The article content makes sense, sure. My LibreOffice could not display the equations, but I am sure those are correct; did you submit the article as a PDF?
Was there any feedback with the rejection?
Caveat 1: several of the questions I ask here may be moot, depending on the context and the expertise of the typical audience.
Caveat1 2: I am not trying to be critical here, or at least I want to be constructive in any criticism! I am trying to put myself in the editor's shoes and spitball some ideas why they might have rejected the article. Please forgive any bluntness as I have not yet had breakfast. So here goes.
If I were the editor, I would be making the following observations and/or asking the following questions.
1) Where are the abstract, summary, discussion, conclusion? What exactly is the question being answered i.e. what is the point, or the problem being solved? What is the context of the problem (e.g. motion control in non-analog PLCs)? Perhaps the "So why does it matter" paragraph could be integrated into an abstract and provide the point; but where it is, near the end of the article, it does not help with that.
1.1) I.e. what does this article offer that is new or interesting, and
can I find out right away or
do I have to read the whole thing before I can answer that question? The latter approach is for novels; the former is for articles. The editor's task is ultimately to generate net revenue i.e. revenue in excess of the effort to publish, and that via publishing articles, so ultimately the
only valid reason to accept an article for publication is
that they believe the publication's target audience will have a reason to read it. "For all the Athenians and strangers which were there spent their time in nothing else, but either to tell, or to hear some new thing." Every item I write here ties back to this primary issue.
2) This article would improve with proofing.
- AFICT it needs a spellcheck on the current version, e.g.
- The grammar might work better if it were in a literary/publication style; it is currently conversational (maybe you spend too much time in fora like this) and often wonky or redundant e.g.
- ... cubic splines of order three.
- ... relatively distance intervals.
- The blue line shows the y values being using linear interpolation as a function of the x value on the x axis.
- The same also applies to the velocity and acceleration as well.
- The radius of the cam does this by varying the radius as a function of angle
3) PLCs are mentioned in the first sentence but never again explicitly. What is a PLC? Why are PLCs relevant? How are splines/cams used in the context of PLCs?
4) Along that line, a fuller definition of "cam" would be helpful. Almost every reference to "cam" or "cam tables" is as a synonym for spline e.g. "... of a spline or cam table." If it's only a synonym, then it's redundant, so why is it mentioned and/or defined and/or important? It feels like the first five sentences lay out a skeleton for the abstract of the article, but the changes in context - cam shapes, cam tables, virtual cams, cams with (physical?) radii and angles - from sentence to sentence will be followed by the
cognoscenti only, and the article is not for them. What is the difference and/or significance and/or context of these terms: cam; virtual cam; cam table; cam shape; etc.
4.1) Further along that line, perhaps a definition of spline might help as well; as currently written, the article assumes an understanding of splines. E.g., start with Wikipedia: "In mathematics, a spline is a special function defined piecewise by polynomials."
4.2) Hmm, you also wrote this:
In the past [what does that mean? What was different in this nebulous past, are splines really such a recent invention that ...] one would simply do a linear interpolation for position, but this will result in discontinuities in velocity and acceleration, which isn’t good if feed forwards are being used. [wait, that's a new term; what the heck are feed forwards and why are discontinuities a problem?]
5) Ah, so putting those last two together, we can now see that the problem is about interpolation and discontinuities! Oh, and by the way, there it is: the
raison d'être for splines, cams, and the guts of the abstract this article. We finally found it, but never mind: it's the third paragraph from the end, so no one will ever know
.
6) Perhaps a worked example of splines, with application to cams in a PLC would add some meat. It would be best to add something novel. There are general statements about splines, some of which could perhaps be derived from Wikipedia, but little detail other than the plot.
7) What is the magazine and/or its area of interest? What does this article contribute in that context?
Summary
From the editor's standpoint, this is perhaps interpreted as a transcribed monologue, or answer to a problem that is either unstated or hidden near the end of the article. It is essentially un-proofed, so that is on the editor's, or their team's, shoulders.
Is that what they want to spend time and resources on now as an eventual article in their magazine with an expectation of it eventually generating revenue? Again, I apologize for the bluntness of my
opinion, but you asked.