Would you walk up to a person and immediately ask them for their business card? You probably would not do this. So, why would you send an invitation on LinkedIn to connect with someone without an introduction? And, yet, people do this everyday.
If you want to connect with someone, let them know how you know them. Generally, I don’t connect with people I have not met in person or virtually, but if you write me a nice introductory letter I probably will. If you have not had contact with someone for a while, remind them how you know each other. Having a good profile picture will help, too.
I always send a short message, even to people I know, when I want to connect. It is a friendly thing to do. Don’t use the standard generic default message that LinkedIn provides. It is impersonal.
LinkedIn is simply a tool used to facilitate connections among people. Manners still apply.