A Traditional Motion-Law.  Its name is often give Constant-Acceleration, or Triangular Velocity.

It has the lowest nominal maximum Constant Acceleration of the Dwell-Rise-Dwell type motion-laws. For this reason, historically, it was recommended for cam motion-design. It is still commonly used for Servo and Stepper motions.

However, it has many disadvantages - see Application-Notes, below.

Start Position

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

End Position

Start Velocity & End Velocity

Start Acceleration & End Acceleration

Start Jerk & End Jerk

None

Start-Range

End- Range

0 ≤ Start-Range < End-Range ≤ 1

Velocity Coefficient :

Acceleration Coefficient :

Jerk Coefficient :

Jerk at Crossover :

The Constant-Acceleration motion-law was used in the past because it has the lowest nominal acceleration of the Traditional Motion-Laws. However, it has infinite-jerk at three points: at its start, end, and at its crossover. This makes it a very poor choice form a dynamic-response viewpoint. Infinite-Jerk incites vibrations in any mechanical system. We do not recommend this motion-law if the Period-Ratio is less than 10, or even 20.

Dynamic Performance

The actual acceleration of a payload is significantly more than the nominal Constant-Acceleration value because of induced vibrations. For this reason, this motion-law should only be used in applications where inertia effects are insignificant.

Pressure-Angle Considerations

This motion-law produces a relatively large pressure-angle - and so might need a large cam for a given lift. The pressure-angle for this motion-l varies quite severely throughout this Motion-Law indicating that it is unsuitable for roller follower applications because of the severe accelerations imposed on the roller that induce roller slip.

Drive-Torques

This law performs badly in terms of drive torque considerations. This law has a discontinuity in Drive Torque, indicating shock loading and noise in operation. Particularly notable is the sudden reversal of the inertia torque factor, and hence of the torsional strain energy, at the crossover of the motion segment. These reversals contribute to noise, shock loading, and vibration during operation.