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Tutorial 9: Asymmetrical Motions
This topic applies to those segments that have the Segment Range parameters in the Segment-Editor.
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 (or it is at the middle 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 0.5 y-units.
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:
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 )
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.
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.
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.
Velocity - No Change
Acceleration Characteristic Value: Segment 1: Ca1 = Ca / 2λ
Acceleration Characteristic Value Segment 2: Ca2 = Ca / 2(1-λ)