Apple - OS X right click/context menu via keyboard

The context menu can primarily be opened by a right mouse click (or a control click) only.

However, if you want to right click on a specific area on the screen without using the mouse, you may use Mouse Keys from Universal Access settings in System Preferences. With it, you can control the mouse by using the keyboard number pad. When activated, a right mouse click then can be achieved by Ctrl+5 on a keyboard with a numpad or Fn+Ctrl+i on a laptop. This will allow you to 'right-click' your word.

Go to System Preferences --> Universal Access --> Mouse --> Enable Mouse Keys (ON)

Found on: https://stackoverflow.com/a/11238186/1919382

There is no way in general on the Mac to determine the screen coordinates of the current insertion point. So there is no way to automate a click at the current insertion point.

In some apps, there might be a way to get the coordinates via AppleScript, or it might be possible to get them using some sort of private API or other system hackery, but there is no general solution to this problem that is supported by Apple APIs.

It is, apparently, quite a common UI gesture on Windows, but it is not something you can do on the Mac.

I was also looking for this kind of feature and found a good alternative.

Most context menu items in OS X can also be found in the top menu bar, and you can access this with a keyboard shortcut. By default it's set to ctrl+F2, however this often doesn't work. You can change the binding on the Keyboard preference pane.

This this post has more details http://reviews.cnet.com/8301-13727_7-57591609-263/access-menus-via-the-keyboard-in-os-x/