Throw: Rapid-Return Finite Jerk
The 'Rapid-Return 1' motion-law is Not available in the Motion-Law Selector. The Rapid-Return-1' motion-law is a Rise & Return motion-law that is continuous in Velocity and Acceleration throughout. Construct the 'Rapid-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 The Position is a maximum, 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. The Jerk is discontinuous at the mid-point. [The Jerk is also discontinuous at its start an end- points]. The position graph makes a rapid-return at the mid-point because there is a large negative, but continuous, acceleration at the mid-point. The transition from Rise to Return is more rapid than Quick-Return 1 and Quick-Return 2. Thus we call it a Rapid-Return 1. See Also: •Quick Return 1: Finite Jerk @ Start/End/Mid-Point •Quick Return 2: Zero Jerk @ Start/End/Mid-Point •Rapid Return 2: Smooth-Start/End * An acceleration discontinuity would give a very poor dynamic response if applied to any mechanical system.
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It 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 •Unspecified Jerk End: Segment 2 @ End •Position 2 = 0 •Zero Velocity •Zero Acceleration •Unspecified Jerk
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