Throw: Quick-Return with Zero Jerk
It is continuous in Position, Velocity and Acceleration We construct this Throw segment with two Flexible Polynomial segments. Usually, the segments have an equal duration, but this is not necessary. Continuity at the Mid-Point At the mid-point, the Position is at its maximum and the Velocity is zero. At the mid-point, Acceleration is finite and negative. At the mid-point, Jerk is continuous and zero. Position, Velocity, Acceleration, and Jerk are Zero at the Start, End and Mid-Point Position, Velocity, Acceleration, and Jerk are Continuous. The Throw is Quick-Return because it has a large, negative acceleration at its maximum displacement. See Also: •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.
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Start: Rise Segment 1 @ Start •Position = 0 •Zero Velocity •Zero Acceleration •Zero Jerk Mid-Point: Segment 1 @ End = Segment 2 @ Start •Position = 1 •Zero Velocity •Match, but unspecified Acceleration* (Actual = –40mm/s2) •Zero Jerk End: Segment 2 @ End •Position 2 = 0 •Zero Velocity •Zero Acceleration •Zero Jerk * It is possible to reduce this slightly - to approximately 28, before it begins to make the motion-law less smooth.
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One Segment 'Rise Segment'
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Flexible Polynomial Parameters Settings Start: •Position = 0 •Zero Velocity •Zero Acceleration •Zero Jerk (Actual Jerk = 40mm/s3 End •Position = 1mm. •Zero Velocity •Unspecified* Acceleration (Actual Value = –10mm/s2) •Zero Jerk Motion Coefficients 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. |