Motion Profile Feasibility Calculator — Minimum Motion Time, Peak Velocity & Feasibility Ratio
Calculate minimum motion time, feasibility ratio and peak velocity using travel distance, target time, velocity, acceleration and jerk limits.
Enter the known values and review the calculated result
Input parameters
Use consistent values and select the intended engineering units.
Motion profile
Motion parameters
Results
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Method, application and limitations
Review the calculation method, intended application and engineering assumptions before using the result in a design decision.
Formula and calculation method
Minimum motion time formula:
For trapezoidal profile:
tacc = vmax / amax
dacc,full = 0.5 · amax · tacc2
dtotal,acc = 2 · dacc,full
If dtotal,acc ≥ s:
- vpeak = √(s · amax)
- t = vpeak / amax
- tmin = 2 · t
If dtotal,acc < s:
- dconst = s − dtotal,acc
- tconst = dconst / vmax
- tmin = 2 · tacc + tconst
- vpeak = vmax
For S-curve profile:
tj = amax / jmax
dacc,full =
amax · tj2
+ amax · (vmax / amax − tj) · tj
+ 0.5 · amax · (vmax / amax − 2 · tj)2
dtotal,acc = 2 · dacc,full
If dtotal,acc ≥ s:
- t = ∛((3 · s) / (2 · jmax))
- tmin = 2 · t
- vpeak = jmax · t2
If dtotal,acc < s:
- tacc = vmax / amax + tj
- dconst = s − dtotal,acc
- tconst = dconst / vmax
- tmin = 2 · tacc + tconst
- vpeak = vmax
Feasibility ratio formula:
t / tmin = ttarget / tmin
where:
- s — Travel distance (m)
- ttarget — Target motion time (s)
- vmax — Maximum velocity (m/s)
- amax — Maximum acceleration (m/s²)
- jmax — Maximum jerk (m/s³)
- tmin — Minimum motion time (s)
- vpeak — Peak velocity (m/s)
When to use this calculator
When to use this calculator:
- Check whether a required travel distance can be completed within a target motion time.
- Compare a trapezoidal motion profile against an S-curve motion profile for the same travel distance and motion limits.
- Estimate the peak velocity required by a move before selecting a velocity limit.
- Identify whether the move is limited by acceleration, velocity or jerk.
- Evaluate whether the selected target motion time has margin above the calculated minimum motion time.
How to interpret the result
Minimum motion time is defined as the shortest calculated time required to complete the travel distance under the selected velocity, acceleration and jerk limits.
Feasibility ratio is defined as target motion time divided by minimum motion time. A value below 1.1 triggers warning, while a value equal to or above 1.1 is treated as safe.
Peak velocity is defined as the highest velocity reached by the calculated motion profile. It equals the velocity limit when the profile reaches constant velocity, or a lower calculated value when the move is acceleration-limited or jerk-limited.
- Safe — target motion time / minimum motion time ≥ 1.1.
- Warning — target motion time / minimum motion time < 1.1.
- Invalid — travel distance, target motion time, velocity limit or acceleration limit is not greater than zero; for S-curve mode, jerk limit is not greater than zero; or the calculated motion values are not physically valid.
Increasing travel distance increases the required minimum motion time. Increasing the velocity limit, acceleration limit or jerk limit can decrease the minimum motion time when that limit is active.
Calculation example
Example:
A user wants to check whether a 1.2 m axis move can be completed in 2.0 s using a trapezoidal profile.
- s — Travel distance = 1.2 m
- t — Target motion time = 2.0 s
- v — Maximum velocity = 1.0 m/s
- a — Maximum acceleration = 2.0 m/s²
- Profile type = Trapezoidal
The calculator returns tmin = 1.700 s, t / tmin = 1.176 and vpeak = 1.000 m/s.
Assumptions and limitations
- The selected profile type is either trapezoidal or S-curve.
- Travel distance, target motion time, velocity limit and acceleration limit are positive finite values.
- For S-curve mode, jerk limit is a positive finite value.
- The move is evaluated from the provided travel distance and motion limits only.
- The feasibility margin is evaluated using target motion time divided by calculated minimum motion time.