A Gantry Crane Problem Solved

[+] Author and Article Information
William J. O’Connor

Lecturer in Dynamics and Control at University College Dublin, National University of Ireland, Department of Mechanical Engineering, University College Dublin, Belfield, Dublin 4, Ireland e-mail: william.oconnor@ucd.ie

J. Dyn. Sys., Meas., Control 125(4), 569-576 (Jan 29, 2004) (8 pages) doi:10.1115/1.1636198 History: Received August 29, 2002; Revised July 08, 2003; Online January 29, 2004
Copyright © 2003 by ASME
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Grahic Jump Location
One way to initialize a virtual cable, when load mass over target
Grahic Jump Location
The gantry crane model with (on right) assumed positive transverse force waves f(x−ct) and g(x+ct), components of −T∂y/∂x, producing, as they pass, transverse velocities v=∂y/∂t in opposite directions. Both waves will exert a positive (rightwards) force on the load mass, and a negative (leftwards) force on the trolley, and will be reflected without inversion on reaching load and trolley respectively.
Grahic Jump Location
A 3-m manoeuvre of a 4-m cable, with asymptotic arrival at target, achieved by constant launch velocity until halfway to target, with continuous wave absorption throughout (during and after this launch). Max trolley speed 1 m/s, L=4 m, ρ=0.1 kg/m, m=2 kg,T=23.54 N,c=15.34 m/s,Z=1.534 Ns/m.
Grahic Jump Location
Trolley velocity maintained at maximum until launch displacement is half target distance (at t=5.27 s). Then returning waves are absorbed until system is stationary. Same parameters as Fig. 3, except larger target distance of 8 m to show load “pendulum” swings during launch phase. The unevenness in load speed is due to force waves up and down the cable.
Grahic Jump Location
Example of an “exact” movement of 3-m with same system parameters as for Fig. 3. In contrast with Figs. 3 and 4, after a single, smooth sweep and rapid deceleration, the load arrives at the target and stops L/c seconds before the trolley has stopped. The trolley velocity at all points is the sum of the launch and absorb velocities (Eq. 8).



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