>> Time table I think shows regular trains.
The timetable shows all public transport in Switzerland, which includes trains, buses, boats, cable cars, cogwheel trains and funiculars.
>> What about any separate time table for cogwheel train to Rigi?
The Rigi website will show you the same times for the cogwheel train as the main Swiss Timetable will, but the main Swiss Timetable is better for helping you to plan your connections to and from the Rigi mountain transport, i.e. to and from Luzern or wherever else you are starting from or going to.
>> Do I take a regular train from luzern to Vitznau and then take a cogwheel train to Rigi and Arth Goldau?But where to find this route of cogwheel?
There is no train to Vitznau: it is reached by bus or boat. The boat is more scenic.
There are two cogwheel trains to the Rigi, one on each side of the mountain, i.e. one between Vitznau and Rigi Kulm and one between Arth-Goldau and Rigi Kulm. The routes are shown on the map for which Lucas has already provided you a link.
All you need to do is use the Swiss Timetable, putting in "From Luzern" "To Rigi Kulm" and choose an option that includes the boat to Vitznau, which will be denoted on the timetable as "BAT" or "BAV".
>> Similarly for Mt.Titlis where to find time table for car rides starting from Engelberg and boat rides time table from Hergiswil to Luzern?
Use the Swiss Timetable. Given you are short on time, I would skip the boat trip between Luzern and Hergiswil, as it only runs 5-6 times a day when you are there. Take the train the whole way between Luzern and Engelberg instead. Put "From Luzern" "To Kleintitlis" into the timetable and it will give you the whole route from Luzern to the top of the Titlis.
>> As I mentioned I wish to make trips to Mt.Titlis and Mt.Rigi on same day.Same problem I am facing of not finding a time table for cogwheel train to Pilatus from Alpnachstad.
Use the Swiss Timetable. For Pilatus put "From Luzern" "To Pilatus Kulm" "Via Alpnachstad". It will give you connections for the whole trip from Luzern to the top of the Pilatus.
>> Can you suggest a schedule for me to visit Pilatus on 17/09/2017 morning and on 18/09/2017 both Mt.Titlis and Rigi?
Please try to plan it out yourself by using the Swiss Timetable, and if you have any further questions, don't hesitate to ask.