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Research Papers

Clearance-Induced Position Uncertainty of Planar Linkages and Parallel Manipulators

[+] Author and Article Information
Kwun-Lon Ting

Center for Manufacturing Research,
Tennessee Technological University,
Cookeville, TN 38505
e-mail: kting@tntech.edu

Kuan-Lun Hsu

Mechanical Engineering Department,
Tennessee Technological University,
Cookeville, TN 38505

Jun Wang

Professor
School of Mechanical Engineering,
Hubei University of Technology,
Wuhan 430068, Hubei, China

1Corresponding author.

2(Ting, 1989, “Mobility Criteria of Single-Loop N-Bar Linkages,” ASME J. Mech. Des., 111(4), pp. 504–507; Ting and Liu, 1991, “Rotatability Laws for N-Bar Kinematic Chains and Their Proof,” ASME J. Mech. Des., 113(1), pp. 32–39; Shyu and Ting, 1994, “Invariant Link Rotatability of N-Bar Kinematic Chains,” ASME J. Mech. Des., 116(1), pp. 343–347; and Xue, Ting, and Wang, 2011, “Mobility Criteria of Planar Single-Loop N-Bar Chains With Prismatic Joints,” ASME J. Mech. Rob., 3(1), p. 011011).

Manuscript received August 9, 2016; final manuscript received July 31, 2017; published online September 6, 2017. Assoc. Editor: Marc Gouttefarde.

J. Mechanisms Robotics 9(6), 061001 (Sep 06, 2017) (7 pages) Paper No: JMR-16-1230; doi: 10.1115/1.4037619 History: Received August 09, 2016; Revised July 31, 2017

The paper presents a simple and effective kinematic model and methodology to assess and evaluate the extent of the position uncertainty caused by joint clearances for multiple-loop linkage and manipulators connected with revolute or prismatic pairs. The model is derived and explained with geometric rigor based on Ting's rotatability laws.ff2 The significant contributions include (1) the clearance link model for a P-joint that catches the translation and oscillation characteristics of the slider within the clearance and separates the geometric effect of clearances from the input error, (2) the generality of the method, which is effective for multiloop linkages and parallel manipulators, and (3) settling the dispute on the position uncertainty effect to parallel and serial robots due to joint clearance. The discussion is illustrated and carried out through symmetrically configured planar 8 bar parallel robots. It is found that at a target position, the uncertainty region of a three degrees-of-freedom (DOF) three-leg parallel robot is enclosed by a hexagon with curve edges, while that of its serial counterpart is enclosed by a circle included in the hexagon. A numerical example is presented. The finding and proof, though only based on three-leg planar 8 bar parallel robots, may have a wider implication suggesting that based on the kinematic effect of joint clearance, parallel robots tends to inherit more position uncertainty than their serial counterparts. The use of more loops in not only parallel robots but also single-DOF linkages cannot fully offset the adverse effect on position uncertainty caused by the use of more joints.

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References

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Ting, K.-L. , 1989, “ Mobility Criteria of Single-Loop N-Bar Linkages,” ASME J. Mech. Des., 111(4), pp. 504–507.
Ting, K.-L. , and Liu, Y.-W. , 1991, “ Rotatability Laws for N-Bar Kinematic Chains and Their Proof,” ASME J. Mech. Des., 113(1), pp. 32–39. [CrossRef]
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Figures

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Fig. 1

Three types of parallel manipulators: (a) 3RRR, (b) 3PRR, and (c) 3RPR

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Fig. 2

Clearance model of a revolute pair

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Fig. 3

Clearance model of a prismatic pair

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Fig. 4

Uncertainty-free end effector position

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Fig. 5

Equivalent 3RRR parallel manipulator with clearance links

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Fig. 6

Possible configurations of the 8 bar linkage

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Fig. 7

Exact position and clearance-induced uncertainty region of point C

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Fig. 8

Approximate approach for considering clearance-induced uncertainty region

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Fig. 9

Exact and approximate clearance-induced uncertainty region of point C

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Fig. 10

(a) End effector target position of a 3RPR parallel manipulator and (b) equivalent 3RPR parallel manipulator with clearance links

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