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 Coefficients :

Jerk Coefficient :

Jerk at Crossover :

Torque Coefficients :

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. The Jerk at Crossover is relatively low.

However, the high peak acceleration means every effort should be made to increase the duration of the segment.

Pressure Angle Considerations

The maximum acceleration and velocity are relatively large, which increase the maximum pressure-angle.

Drive Torques

It has a high peak torque.