Spatially resolved profiles of the H alpha, [N II] 6584 Angstrom, and [O III] 5007 Angstrom lines have been obtained with the Manchester echelle spectrometer combined with the 2.1 m San Pedro Martir telescope over the planetary nebula NGC 2440. The resulting position-velocity (PV) arrays are compared with ground-based and HST archival imagery, revealing the complex structure that prevails in this object. This work represents the first detailed kinematical study of NGC 2440. Several bipolar structures are shown to be emerging at different position angles from the core, as expected from bipolar, rotating, episodic outflows with different degrees of collimation. Line splitting reaches main peak to peak separations of 175 km s(-1) and 145 km s(-1) in the western and eastern main lobes, respectively. The FWZI values of the complex profiles span a range of 250 km s(-1) near the core and 150 km s(-1) in the outer regions. The nebular core is found to be a toroid expanding radially at greater than or equal to 22 km s(-1), and the systemic heliocentric radial velocity of NGC 2440 is found to be 65 km s(-1). When combined with existing measurements of the upper limit to the angular expansion, and assuming a tilt for the axis of the central toroid of 40 degrees in the plane of the sky, this lower limit for the expansion velocity implies a distance of greater than or equal to 1.45 kpc to NGC 2440. Puzzling kinematical features are the faint velocity components receding with radial velocity differences of 150 km s(-1) with respect to the systemic radial velocity from prominent knots at both ends of the brightest bipolar configuration. Scattering by dust in these knots of the line profiles from the bright nebular core is a likely explanation for this curious phenomenon.