Overhead cranes are widely used for transporting large and heavy suspended objects such as shipping containers. Acceleration and deceleration of the crane generally induce swinging motion in the suspended payload. A method is presented to find the trajectory for an overhead crane that will ensure the transfer of the payload in the shortest time and with minimum swinging along a specified path. The overhead crane and the suspended payload are modeled as a double pendulum with motion in three dimensional space. The equations of motion of the overhead crane and the payload are transformed in terms of a single path parameter which represents single degree of motion along the path. The resulting set of equations defines the phase space of admissible motion constrained by the path geometry and the forces exerted by the crane. By applying dynamic programming principles to the transformed set of equations of motion, the trajectory with the shortest time and with minimum swinging is determined.
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