Can I apply for a patent for mechanical action?

You'd better improve your description. The mechanical action is recognized and it is impossible to apply for a patent. What you should say is a mechanical structure designed to realize complex movements. If so, you can apply for a utility model patent for the mechanical structure you designed. What you said in your description is to buy a patent, which is also a utility model patent for mechanical structure, if any. You can check it according to your requirements. Usually only one patent can be applied for through the same mechanical structure, and one is not allowed to apply for two patents. Don't worry.