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Research Papers

Tracking Accuracy Analysis of a Planar Flexible Manipulator With Lubricated Joint and Interval Uncertainty

[+] Author and Article Information
Dongyang Sun

College of Aerospace Engineering,
Chongqing University,
Chongqing 400044, China
e-mail: dongyangsunnuaa@gmail.com

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received January 27, 2016; final manuscript received May 5, 2016; published online June 2, 2016. Assoc. Editor: Zdravko Terze.

J. Comput. Nonlinear Dynam 11(5), 051024 (Jun 02, 2016) (9 pages) Paper No: CND-16-1036; doi: 10.1115/1.4033609 History: Received January 27, 2016; Revised May 05, 2016

A method for trajectory tracking accuracy analysis of a two-link flexible manipulator with lubricated revolute joint involving interval uncertainty is presented. In this method, first, fuzzy self-tuning proportion integration differentiation (PID) control is applied to track the desired tip trajectory of the manipulator. The absolute nodal coordinate formulation (ANCF) is employed for the finite element discretization of the flexible manipulator. And lubricated revolute joint is modeled based on the infinitely short journal bearing with Gümbel conditions. Second, uncertainty of clearance size is considered, and interval analysis method is applied. Numerical simulation is posted to investigate the cushioning effect of lubricants on the clearance and influence of uncertainty on control accuracy of the manipulator. The results show that the lubricants can improve the stability of motion and operation precision of the manipulator; however, uncertainty of the manipulator may reduce the control accuracy of the manipulator.

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Figures

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Fig. 1

Cross section of a lubricated journal bearing

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Fig. 2

Two-link flexible manipulator model

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Fig. 3

The fuzzy self-tuning PID controller

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Fig. 4

Membership function for elk/Ge, delk/Gde, ΔKp/Gp, ΔKi/Gi, and ΔKd/Gd

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Fig. 5

Interval uncertain analysis for a manipulator

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Fig. 6

Circle trajectory tracking of manipulator

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Fig. 7

The desired trajectory and the actual trajectory of the manipulator tip

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Fig. 8

Error of (a) shoulder angle and (b) elbow angle

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Fig. 9

Error in (a) X-direction and (b) Y-direction of the elbow tip

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Fig. 10

Translational acceleration of the elbow tip in X-direction

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Fig. 11

Translational acceleration of the elbow tip in Y-direction

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Fig. 12

Applied torques to shoulder motor

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Fig. 13

Applied torques to elbow motor

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Fig. 14

Error of shoulder angle for the manipulator (c = 0.2 mm, 0.3 mm, 0.4 mm, and 0.5 mm): (a) dry contact model and (b) lubricated model

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Fig. 15

Error of elbow angle for the manipulator (c = 0.2 mm, 0.3 mm, 0.4 mm, and 0.5 mm): (a) dry contact model and (b) lubricated model

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Fig. 16

Error in X-direction of the elbow tip (c = 0.2 mm, 0.3 mm, 0.4 mm, and 0.5 mm): (a) dry contact model and (b) lubricated model

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Fig. 17

Error in Y-direction of the elbow tip (c = 0.2 mm, 0.3 mm, 0.4 mm, and 0.5 mm): (a) dry contact model and (b) lubricated model

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Fig. 18

Error region of (a) shoulder angle and (b) elbow angle

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Fig. 19

Error region in (a) X-direction and (b) Y-direction of the elbow tip

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