يتمدد صديقي على بساط التمرين بالأسطوانة الإسفنجية.

يتمدد is the imperfect-tense verb يَتَمَدَّدُ, from تَمَدَّدَ.

• Root: م د د
• Pattern: Form V
• Basic idea: to stretch oneself, lie stretched out, extend the body

In this sentence, it suggests something like stretches out, lies back, or rolls out the body, depending on the exact context.

Because Arabic very often uses verb–subject order in a verbal sentence.

So:

• يتمدد صديقي = literally stretches my friend
• Natural English: My friend stretches out

This is normal in Modern Standard Arabic. If you put the subject first, that is also possible, but it changes the feel slightly.

Yes. In Arabic, the subject often comes after the verb.

So in:

• يتمدد صديقي

the subject is صديقي = my friend.

This is a very common pattern in Arabic verbal sentences.

The -ي means my.

• صديق = friend
• صديقي = my friend

This attached -ي is a possessive suffix. Once a noun has a possessive suffix, it is already definite, so you do not add الـ.

So Arabic does not say الصديقي for my friend.

Because بساط التمرين is an iḍāfa construction, often called a construct phrase.

It works like this:

• بساط = mat / rug
• التمرين = the exercise

Together:

• بساط التمرين = exercise mat or literally mat of the exercise

In an iḍāfa:

• the first noun usually does not take الـ
• the second noun determines whether the whole phrase is definite

So بساط التمرين can mean the exercise mat, even though بساط itself has no الـ.

بساط literally means something like rug, carpet, or mat.

In this sentence, the best English meaning is mat, because the context is exercise. So بساط التمرين is naturally understood as exercise mat.

Arabic words often cover a wider range than a single English word.

Here بـ means with, by means of, or using.

So:

• بالأسطوانة الإسفنجية = with the foam roller / using the foam roller

This is the instrumental use of بـ.

A helpful comparison:

• بـ = with, by means of, using
• مع = with, together with

So this sentence is talking about the tool being used, not just something accompanying him.

Literally, الأسطوانة الإسفنجية means the foam cylinder/roller.

Parts:

• أسطوانة = cylinder, roller
• إسفنجية = spongy / foam

The adjective الإسفنجية is feminine because أسطوانة is a feminine noun in Arabic.

Arabic adjectives must agree with the noun they describe in:

• gender
• number
• definiteness
• case

So because الأسطوانة is:

• feminine
• singular
• definite

the adjective must also be:

• feminine
• singular
• definite

That is why you get الأسطوانة الإسفنجية.

Because this is noun + adjective, not an iḍāfa.

In Arabic, if the noun is definite, the adjective must also be definite.

So:

• أسطوانة إسفنجية = a foam roller
• الأسطوانة الإسفنجية = the foam roller

This is different from بساط التمرين, which is an iḍāfa construction.

In normal Arabic writing, case endings are usually not written, but they are still understood grammatically.

If fully vocalized, the sentence would be roughly:

يَتَمَدَّدُ صَدِيقِي عَلَى بِسَاطِ التَّمْرِينِ بِالْأُسْطُوانَةِ الإِسْفَنْجِيَّةِ

The main points are:

• على makes the following noun genitive: بِساطِ
• بـ makes the following noun genitive: الأُسْطُوانَةِ
• the adjective follows the noun in case: الإِسْفَنْجِيَّةِ

So even when the endings are not written, the grammar is still there.

Because ت is a sun letter.

With sun letters, the ل of الـ is not pronounced; instead, it assimilates to the next consonant.

So:

• التمرين is pronounced at-tamrīn

By contrast, الأسطوانة keeps the l sound, because it does not begin with a sun letter.

Yes, that is also grammatical.

The difference is mostly one of emphasis:

• يتمدد صديقي... = a normal verbal sentence, very common in MSA
• صديقي يتمدد... = puts a bit more focus on my friend

So both are correct, but the original version sounds very natural in formal written Arabic.