Abstract: In order to solve the problem of synthetic control for trajectory position and motion and study the mechanism of motive method to fulfill locus, functional analysis is used to study the complicated relation of space time. The geometric locus displacement function is a special motion equation only consisting of displacement, if time is chosen as parameter. Its differential equation is composed of geometric parameter transformation and derivation to time. This function structure makes it enable that space factor and time factor are treated separately. Locus norm function can be divided map relation into space parameter and time parameter. It can be used to sim-plify relation of space and expand the space of geometric space. The geometric parameter transformation is determined by or-bital function，it can be calculated off line. The intervening variable of geometric parameter derivation may be selected as reference time. Choosing processing parameter as reference time, the machining progress can be controlled by manufactur-ing process. Motional regularity consists of geometric relation and time relation. Therefore, the geometric properties can be accurately carried out by controlling motion regularity. A new method for trajectory control is presented, which uses motion law takinfg the place of position parameters to control, and uses self defined time to substitute real time to control proceeding. It is proved that it is a good way to control geometry and motion comprehensively, to reduce computation times and to increase the ability of environmental adaptation for path planning.

Key words: Reference time, Standard time, Trajectory function