The 'Quick-Return-2' motion-law is Not available in the Motion-Law Selector.
The 'Quick-Return-2' motion-law is a motion-law that is continuous in Velocity, Acceleration and Jerk.
Construct the 'Quick-Return 2' motion with two Flexible Polynomial Segments.
The first segment is the 'Rise', and the second the 'Return'. Each segment is a 'mirror' of each other.
Usually, the segments have an equal duration, but this is not necessary.
Continuity at the Mid-Point Blend-Point
The Position is maximum [P=1], and the Velocity is zero at the mid-point.
The Rise segment [below, in Blue] ends with a finite, negative acceleration.
The Return segment [below, in Red] starts with the same finite, negative acceleration.
There is acceleration continuity when the two segments follow each-other.
The Jerk is continuous and zero at the mid-point.
The Jerk is also zero at its start an end.
The position graph makes a quick-return at the mid-point because there is a large negative, but continuous, acceleration at the mid-point.
•Quick Return: Finite Jerk @ Start/End/Mid-Point
•Rapid Return: Finite Jerk @ Start/End/Mid-Point
•Rapid Return: Smooth-Start/End
* An acceleration discontinuity would give a very poor dynamic response if applied to any mechanical system.
'Quick-Return Motion 2' is designed with two Flexible-Polynomial Segments - usually of equal duration, but not necessarily.
Two Segments with Acceleration Continuity
Start: Rise Segment 1 @ Start
•Position = 0
Mid-Point: Segment 1 @ End = Segment 2 @ Start
•Position = 1
•Match, but unspecified Acceleration* [Actual = –40mm/s2]
End: Segment 2 @ End
•Position 2 = 0
* It is possible to reduce this slightly - to approximately 28, before it begins to make the motion-law less smooth.
Flexible Polynomial Parameters Settings
•Position = 0
•Zero Jerk [Actual Jerk = 40mm/s3
•Position = 1mm.
•Unspecified* Acceleration [Actual Value = –10mm/s2]
Cv = 1.975
Ca = 5.120
Cd = –10 [Deceleration]
Cj max = 19.491
Cj min = –39.402
Cj @ Crossover = –35.556
Note: The Segment is two times longer than the Two Segment Motion above. The maximum motion-values are: 1/2 of the Velocity,, 1/4 of the Acceleration, , 1/8 of the Jerk.