﻿ Throw - Rapid-Return 1: Finite-Jerk @ Start/End/Mid-Point Motion-Law

# Throw - Rapid-Return 1: Finite-Jerk @ Start/End/Mid-Point Motion-Law

### 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.

 • 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.

#### Two Segment 'Rapid-Return Motion 1'

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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