Throw - Quick-Return: 1: Finite Jerk @ Start/End Motion-Law

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Throw - Quick-Return: 1: Finite Jerk @ Start/End Motion-Law

Throw: Quick-Return 1: Finite Jerk


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Quick-Return-1 motion-law is a Rise & Return motion-law.

It is continuous in Position, Velocity and Acceleration.

Construct the 'Quick-Return 1' motion with two Flexible Polynomial Segments.

The first segment is the Rise, and the second segment is 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

At the mid-point, the Position is at a maximum value [in the image, max P=1], and the Velocity is zero.

At the mid-point the segments both have a finite, negative acceleration.

The acceleration is continuous. The Jerk is also continuous and zero at the mid-point.

We can call this a Quick-Return Motion because at the point where the Rise becomes the Return, there is a negative, but continuous acceleration.

See Also:

Quick Return: Zero Jerk @ Start/End/Mid-Point

Rapid Return: Finite Jerk @ Start/End/Mid-Point

Rapid Return: Smooth-Start/End

Two Segment 'Quick-Return Motion 1'


'Quick-Return Motion 1' 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

Zero Velocity

Zero Acceleration

Unspecified Jerk [Actual = 320mm/s3]

Mid-Point: Segment 1 @ End = Segment 2 @ Start

Position = 1

Zero Velocity

Match, but Unspecified Acceleration =Actual = –26.666mm/s2

Zero Jerk [

End: Segment 2 @ End

Position 2 = 0

Zero Velocity

Zero Acceleration

Unspecified Jerk  [Actual = –320mm/s3]

Note, the Jerk is near to its maximum acceleration crossover [at about 75 and 255] and velocity. Thus if there is backlash in the following mechanical system, crossover will have a relative high -impact value.

Rise Only Segment


It is designed with one Flexible-Polynomial Segment:


Position = 0

Zero Velocity

Zero Acceleration

Unspecified Jerk [Actual = 40mm/s3]


Position = 1

Zero Velocity

Unspecified Acceleration

Zero Jerk

Cv = 1.733

Ca = 4.583

Cd = –6.666

Cj max = 40

Cj min  = –22.5

Jerk at Crossover = -21.5