A Traditional Motion-Law.  Its name is often reduced to Poly-4567.

A motion with continuous Velocity and Acceleration, from start to end. The Jerk is finite at its start and end. It has finite Jerk throughout.

It has a high maximum-velocity, high maximum-acceleration, high crossover jerk. Only the Modified-Trapezoidal (of those with finite Jerk) has a greater crossover jerk.

At its start and end, the Y-axis values do not change much with a significant X–axis change - e.g. 0.02% Y-axis with 5% X-axis change.

Therefore, a cam needs accurate machine if it is to reproduce this segment. A larger cam often helps, or an encoder with a high resolution.

If possible, increase the segment-width to reduce its maximum Velocity, Acceleration and Jerk values.

Start Position

The Start-Position usually flows from the End-Position of the Previous-Segment.

End Position

Start Velocity and End Velocity

Start Acceleration and End Acceleration

Start Jerk and End Jerk

None

None

Velocity Coefficient :

Acceleration Coefficient :

Jerk Coefficient :

Jerk at Crossover :

Dynamic Performance:

This Motion-Law is recommended in applications where the period ratio is between about 5 and 10. It has a low residual vibration. However, the high peak acceleration means every effort should be made to increase the duration of the segment.

Pressure Angle Considerations

This has a relatively large maximum-acceleration and maximum velocity, which increase the maximum pressure-angle.

Drive Torques

It has a high peak torque.