Trapezoidal Velocity Motion Profile Calculator

Industrial robotics & motion control: Calculate 1D/3D trapezoidal velocity profile kinematics, acceleration duration, constant-velocity cruise time, and total motion cycle time.

Kinematic Motion Limits

Total Move Distance S (mm): Linear path displacement

Target Max Speed v_max (mm/s): Desired cruise speed

Max Acceleration a_max (mm/s²): Acceleration rate (~0.6 g)

Max Deceleration d_max (mm/s²): Braking rate

Settling / Dwell Time (ms): In-position servo settling

Target Cycle Rate (PPM): Target picks per minute

Profile Segments & Motion Timing

Total Move Time (T_move)

Actual Peak Speed (v_peak)

Acceleration Segment (t_a)

Cruise Segment (t_c)

Deceleration Segment (t_d)

Max Cycle Throughput

Single-way stroke rate

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Frequently Asked Questions

Why does a triangular profile occur for short moves?

When move distance S is small, there is insufficient distance for the motor to accelerate all the way to target top speed before it must immediately begin decelerating to stop at the destination without overshoot.

What is the advantage of S-Curve profiles over Trapezoidal profiles?

Trapezoidal profiles have instantaneous jumps in acceleration (infinite jerk d³x/dt³), causing structural vibrations, gear backlash rattling, and sensor noise. S-curve (7-segment) profiles bound the derivative of acceleration (jerk), ensuring silky smooth mechanical starts and stops.

What is in-position settling dwell time?

After the mathematical trajectory finishes at t_move, mechanical vibrations and PID integral windup require a short settling interval (typically 20 to 100 ms) before the feedback encoder settles within the target position tolerance window.