Constant-acceleration profile
Trapezoidal motion
Inputs
Rest-to-rest travel distance for the stated linear or angular axis.
Time for each equal acceleration and deceleration phase.
Constant-velocity phase time; enter zero only for a triangular profile.
Results
Profile acceleration
2.6667
Peak speed
0.66667
Total move time
1
Move distance
500
a = s / [ta(ta + tc)]; vmax = a·ta; T = 2ta + tc
A first-pass number, not a code check, certification, or approval. Read the method and its limits below. What this is and is not.
Nearby: Reflected inertia · Pneumatic cylinder force · Clamp-force transfer · Lead-screw force & travel
Method
Formula, when it applies, and when it does not
Resolve peak speed, acceleration, and total time for a rest-to-rest symmetric trapezoidal profile with move distance and phase times.
a = s / [ta(ta + tc)]; vmax = a·ta; T = 2ta + tc
When
- Rest-to-rest motion
- Symmetric constant acceleration
- No jerk limit or load dynamics
Don’t
- This is an ideal symmetric trapezoidal/triangular profile. It excludes jerk limits, structural compliance, load inertia, friction, servo tuning, actuator force limits, and safety margins.