The following applies to Traditional Motion-Laws. They must have the 'Segment Range' parameter 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' [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 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 usually has 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 [0.75 - 1.0 of total duration]
Displacement : 0.75 to 1.0 units
Segment Range : = 0.5 to 1.
Velocity - No Change
Acceleration Segment 1: Ca1 = Ca / 2λ ;
Acceleration Segment 2: Ca2 = Ca / 2(1-λ)