﻿ Throw - Rapid-Return 2: Zero-Jerk @ Start/End Motion-Law, Finite at Mid-Point

# Throw - Rapid-Return 2: Zero-Jerk @ Start/End Motion-Law, Finite at Mid-Point

### Throw: Rapid-Return with Zero Jerk

'Rapid-Return 2' is Not available in the Motion-Law Selector

The Rapid-Return-2' motion-law is a Rise & Return motion-law that is continuous in Velocity and Acceleration throughout.

Construct it 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 Acceleration is 'finite', but continuous.

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. There is acceleration continuity.

The Jerk is discontinuous at the mid-point. [The Jerk is zero at its start an end].

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 motion from Rise to Return at the mid-point is more rapid than Quick-Return 1 and Quick-Return 2 and Rapid-Return 1. Thus we call it a Rapid-Return 2.

Generally, this motion is not recommended.

 • Quick Return 1: Finite Jerk @ Start/End/Mid-Point
 • Quick Return 2: Zero Jerk @ Start/End/Mid-Point
 • Rapid Return 1: Finite-Jer @ Start/End/Mid-Point

#### Two Segment 'Rapid-Return 2'

It is designed with two Flexible-Polynomial Segments

Two Segments with Acceleration Continuity

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
 • Unspecified Jerk

End: Segment 2 @ End

 • Position 2 = 0
 • Zero Velocity
 • Zero Acceleration
 • Zero Jerk

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