جهاز التجديف قرب الدراجة الثابتة.

In Modern Standard Arabic, present-tense sentences like this usually do not use a separate verb for is/are.

So:

جهاز التجديف قرب الدراجة الثابتة

is understood as:

The rowing machine is near the stationary bike

This is called a nominal sentence. If you wanted was or will be, then Arabic would normally add a verb such as كان or سيكون.

Because جهاز التجديف is an iḍāfa construction, often called a construct phrase.

It literally means:

machine of rowing

In an iḍāfa:

• the first noun usually does not take الـ
• the whole phrase becomes definite if the second noun is definite

So:

• جهاز التجديف = the rowing machine
• not الجهاز التجديف in normal MSA

This is a very common point for English speakers, because Arabic marks definiteness differently inside this kind of phrase.

No. التجديف is a noun, more specifically a verbal noun meaning rowing.

English often uses a noun almost like an adjective:

rowing machine

Arabic commonly expresses that idea as:

machine of rowing = جهاز التجديف

So التجديف is not an adjective here. It is the activity noun rowing.

قرب here means near or close to.

So:

قرب الدراجة الثابتة = near the stationary bike

This is a compact MSA way to express location. You will also commonly see:

• قريب من الدراجة الثابتة = close to the stationary bike
• بالقرب من الدراجة الثابتة = near the stationary bike

All of these are natural. The sentence you were given uses the shorter structure with قرب.

Because in Arabic, adjectives normally come after the noun they describe.

So:

• الدراجة الثابتة
• literally: the bike the-stationary
• naturally: the stationary bike

This is the normal adjective order in Arabic.

Also, ثابتة literally means fixed or stationary, which is why this phrase is used for an exercise bike or stationary bike.

Because Arabic adjectives usually agree with the noun they describe.

Since الدراجة is:

• feminine
• singular
• definite

the adjective must match it:

• الثابتة

So both words are definite:

• الدراجة = the bike
• الثابتة = the stationary

Together: the stationary bike

This matching of noun and adjective is very important in Arabic.

If you fully vowel the sentence, it is:

جهازُ التجديفِ قربَ الدراجةِ الثابتةِ

Here is what is happening:

• جهازُ is nominative because it is the main subject/topic of the sentence
• التجديفِ is genitive because it is the second part of the iḍāfa جهاز التجديف
• قربَ is accusative because it functions as an adverbial expression of place
• الدراجةِ is genitive after قرب
• الثابتةِ is also genitive because it is an adjective describing الدراجة

Even if short vowels are usually not written, these relationships are still there grammatically.

Because all three words with الـ begin with sun letters, so the l sound of الـ assimilates to the next consonant.

In this sentence:

• التجديف starts with ت
• الدراجة starts with د
• الثابتة starts with ث

So they are pronounced roughly as:

• at-tajdīf
• ad-darrāja
• ath-thābita

This is why the sentence sounds more like:

jihāzu t-tajdīfi qurba d-darrājati th-thābitati

rather than pronouncing a clear l in each الـ.

Yes, Arabic has some flexibility in word order.

The given sentence:

جهاز التجديف قرب الدراجة الثابتة

is the most straightforward way to say:

The rowing machine is near the stationary bike

You could also front the location for emphasis:

قرب الدراجة الثابتة جهاز التجديف

That still means the same thing, but it sounds more marked or literary.

Be careful, though: if you switch the two main noun phrases completely, you change the meaning:

الدراجة الثابتة قرب جهاز التجديف = The stationary bike is near the rowing machine