Work out acceleration profile (trapezoidal) instantly with clear inputs, formula shown and shareable results.
Working backwards from a required move time, the area under the trapezoid must equal the distance: d = v x t x (1 - accel fraction). That gives peak velocity, and dividing by the acceleration time gives the acceleration the drive must deliver. A one-third split is the classic compromise.
Trapezoid from time
v_peak = d / (t x (1 - f)); a = v_peak / (f x t), where f is the acceleration share
One third each for accelerate, cruise and decelerate minimises peak acceleration for a given time. Shorter acceleration phases raise torque demand sharply.
At 50% the profile becomes triangular with no cruise phase, giving the highest peak velocity and the greatest jerk at the midpoint.