xu Wang

State Key Laboratory of Mechanical System and Vibration,
Shanghai Jiao Tong University,
800 Dongchuan Road,
Shanghai 200240, China
e-mail: saddy_xgd@sjtu.edu.cn

Weizhong Guo

State Key Laboratory of Mechanical System and Vibration,
Shanghai Jiao Tong University,
800 Dongchuan Road,
Shanghai 200240, China
e-mail: wzguo@sjtu.edu.cn

1Corresponding author.

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the Journal of Mechanisms and Robotics. Manuscript received November 29, 2018; final manuscript received March 30, 2019; published online May 21, 2019. Assoc. Editor: Xianwen Kong.

J. Mechanisms Robotics 11(4), 041014 (May 21, 2019) (20 pages) Paper No: JMR-18-1435; doi: 10.1115/1.4043457 History: Received November 29, 2018; Accepted April 03, 2019

The looped-synchronous mechanism (LSM) is a special one degree-of-freedom (DOF) closed chain of transmission with a large number of duplicated units that synchronizes the motion of many output links. This kind of mechanism can be found in many applications such as stator blade adjusting mechanisms for various aero-engines. The LSMs are composed of a large number of links and joints and must be designed by specific means. Spatial Assur-group, which is a concept extended from traditional Assur-group(in planar scope), and usually with a little number of parts and joints, is used in this work to design LSM. First, based on the formula of DOF of spatial Assur-group, all possible combinations are listed and two feasible combinations are chosen as the main body of each unit of LSM, combining with a prime mover to meet the requirement to be inexpandable and adjustable. Second, the condition for transmission ratio of the used Assur-group to be 1 is distilled for being synchronous and looped under the situation that all units of LSM have the same topology. To meet the condition, the needed dimensional conditions are researched and mathematical deduction is used to figure out the possibilities. Third, after confirming that it is impossible to meet the condition strictly, an optimization method in the environment of Simulink is used to approach the condition as close as possible. Finally, numerical and dynamic simulations are carried out to verify the effectiveness of the mentioned methods.

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Figures

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Fig. 1

A general graph of LSM: (a) the isometric view and (b) the vertical view

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Fig. 2

A simple display of vane actuation system using parallel mechanism and gear drive: (a) using the parallel mechanism, (b) the subsystem of (a), (c) using the gear drive (the vertical view), and (d) using the gear drive (the isometric view)

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Fig. 3

An example of the usage of Assur-group to form the planar mechanism such as (a) the prime mover, (b) the used Assur-group, (c) four-bar one in, (d) the same used Assur-group, (e) and six-bar one in

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Fig. 4

A process to form LSM using spatial Assur-group. The requirement of being looped has not been met yet: (a) one basic spatial Assur-group, (b) two same basic spatial Assur-groups linked together, (c) n same basic spatial Assur-groups linked together, (d) all inner joint Ji is transferred to a mechanism-level one, and (e) the remaining inner joint Jn+1,p is transferred to a mechanism-level one

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Fig. 5

The basic spatial Assur-group (with two movable parts) of LSM (a) and the corresponding four-bar linkage mechanism (b)

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Fig. 6

The connection configuration between the prime mover and the nth chain: (a) the prime mover RPSR, (b) only one inner joint, Jn+1,p, has not been transferred to a mechanism-level one, and (c) the connection between (a) and (b)

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Fig. 7

A graph when point B is overlapped with A, so as the joints Jn+1,p and J1,p are located at the same position

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Fig. 8

The diagrammatic sketch of the mechanism RSSR, where the axes of these two rotation joints intersect at one point O

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Fig. 9

The diagrammatic sketch of the mechanism RSSR, where the axes of these two rotation joints are parallel with each other (α = 0): (a) the isometric view and (b) the front view

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Fig. 10

The diagrammatic sketch of the mechanism RSCR, where the axes of these two rotation joints intersect at one point O

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Fig. 11

The diagrammatic sketch of the mechanism RSCR, where the axes of these two rotation joints are parallel with each other (α = 0): (a) the isometric view and (b) the front view

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Fig. 12

The Simulink model for the optimization of the transmission ratio for RSSR

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Fig. 13

A diagrammatic sketch of LSM which is of circular configuration

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Fig. 14

Trajectories of the design parameters during the optimization process

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Fig. 15

The input and output curves: (a) under the initial design parameters and (b) under the optimized design parameters

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Fig. 16

The three-dimensional model of LSM with circle configuration. Pdr is set just for measuring and will not occur in real LSM: (a) the details of the prime mover and (b) the vertical view of the whole system.

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Fig. 17

The curves of the displacements of joint Pdr with circle configuration: (a) under the initial design parameters and (b) under the optimized design parameters

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Fig. 18

The difference value between the input and output under the optimized design parameters

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Fig. 19

The dead point of part n during the simulation process under the initial design parameters. For case study 1, n = 25. For case study 2, n = 32.

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Fig. 20

A diagrammatic sketch of LSM, which is of rectangular configuration

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Fig. 21

Trajectories of the design parameters for α1~4 = 18 deg during the optimization process

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Fig. 22

The input and output curves for α1~4 = 18 deg: (a) under the initial design parameters and (b) under the optimized design parameters

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Fig. 23

The vertical view of the three-dimensional model of LSM with a rectangular configuration. Pdr is set just for measuring and will not occur in real LSM.

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Fig. 24

The curves of the displacements of joint Pdr with a rectangular configuration: (a) under the initial design parameters and (b) under the optimized design parameters

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Fig. 25

The difference value between the input and output under the optimized design parameters

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Fig. 26

A diagrammatic sketch of LSM, which is of irregular configuration

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Fig. 27

Trajectories of the design parameters for α2 = 16 deg during the optimization process

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Fig. 28

The input and output curves for α2 = 16 deg: (a) under the initial design parameters and (b) under the optimized design parameters

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Fig. 29

Trajectories of the design parameters for α4 = 20 deg during the optimization process

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Fig. 30

The input and output curves for α4 = 20 deg: (a) under the initial design parameters and (b) under the optimized design parameters

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Fig. 31

The vertical view of the three-dimensional model of LSM with an irregular configuration. Pdr is set just for measuring and will not occur in real LSM.

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Fig. 32

The curves of the displacements of joint Pdr with an irregular configuration: (a) under the initial design parameters and (b) under the optimized design parameters

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Fig. 33

The difference value between the input and output under the optimized design parameters: (a) α2 = 16 deg and (b) α4 = 20 deg

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Fig. 34

Summary of the work. Also a design process of LSM.

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Fig. 35

A simple design process of parallel mechanism

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