What is a trapezoidal motion profile?

A trapezoidal profile divides a move into three phases: acceleration (velocity ramps up at a constant rate), constant velocity (coast), and deceleration (velocity ramps back to zero). The velocity-vs-time graph looks like a trapezoid.

What is a triangular profile?

When the move distance is too short to reach peak velocity, there is no coast phase. The axis accelerates to a lower peak and immediately decelerates. The velocity-vs-time graph is a triangle.

Jerk (da/dt) is the rate of change of acceleration. In a pure trapezoidal profile the acceleration switches instantaneously, so theoretical jerk is infinite at the transition points. This tool reports the average jerk as acceleration divided by the step time (1 ms), which is a practical measure of the impulse applied to the mechanism.

Can I use different acceleration and deceleration rates?

Yes. Many servo drives use asymmetric profiles — faster acceleration and slower deceleration, or vice versa. Enter them separately in the respective fields.

What units does this tool use?

The tool is unit-agnostic. Use consistent units: if velocity is mm/s and acceleration is mm/s², distance must be mm and the output times will be in seconds. The unit labels are advisory only.

Acceleration Profile Helper

Compute trapezoidal motion profiles for robotics and automation — acceleration time, peak velocity, distance covered, and jerk for a move.

Motion Parameters

Peak velocity (e.g. mm/s)

Acceleration (mm/s²)

Deceleration (mm/s²)

Total move distance (mm)

Phase Breakdown

Phase	Time (s)	Distance

Summary

The Acceleration Profile Helper computes trapezoidal (and triangular) motion profiles used in robotics, CNC machines, and servo drives. Enter your target velocity, acceleration rate, and total move distance and get back the full profile: acceleration phase time and distance, constant-velocity coast phase, deceleration phase, total move duration, and average jerk. The tool automatically handles triangular profiles when the move is too short to reach peak velocity.

How it works

Enter the peak (target) velocity in your chosen units.
Enter the acceleration and deceleration rates (can be different).
Enter the total move distance.
The tool checks whether the move is long enough to reach peak velocity.
If not, it computes a triangular profile with a lower achieved peak.
Results show time and distance for each phase plus total move time and jerk.

Use cases

Sizing servo drives and stepper motors for pick-and-place robots.
Checking whether a CNC axis can reach programmed feed rate within a short segment.
Computing move time budgets for cycle-time analysis.
Validating jerk limits against mechanical resonance requirements.
Teaching motion-control concepts in engineering courses.
Cross-checking PLC or motion-controller profile outputs.

Frequently Asked Questions

Last updated: 2026-06-18 · Reviewed by Nham Vu