How to explain "Based on..., S+V..."

[simile]

The problem sentence is:
Based on this concept, Mestral invented Velcro.

How to explain the part of "Based on..."
We know that the original sentence for
"Sitting in a chair, Mary read a book." is
"Mary sat in a chair, and she read a book."

But what about the structure "Based on..."?
??Mestral is based on this concept, so Mestral invented Velcro.??
The subject of the first sentence should be obviously not the same as that of the second one.
So what is actually the original form of the "Bease on..." sentence before sentence reduction?

[BobK]

Originally Posted by simile

The problem sentence is:
Based on this concept, Mestral invented Velcro.

How to explain the part of "Based on..."
We know that the original sentence for
"Sitting in a chair, Mary read a book." is
"Mary sat in a chair, and she read a book."

But what about the structure "Based on..."?
??Mestral is based on this concept, so Mestral invented Velcro.??
The subject of the first sentence should be obviously not the same as that of the second one.
So what is actually the original form of the "Bease on..." sentence before sentence reduction?

The problem is (as your analysis suggests) that the sentence is incorrect; the first clause is mis-related. These are OK:

Based on this concept, Velcro was invented by Mestral.
Based on this concept, Velcro is the invention of Mestral.

But

Mestral based their invention of Velcro on this concept.
Mestral invented Velcro, [which is] based on this concept

In the first two, Velcro is the subject; so you can use the Based on structure (that is, beginning the sentence with those words). In the second two, it is the object, so you have to paraphrase.

(Of course, people widely use the mis-related version. When there's no ambiguity, I have no serious problem with it. But if you want to pass any EFL exams, avoid it.)

b

[MikeNewYork]

Originally Posted by simile

The problem sentence is:
Based on this concept, Mestral invented Velcro.

How to explain the part of "Based on..."
We know that the original sentence for
"Sitting in a chair, Mary read a book." is
"Mary sat in a chair, and she read a book."

But what about the structure "Based on..."?
??Mestral is based on this concept, so Mestral invented Velcro.??
The subject of the first sentence should be obviously not the same as that of the second one.
So what is actually the original form of the "Bease on..." sentence before sentence reduction?

I have a different view on this than that of Bob K. IMO, "based on this concept" is an adverbial participial phrase, not an adjectival particpial phrase.
That is why it doesn't compare to "Sitting in a chair, Mary..."

The adverbial phrase modifies the verb "invented", not the noun Mestral or Velcro. As such, it is not misplaced in the sentence.