Is there any software for designing and testing Technic mechanisms?
I searched for more than a month and I found Lego Digital Designer (LDD) is the balance between simplicity and functionality.

You can learn LDD in a few hours. Very good videos available on youtube

LDD is not just 3d rendering tool. It understands the connectivity between technic beams and pegs. Very impressive.

The most impressive feature in LDD is that it can simulate the technic gears. Take a look at this video and see it for yourself: https://www.youtube.com/watch?v=13wietMv0g8

These two videos will save lots of time:

Lego Digital Designer Tips and Tricks - 1/2

Lego Digital Designer Tips and Tricks - 2/2

Update:

This post helped me to import so many existing Lego lits in LDD. I learned a lot form existing designs. Also, I can find the part numbers that I am looking for, or just copy them from the model. 

Can I import existing Lego kits into Lego Digital Designer?