Learn Hardcore Ukrainian: Лікар оглянув суглоб.

Лікар is in the nominative case, which is the normal case for the subject of a sentence. In a basic Ukrainian sentence, the pattern is often subject + verb + object, so Лікар оглянув суглоб naturally means The doctor examined the joint.

Why does суглоб not change form if it is the direct object?

It actually is in the accusative case, but for many masculine inanimate nouns in Ukrainian, the accusative singular looks exactly the same as the nominative singular. So:

суглоб = nominative singular
суглоб = accusative singular

That is normal. Compare this with a masculine animate noun, where the accusative usually changes, for example лікар → лікаря.

What does оглянув tell me about the verb?

Оглянув tells you three things at once:

it is past tense
it is singular
it is masculine

So the sentence is about a masculine subject, or at least a subject treated grammatically as masculine. If the doctor were explicitly female, you would normally expect оглянула.