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While there are a lot of different motion profiles in use today, a good starting point is the point-to-point move. For a large number of applications including medical automation, scientific instrumentation, pointing systems, and many types of general automation, the point-to-point move is used more frequently than other other profile. Because of this, optimization of this profile will have the largest overall impact on system performance. Point-to-point means that from a stop, the load is accelerated to a constant velocity, and then decelerated such that the final acceleration, and velocity, are zero at the moment the load arrives at the programmed destination.

The two profiles commonly used for point-to-point profiling are the S-curve profile, and its simpler cousin the trapezoidal profile. They are shown in Figure 1.

In the context of a point-to-point move, a full S-curve consists of 7 distinct phases of motion. Phase 1 starts moving the load from rest at a linearly increasing acceleration until it reaches the maximum acceleration. In phase II. the profile accelerates at this max. acceleration rate until it must start decreasing as it approaches the max. velocity. This occurs in phase III when the acceleration linearly decreases until it reaches zero. In phase IV the velocity is constant until deceleration begins, at which point the profiles decelerates in a manner symmetric to phases I, II and III.

A trapezoidal profile, on the other hand, has 3 phases. It is a subset of an S-curve profile, having only the phases corresponding to #2 of the S-curve profile (constant acceleration), #4 (constant velocity), and #6 (constant deceleration). This reduced number of phases underscores the difference between these two profiles: The S-curve profile has extra motion phases which transition between periods of acceleration, and periods

S-curve and trapeziodal profiles

of non-acceleration. The trapezoidal profile has instantaneous transitions between these phases. This can be seen in the acceleration graphs of the corresponding velocity profiles for these two profile types. The motion characteristic that defines the change in acceleration, or transitional period, is known as “jerk.” Jerk is defined as the rate of change of acceleration with time. In a trapezoidal profile, the jerk (change in acceleration) is infinite at the phase transitions, while in the S-curve profile the jerk is a constant value, spreading the change in acceleration over a period of time.