مبدل السرعات قرب ترس الدراجة.

This is an iḍāfa construction, often called a genitive construction.

• مبدل = changer / shifter
• السرعات = the speeds / gears

Together, مبدل السرعات literally means changer of the speeds, which is the natural Arabic way to say gear shifter.

A few important things about iḍāfa:

• The first noun usually does not take ال
• The second noun is in the genitive case
• The whole phrase can still be definite if the second noun is definite

So مبدل السرعات is a standard way to form a compound noun in Arabic.

Because in an iḍāfa, definiteness is often carried by the second noun.

Here:

• السرعات is definite because it has ال
• Therefore the whole phrase مبدل السرعات becomes definite: the gear shifter

So Arabic does not say المبدل السرعات here. That would be incorrect in this structure.

Literally, السرعات means the speeds. Singular: سرعة = speed.

In Arabic, especially in mechanical or everyday contexts, the word for speeds is often used where English would say gears. So:

• مبدل السرعات = gear shifter
• literally: speed changer

This is normal usage and not strange in Arabic.

قرب means near or nearby here.

In this sentence, it functions like an adverbial expression of place:

• قرب ترس الدراجة = near the bicycle gear

In fuller grammatical terms, قرب is often treated as a ẓarf (adverbial noun of place), and it is followed by a noun in an iḍāfa-like relationship:

• قربَ ترسِ الدراجةِ

So the sentence is saying where the gear shifter is located.

Yes. Both are possible, but they are structured differently.

• قرب ترس الدراجة = near the bicycle gear
• قريب من ترس الدراجة = close to the bicycle gear

The first uses قرب as an adverbial noun. The second uses قريب as an adjective-like word followed by من.

Both are natural, but قرب is shorter and very common in this kind of sentence.

Again, this is an iḍāfa construction:

• ترس = gear / cog
• الدراجة = the bicycle

So ترس الدراجة literally means the gear of the bicycle, or more naturally, the bicycle’s gear.

In iḍāfa:

• the first noun normally does not take ال
• the second noun can make the whole phrase definite

So ترس الدراجة already means the bicycle gear. You do not add ال to ترس here.

Because Arabic normally leaves out the present-tense to be in simple sentences.

So:

• مبدل السرعات قرب ترس الدراجة literally looks like
• The gear shifter near the bicycle gear

But in natural English, we translate it as:

• The gear shifter is near the bicycle gear

This is very normal in Arabic. In the present tense, the copula is usually omitted.

This is a nominal sentence.

You can think of it as:

• مبدل السرعات = the topic / subject
• قرب ترس الدراجة = the predicate, telling where it is

So the structure is roughly:

• [subject] + [location]

In traditional grammar terms:

• مبدل السرعات = مبتدأ
• قرب ترس الدراجة = خبر

This is a very common Arabic pattern for saying where something is.

A likely fully vocalized form is:

مُبَدِّلُ السُّرُعاتِ قُرْبَ تُرْسِ الدَّرَّاجَةِ.

Breaking that down:

• مُبَدِّلُ: nominative, because it is the subject
• السُّرُعاتِ: genitive, because it is the second term in an iḍāfa
• قُرْبَ: accusative as an adverbial noun of place
• تُرْسِ: genitive after قرب
• الدَّرَّاجَةِ: genitive as the second term in the iḍāfa ترس الدراجة

In normal Arabic writing, these short vowels are usually not written.

It is derived from a verb.

مبدل comes from the verb بدّل = to change / switch / replace.
So مبدل is an active participle form meaning something like:

• changer
• switcher
• shifter

In many contexts, Arabic uses active participles as ordinary nouns, so here مبدل simply functions as the noun shifter.

Yes, Arabic has some flexibility.

For example, you could also find something like:

• قرب ترس الدراجة مبدل السرعات

But the original order:

• مبدل السرعات قرب ترس الدراجة

is the clearest and most straightforward for a learner. It starts with the thing being talked about, then gives its location.

So while word order can vary, the original sentence is very natural and easy to parse.