Throw: Quick-Return with Finite Jerk

The 'Quick-Return 2' motion-law is Not available in the Motion-Law Selector.

The 'Quick-Return-2' motion-law is a Rise & Return motion-law that 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 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 maximum [in the image, max P=1], and the Velocity is zero.

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. Thus, there is acceleration continuity when the segments follow each-other.

The Jerk is continuous and zero at the mid-point. [The Jerk is un-specified and not 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, negative acceleration at the mid-point.

See Also:

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 (negative) value at the acceleration crossover of the Rise and Return segments. Thus do not use this motion-law where there is backlash in the following mechanical system.

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


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