Old astrophotographic plates are precious sources of historical data for astronomical studies, especially regarding the improvement of natural satellite orbits. Today, with the advent of new, accurate techniques, these old data can be re-processed so as to give positions that are much more accurate than those initially obtained. Various recent projects, including our Chinese project, have involved measuring and reducing these old plates again. Here we present a method for measurement and reduction that involves the digitization of plates using an advanced commercial scanner, namely the EPSON 10000 XL. We selected a set of 27 plates of the satellites of Jupiter, Saturn and Uranus taken from 1987 to 1990. A total of 125 satellite positions were derived from the new measurement and reduction of these plates using the UCAC4 catalogue. A comparison of the new observed positions with recent ephemerides has shown a general consistency with satellite theory of about 100 mas. The new positions present an accuracy equivalent to the most recent CCD observations, and better than the original positions. Moreover, nearly 30 per cent of the 125 positions obtained in this work are published for the first time here. This paper is a preliminary contribution to the larger project of new measurements and reductions of all the old Chinese plates of natural satellites, which should allow further improvements in the knowledge of the orbits of these satellites.