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Kinematics and error analysis of cooperative cable parallel manipulators for multiple mobile cranes

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Abstract

Combining mobile cranes with the cable parallel manipulators (CPMs), a cooperative CPMs for multiple mobile cranes (CPMMCs) was designed in this paper. The kinematics were derived on the basis of the configuration of the CPMMCs, aiming at numerical estimation of workspace subject to the constraints on the cable tensions and mobile cranes’ structure. Kinematic error, caused by machining, assembly and operation, is one of the major error sources for CPMMCs during high-precision hoisting, which can be estimated by means of error modeling. Kinematics error model was established based on closed-loop vector method. The influences of different error sources on the accuracy are investigated with sensitivity analysis in statistics. Finally, the system is simulated with expected trajectory of the payload based on the established kinematics and error model of the CPMMCs. The simulation results not only provide rationale for design of the CPMMCs, but also of certain guiding significance in practical engineering application.

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Abbreviations

m :

Mass of the load

D :

Distance between each mobile crane

d :

The horizontal distance between the pulley center and hoisting point of load

L :

Length of boom

h :

Vertical distance between the lower hinge joints of boom and cylinder

a :

Horizontal distance between the lower hinge joint of boom and the slewing axis

e :

Horizontal distance between the lower hinge joint of hydraulic cylinder and the slewing

ls :

Distance between the lower hinge joint of boom and the upper hinge joint of cylinder

l :

Cable length between the hoisting point to the endpoint of boom

lc :

Length of luffing hydraulic cylinder

φ :

The slewing angle

γ:

The inclination angle of cable

R :

The working radius

T :

The tension of cable

de A :

Position error of the pulley center

dq A :

Kinematics error sources of mobile crane

J A :

Jacobian matrix of the three groups of the mobile crane

de 0 :

Position error of the end-effector of the CPM

dq 0 :

Kinematics error sources of the CPM

J 0 :

Jacobian matrix of the CPM

de :

Position error of the end-effector

dq :

24 error sources for kinematic parameters

J :

Jacobian matrix of the CPMMCs

S :

Local sensitivity

\( \overline{S} \) :

Global sensitivity

V :

Volume of the workspace

S k :

Sensitivity coefficient

σ:

The standard deviation of the kinematics error sources

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Acknowledgments

This work was supported by the National Natural Science Foundation of China (51275515) and the Fundamental Research Funds for the Central Universities (2013RC09).

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Authors and Affiliations

  1. School of Mechanical and Electrical Engineering, China University of Mining and Technology, Xuzhou, 221116, China

    Sen Qian, Bin Zi, Dan Zhang & Long Zhang

  2. School of Mechanical and Automotive Engineering, Hefei University of Technology, Hefei, 230009, China

    Bin Zi

  3. Faculty of Engineering and Applied Science, University of Ontario Institute of Technology, Oshawa, ON, L1H 7K4, Canada

    Dan Zhang

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  1. Sen Qian
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  2. Bin Zi
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  3. Dan Zhang
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  4. Long Zhang
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Correspondence to Bin Zi.

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Qian, S., Zi, B., Zhang, D. et al. Kinematics and error analysis of cooperative cable parallel manipulators for multiple mobile cranes. Int J Mech Mater Des 10, 395–409 (2014). https://doi.org/10.1007/s10999-014-9250-5

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  • DOI: https://doi.org/10.1007/s10999-014-9250-5

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