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Research Papers

Dynamic Response and Nonlinear Characteristics of Spatial Parallel Mechanism With Spherical Clearance Joint

[+] Author and Article Information
Chen Xiulong

College of Mechanical and
Electronic Engineering,
Shandong University of
Science and Technology,
Qingdao 266590, China
e-mail: cxldy99@163.com

Li Yuewen

College of Mechanical and
Electronic Engineering,
Shandong University of
Science and Technology,
Qingdao 266590, China
e-mail: lyw15764237581@163.com

Jia Yonghao

College of Mechanical and
Electronic Engineering,
Shandong University of
Science and Technology,
Qingdao 266590, China
e-mail: 365115293@qq.com

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received August 13, 2018; final manuscript received January 15, 2019; published online February 15, 2019. Assoc. Editor: Javier Cuadrado.

J. Comput. Nonlinear Dynam 14(4), 041010 (Feb 15, 2019) (18 pages) Paper No: CND-18-1362; doi: 10.1115/1.4042636 History: Received August 13, 2018; Revised January 15, 2019

Spherical joint is a type of common kinematic pair in spatial parallel mechanism. The existence of spherical joint clearance has many adverse effects on the mechanism. A method of forecasting the dynamic behaviors of spatial parallel mechanism with spherical clearance joint is proposed. The 4-UPS-UPU spatial parallel mechanism with spherical clearance is taken as the research object, the dynamic response, and nonlinear characteristics of the mechanism are studied. The kinematic model and the contact force model of the spherical clearance are established. The dynamic equation of the spatial parallel mechanism with spherical joint clearance is derived by Newton–Euler method. The above-mentioned dynamic equation is solved by using the ODE113 function that is based on a variable order numerical differential algorithm in matlab. The dynamic responses of moving platform with different clearance values are analyzed. The contact force and the center trajectory of the sphere at the spherical joint are obtained. In addition, the phase trajectory, Poincare map, and bifurcation diagram are analyzed, and the nonlinear characteristics of the spherical clearance joint and the moving platform are obtained. By comparing the results, such as the acceleration of moving platform and the contact force, with virtual prototype simulation, the correctness of the dynamic equation of the spatial parallel mechanism with spherical clearance joint and the analysis results are verified. The researches show that the change of clearance value has a great influence on the motion state of spherical clearance joint, and chaos phenomena appears in the clearance joint with the increase in the clearance value. And the impact phenomenon appears between the spherical joint elements, which makes the mechanism generated vibration.

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Figures

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Fig. 1

Outside view of 4-UPS-UPU parallel mechanism

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Fig. 2

Schematic diagram of 4-UPS-UPU parallel mechanism

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Fig. 3

Spherical joint clearance with contact

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Fig. 5

The force diagram of Hooke joint

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Fig. 4

The 3D model of Hooke joint

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Fig. 12

Phase trajectories and Poincare maps of moving platform: (a) phase trajectories when c = 0.15 mm in the X direction, (b) Poincare map when c = 0.15 mm in the X direction, (c) phase trajectories when c = 0.45 mm in the X direction, (d) Poincare map when c = 0.45 mm in the X direction, (e) phase trajectories when c = 0.80 mm in the X direction, and (f) Poincare map when c = 0.80 mm in the X direction

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Fig. 13

Bifurcation diagram of moving platform with changing clearance value: (a) bifurcation diagram of moving platform in the X direction, (b) bifurcation diagram of moving platform in the Y direction, and (c) bifurcation diagram of moving platform in the Z direction

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Fig. 6

Influence of different clearance on the linear displacement and angular displacement of moving platform: (a1) displacement curve in the X-direction, (a2) partial enlarged drawing of displacement curve in the X-direction, (b1) displacement curve in the Y-direction, (b2) partial enlarged drawing of displacement curve in the Y-direction, (c) displacement curve in the Z-direction, (d) angular displacement in the α-direction, and (e) angular displacement in the β-direction

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Fig. 7

Influence of different clearance on the linear velocity and angular velocity of moving platform: (a1) velocity curve in the X-direction, (a2) partial enlarged drawing of velocity curve in the X-direction, (b1) velocity curve in the Y-direction, (b2) partial enlarged drawing of velocity curve in the Y-direction, (c) velocity curve in the Z-direction, (d) angular velocity in the α-direction, and (e) angular velocity in the β-direction

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Fig. 8

Influence of different clearance on the linear acceleration and angular acceleration of moving platform: (a) acceleration curve in the X-direction, (b) acceleration curve in the Y-direction, (c) acceleration curve in the Z-direction, (d) angular acceleration in the α-direction, and (e) angular acceleration in the β-direction

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Fig. 9

The trajectory of the moving platform:: (a) The trajectory of the moving platform when c = 0.15 mm and (b) the trajectory of the moving platform when c = 0.45 mm

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Fig. 11

The center trajectory of the sphere: (a) center trajectory of the sphere when c = 0.15 mm, (b) center trajectory of the sphere when c = 0.45 mm, and (c) center trajectory of the sphere when c = 0.8 mm and its partial enlarged drawing

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Fig. 14

Phase trajectories and Poincare maps of clearance joint: (a) phase trajectories when c = 0.15 mm in the Y direction, (b) Poincare map when c = 0.15 mm in the Y direction, (c) phase trajectories when c = 0.45 mm in the Ydirection, (d) Poincare map when c = 0.45 mm in the Y direction, (e) phase trajectories when c = 0.80 mm in theY direction, and (f) Poincare map when c = 0.80 mm in the Y direction

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Fig. 15

Bifurcation diagram of clearance joint with changing clearance value: (a) bifurcation diagram of joint in the X direction, (b) bifurcation diagram of joint in the Y direction, and (c) Bifurcation diagram of joint in the Z direction

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Fig. 16

Comparison of simulation results between matlab and adams: (a) acceleration curve in the X-direction, (b) acceleration curve in the Y-direction, (c) acceleration curve in the Z-direction, (d) acceleration velocity in the α-direction, (e) angular acceleration in the β-direction, and (f) contact force curve

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Fig. 10

Influence of different clearance on the contact force of spherical joint with clearance: (a) contact force when c = 0.15 mm, (b) contact force when c = 0.45 mm and (c) contact force when c = 0.80 mm

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