Answer
Wa `alaykum as-Salamu wa Rahmatullahi wa Barakatuh.
Answering your question, Dr. Mohammad S. Alrahawan, Associate Professor at the department of Islamic Studies in English, Al-Azhar University, Egypt, states:
Drawing pictures of animated beings is strictly prohibited in Islam. Prophet Muhammad (peace be upon him) said: The most severely punished of people on the day of Resurrection will be the image-makers, those who tried to imitate creation of Allah. But drawing inanimate pictures such as drawing trees, mountains, etc. is permissible.
The reason of prohibiting the first type is mentioned in the statement of the Prophet, i.e. it is just like you are duplicating those great creations of ALLAH.
Moreover, there are many further reasons why sketching/drawing is not allowed in Islam? First of all, one of the name of ALLAH is Al-Musawwir which means the giver of form, shape and color. It means that only Allah has the power of creating human-beings. Another reason is that Angels of ALLAH hate pictures and dogs. They hate it only because Allah hates them, too.
But dolls are permissible if they are designed for children. The Prophet’s wife `A’ishah (may Allah be pleased with her) said: I used to play with dolls in the house of the Messenger of Allah (peace and blessings be on him) and my friends would come over to play with me. They would hide when they saw the Messenger of Allah (peace and blessings be upon him) approaching, but he was in fact very happy to see them with me, and so we played together. (Al-Bukhari and Muslim)
So it is clear that making toys and playing with dolls especially for children is not prohibited. It is acceptable. If pictures are drawn on textbooks just to explain things to the students, then it is fine. Similarly, Human and animal models can be made for scientific research, as well. Pictures taken for ID card or passport are also acceptable.
Some people have drawing skills and they put all their efforts in sketching and drawing. I would recommend them to use their creativity in calligraphy as it is also a very beautiful form of art. They can also use their talents in drawing inanimate creations such as plants, flowers, mountains and other elements of this beautiful nature that Allah created.
Allah Almighty knows best.