This topic applies to those segments that have the Segment Range parameters 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 (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

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 Characteristic Value: Segment 1:  Ca1 = Ca / 2λ

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