Acceleration, Deceleration & S-Curve Profiles

Speed is the thing you set. Acceleration is how quickly speed changes. Jerk is how quickly acceleration changes, and it is what you feel as a jolt. A linear ramp has a steady acceleration but an instant jolt at each end. An S-curve rounds those ends: the acceleration builds up, holds, and eases off. The S-curve share is the part of the ramp time spent rounding the corners (each end takes half of it). For the same ramp time, the S-curve needs a higher peak acceleration than the linear ramp, up to twice as much for a fully rounded one. The step profile is shown only for comparison.

Reflected inertia at the motor shaft: J_total = J_motor + J_load ÷ N² + J_others, where N is the gear ratio (motor turns per load turn). The torque needed to accelerate is J_total × angular acceleration, plus the torque the load needs at constant speed. Motor current follows torque (plus the magnetising current), so a short ramp on a high inertia means high torque and current; the drive then hits its current limit, extends the ramp or trips. A higher load inertia means more torque, a longer ramp, and more risk of overshoot and vibration. Lengthen the ramp, use an S-curve, and tune the torque limit.

For a ramp stop with constant deceleration a, the distance is S = (V₀² − V_f²) ÷ (2 × a), which for a stop to zero in time T is V × T ÷ 2. An S-curve ramp of the same total time covers the same distance (its speed curve is symmetrical), but with a higher peak deceleration. The drive does not start slowing the instant a stop is requested: add the distance travelled during the reaction time. A longer ramp means a longer stopping distance, so check the space available and the safety requirements. An emergency stop is a different method: see the braking page.

The profile maths follow standard motion-control definitions and are simplified for learning. Real drives implement ramps and S-curves in different ways and have their own current limits, so use the drive manual for exact behaviour.