﻿ Tutorial 9: Asymmetrical Motions

# Tutorial 9: Asymmetrical Motions

## Dwell-Rise-Dwell Asymmetrical Motion

This topic applies to those segment that include the 'Segment Range' parameter in the Segment-Editor.

Symmetrical Motions

Symmetrical Motions most typically start and end with zero velocity and acceleration.

If we take the full duration of the segment to be a period of 1.0 'X-unit', then the maximum velocity is at 0.5 'X-units' [the mid-point of the motion]. This is the point at which the acceleration becomes deceleration [or vice-versa], which is the 'motion-law crossover'.

The displacement of a symmetrical motion at its 'crossover' is also 0.5 'y-units'.

Asymmetrical Motions

Asymmetrical motions also start and end with zero velocity and acceleration. However, the crossover of an asymmetrical motion is not at 0.5'x-units'.

The displacement of an asymmetrical motion at its 'crossover' is also not at 0.5 'y-units'

The asymmetry factor is λ

When to use Asymmetrical Motions

Often, you want a machine tool to accelerate quickly [or slowly], so that its peak velocity is sooner[or later] than 0.5'x-units'.

If the acceleration period is less than [or more than] 0.5 'x-units', the deceleration period must be more than [or less than] 0.5 'x-units'.

The maximum values of acceleration and deceleration will be different, although the maximum velocity does not change.

The displacement at crossover is not at 0.5 'y-units'.

Symmetrical Motion λ = 0.5

Motion: Mod-Sine Motion Law.

Crossover @ 0.5 = 180º machine angle

Note: The 'standard' Mod-Sine motion design is one segment. To help us understand the asymmetrical law, we show it with two segments:

Segment 1:

Machine angle : 0 to 180º  [ 0 - 0.5 of total duration]

Displacement : 0 to 0.5 units

Segment Range : 0 to 0.5. [ See : 'Segment Range in Segment-Editor' ]

Segment 2:

Machine Angle : 180 to 360º [ 0.5 - 1.0 of total duration]

Displacement : = 0.5 to 1.0 units

Segment Range : 0.5 to 1.

Asymmetrical Motion λ = 0.25

Motion: Mod-Sine Motion-Law

Crossover: 0.25 = 90º machine angle.

Asymmetrical motions are modelled with two segments- always.

Segment 1:

Machine angle : 0 to 90º [0.25 of total duration = λ ]

Displacement : 0 to 0.25 units [0.25 of total displacement = λ ]

Segment Range : = 0 to 0.5.

Segment 2:

Machine angle : 90 to 360º [0.25 - 1.0 of total duration]

Displacement : 0.25 to 1.0 units

Segment Range : = 0.5  to 1.

### Characteristics Values:

Velocity - No Change

Acceleration Segment 1:  Ca1 = Ca / 2λ ;

Acceleration Segment 2:  Ca2 = Ca / 2(1-λ)

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