Segment Continuity

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Segment Continuity

see also: Impact, Acceleration Shock, How to Blend Two Segments

Motion Discontinuity

Motion-Law Discontinuity

Motion-Law Discontinuity

There is a motion discontinuity of a motion-derivative when its Y-axis has two values at one instant on its X–axis.

We identify the lowest motion-derivative in which the motion-discontinuity occurs. For example, we say the motion has an acceleration-discontinuity.

All motion-laws have a motion-discontinuity at some motion-derivative. A motion-discontinuity above the Jerk motion-derivative is usually ignored.

Motion-Laws that have an acceleration discontinuity are usually not recommended for machines design.

There are two example motions to the left.

In the top image, the motion-law is the Constant Acceleration & Deceleration Motion-Law. It has three(3) motion-discontinuities. The motion-discontinuity that is in the middle of segment is the most important, as it changes from a maximum acceleration to the maximum deceleration.

The motion in the bottom image, is not a standard Dwell-Rise-Dwell type motion. However, it also has an Acceleration-Discontinuity.

This discontinuity can easily be eliminated if the motion-laws are Flexible-Polynomial motion-laws.

Segment Discontinuity

Segment Discontinuity

Segment Blending

Segment Blending considers the motion-values at the Blend-Points.

It is recommended that you design your motions with Position, Velocity, and Acceleration motion continuity throughout the motion design.

Jerk motion continuity may also be appropriate, but not in all circumstances.

MT-Warning In MotionDesigner it is possible to design motions with motion-discontinuities at any motion-derivative, even Position. A Position motion-discontinuity is only needed with progressive, indexing motion, in which the position at the end of the index motion is different to the position at the start of the index motion.  Clearly, the mechanical system does not move from one position to the next in zero time. It does not have a positional motion-discontinuity.

Position Blending and Continuity

A Step-change in Position?

Mechanical systems cannot move from one position to a different position in zero time!. It would be a magic trick! Cartoon characters can complete this motion, but not mechanical systems. A Cam would need a step in it!

You must use at least the Match Control button in the Segment and Blend-Point Editors to give Position Continuity.

Velocity Blending and Continuity

A Step-change in Velocity?

In all cases, a mechanical system cannot respond to a Velocity Discontinuity. You are trying to make the system respond as if it has been hit.

A Servo motor would need to change its speed instantly, with infinite acceleration. This is unattainable.

A Cam would have a corner, or kink.

Acceleration Blending and Continuity

A Step-change in Acceleration?

Mechanical systems do not like Acceleration Discontinuities. The mechanical system will tend to vibrate.

We can show an Acceleration Discontinuity with this experiment:

1.Clamp (or hold down) a 300mm ruler at one end, so it hangs over the edge of a table, and

2.Release a coin from zero height onto the ruler, near to its end.

The velocity impact is zero.

There is, however, a step change in force (gravitational force) as you release the coin

The ruler vibrates with a peak displacement amplitude of about two times the final resting position of the ruler with the coin on it

Acceleration Blending and Continuity

A Step-change in Jerk?

Finally, it is sometimes required that adjacent segments have Jerk Continuity.

Jerk-Continuity gives the least mechanical vibration in the mechanical system, at the expense of higher peak nominal accelerations.

When Jerk is Zero at the start of a segment, there is only a tiny change to it position for the first 10º of input. It is almost a dwell for the first 10º.

If it frequently possible to increase the duration of a segment, and thereby reduce the accelerations.