Motion-Discontinuity of CA-CD Motion Law at Cross-Over.
A motion discontinuity means that there are two Y–axis values, of one particular motion-derivative, at one instant on its X–axis.
When we refer to a motion discontinuity, we name the lowest motion derivative at which you can see the motion discontinuity. For example, acceleration motion-discontinuity.
A 'motion-discontinuity' is also termed a 'shock'. 'Shock' is usually pre-pended by the motion-derivative. For example, Acceleration Shock.
Every motion and motion-law has a motion-discontinuity at some motion-derivative. However, those Motion-Laws with a motion-discontinuity at a motion-derivative above Jerk are usually ignored.
There are motion-laws that have discontinuities in the acceleration motion-derivative. These motion-laws are usually not recommended for machines design.
For example: , in the top image, the Constant-Acceleration and Constant Deceleration Motion-Law has three motion discontinuities in a Dwell-Rise-Dwell type motion. Most significant is the motion-discontinuity in the middle of this segment, as it changes from the maximum positive acceleration to the maximum negative acceleration.
For example: , in the bottom image, there is also an acceleration motion-discontinuity. This can be eliminated if the motion-laws are 'flexible-polynomial' motion-laws.
Motion-Discontinuity at Segment Blend-Point.
Segment Blending considers the motion-values at the Blend-Points.
It is recommended that you design your motions that have Position, Velocity, and Acceleration motion continuity throughout the motion design.
Jerk motion continuity may also be appropriate, but not all circumstances.
In MotionDesigner it is possible to design motions with motion-discontinuities at any motion-derivative, even Position. A Position motion-discontinuity is only needed in the Blend-Point Editor 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 do not like moving 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 Blend-Point Editor 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 instantly change speed, with infinite acceleration. This is unattainable
A Cam would have a corner.
Acceleration Blending and Continuity
A Step-change in Acceleration?
Mechanical systems do not like an Acceleration Discontinuity. The mechanical system will tend to vibrate.
We can show an Acceleration Discontinuity with this experiment:
Clamp (or hold down) a 300mm ruler at one end, so it hangs over the edge of a table, and release a coin from zero height on to it.
The velocity impact is zero, because it does not 'hit' the ruler.
There is, however, a step change in acceleration and force as you release the coin
The ruler vibrates with a peak displacement amplitude of about twice the final resting position of the ruler.
Jerk Blending and Continuity
A Step-change in Jerk?
Finally, it is sometimes required that adjacent segments have Jerk Continuity.
Continuity in Jerk typically results in the least mechanical vibration in the mechanical system, at the expense of higher peak nominal accelerations.
For a motion law, zero jerk at the start of a segment require tiny amounts of displacement for the first 10º of input. It is almost a dwell for the first 10º.
Unfortunately, by specifying zero continuity in jerk to get a smoother motion, the motion will generally have a higher acceleration. This is essentially the compromise in motion design. How smooth can I make my motion before the peak nominal velocity and acceleration become unacceptable?
If it is possible to increase the duration of the segments, then the peak nominal accelerations are reduced.