The proto-planetary nebula Hen 3-1475 shows a remarkable highly collimated optical jet with an S-shaped string of three pairs of knots and extremely high velocities. We present here a detailed analysis of the overall morphology, kinematic structure and the excitation conditions of these knots based on deep ground-based high dispersion spectroscopy complemented with high spatial resolution spectroscopy obtained with STIS onboard HST, and WFPC2 [N II] images. The spectra obtained show double-peaked, extremely wide emission line profiles, and a decrease of the radial velocities with distance to the source in a step-like fashion. We find that the emission line ratios observed in the intermediate knots are consistent with a spectrum arising from the recombination region of a shock wave with shock velocities ranging from 100 to 150 km s-1. We propose that the ejection velocity is varying as a function of time with a quasi-periodic variability (with timescale of the order of 100 years) and the direction of ejection is also varying with a precession period of the order of 1500 years. Some slowing down with distance along the axis of the Hen 3-1475 jet may be due to the entrainment process and/or to the enviromental drag. This scenario is supported by geometric and kinematic evidence: firstly, the decrease of the radial velocities along the Hen 3-1475 jet in a step like fashion; secondly, the kinematic structure observed in the knots; thirdly, the point-symmetric morphology together with the high proper motions shown by several knots; and finally the fact that the shock velocity predicted from the observed spectra of the shocked knots is much slower than the velocities at which these knots move outwards with respect to the central source. Based on observations made during service time with the 2.5 m Isaac Newton Telescope operated on La Palma by the Isaac Newton Group of Telescopes in the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofísica de Canarias, and observations made with the Hubble Space Telescope, obtained from the Data Archive at the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS5-26555.