Köpeğin tasmasını takmadan dışarı çıkmıyorum.

Because köpeğin is in the genitive case here: it means of the dog / the dog's.

This sentence contains a very common Turkish pattern:

• köpeğ-in = the dog's
• tasma-sı = its leash / the leash of it

Together, köpeğin tasması means the dog's leash.

So Turkish marks both parts of this relationship:

• the owner/possessor gets -in
• the thing owned gets a possessive ending, here -sı

This is the normal structure for X's Y in Turkish.

This is because of consonant softening.

The base word is:

• köpek = dog

When a vowel-initial suffix is added, the final k often changes to ğ:

• köpek → köpeğin

So this is not a different word; it is just a normal sound change in Turkish morphology.

You will see the same kind of thing in many words.

It breaks down like this:

• tasma = leash / collar
• -sı = 3rd person possessive ending
• -nı = accusative ending

So:

• tasması = his/her/its leash or, in this structure, the dog's leash
• tasmasını = the dog's leash as a specific direct object

The extra n is a buffer consonant used before the accusative after a possessive ending.

So the structure is:

• tasma-sı-nı

Because Turkish uses the possessive ending not only for pronouns like his/her/its, but also when the possessor is a noun.

Compare:

• evin kapısı = the house's door / the door of the house
• köpeğin tasması = the dog's leash

So -sı does not necessarily mean a separate English word like its. It is simply part of the normal Turkish way of saying the dog's leash.

Takmadan means without putting on / without attaching.

It comes from:

• takmak = to put on, attach, fasten
• takma- = not putting on
• takmadan = without putting on

This -madan / -meden form is a very common Turkish structure meaning:

• without doing X

Examples:

• yemeden = without eating
• bakmadan = without looking
• sormadan = without asking

So tasmasını takmadan means without putting on its leash.

This is normal and does not create a double negative in the English sense.

The logic is:

• takmadan = without putting on the leash
• çıkmıyorum = I am not going out

Together:

• I don't go out without putting on the dog's leash

In other words, the speaker is saying:

• I never go outside unless I put the dog's leash on first

So the two negatives do different jobs:

• -madan makes the before-action negative
• çıkmıyorum makes the main action negative

Good question. In Turkish, the present continuous can often be used for habits or regular behavior in everyday speech.

So:

• çıkmıyorum can mean something like I'm not going out / I don't go out
• in context, it can sound like a personal rule or habit

A more general, rule-like version could also be:

• Köpeğin tasmasını takmadan dışarı çıkmam.

That sounds a bit more like:

• I don't go out without putting on the dog's leash
• I never go out without...

So both can work, but:

• çıkmıyorum = very natural in spoken Turkish
• çıkmam = more general/habitual/principle-like

Because Turkish verb endings usually already show the subject.

Here:

• çıkmıyorum

contains the ending that tells you the subject is I.

So Turkish often leaves out pronouns when they are not needed.

You could say Ben köpeğin tasmasını takmadan dışarı çıkmıyorum, but ben would usually only be added for emphasis or contrast.

Dışarı here means outside / out.

In the expression dışarı çıkmak, Turkish commonly uses dışarı as an adverb-like word:

• dışarı çıkmak = to go out / go outside

So it does not need an extra case ending here.

This is a very common fixed expression, and it is best to learn dışarı çıkmak as a unit.

Yes, and that would shift the focus slightly.

Compare:

• köpeğin tasmasını takmadan = without putting on the dog's leash
• köpeğe tasma takmadan = without putting a leash on the dog

The first version focuses more on the leash as the object. The second version focuses more on the dog as the thing receiving the leash.

Both are natural, but the original sentence is perfectly normal Turkish.

Not completely. Turkish word order is flexible, but the given order is very natural.

Here the structure is roughly:

• Köpeğin tasmasını = object
• takmadan = without putting on
• dışarı = outside
• çıkmıyorum = I don't go out

So the sentence builds up to the main verb at the end, which is very typical in Turkish.

You may hear variations for emphasis, but this version sounds smooth and standard. The key thing is that çıkmıyorum usually stays at the end, and dışarı çıkmak tends to stay closely connected in meaning.