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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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