QI Zhao-hui, SONG Hui-tao. Deflection Analysis of Load Trajectories for General Hoisting Mechanisms[J]. Applied Mathematics and Mechanics, 2014, 35(4): 444-458. doi: 10.3879/j.issn.1000-0887.2014.04.010
 Citation: QI Zhao-hui, SONG Hui-tao. Deflection Analysis of Load Trajectories for General Hoisting Mechanisms[J]. Applied Mathematics and Mechanics, 2014, 35(4): 444-458.

# Deflection Analysis of Load Trajectories for General Hoisting Mechanisms

##### doi: 10.3879/j.issn.1000-0887.2014.04.010
Funds:  The National Natural Science Foundation of China(10972044)
• Rev Recd Date: 2014-02-26
• Publish Date: 2014-04-15
• A systematic method for analyzing load trajectory deflections of general hoisting mechanisms was presented. In this method, the first order differential equations for generalized degrees of freedom and wire rope tensions were established based on the governing equations of equilibrium and compatibility conditions. Properties and formulations of the variables involved in these equations were studied in detail, in which the displacements and velocities of tangent points between pulleys and the tension directions of ropes as well as the change rates of tension directions were derived. The compatibility condition for drum parameters, as well as for rope lengths in the system was provided. A method to solve the angular speeds of spatial pulleys was proposed. In the process of solving the differential equations, the pulley’s angular speed which determined the relation of tensions at both ends of the pulley, was derived at each step. The systematic method is applicable to hoisting mechanisms with single reeving branches, and solves the difficult problem of determining the rotating directions of pulleys. To a large extent the proposed method is universal and makes a reference for designing and analyzing general hoisting mechanisms.
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