Dear Mr. F-Kwun Hwang,
Huge thanks for the static version of the gimbal applet. That is exactly what I need for doing my research. I actually do not need animation.
But I would like to ask you to add the following opportunities:Independent moving of each circle (Roll, Jaw and Pitch) without driving the others. Also please make the rotation angels of the same circles measured in degrees and please put 3 indicators to display the degree of rotation of each one. I also need that it will be possible to work with only 2 of the circles let say just Yaw and Pitch for example.The 3rd could be made (temporary) disabled and invisible from the applet by some kind of a button. This ability should be possible for each one of the 3 circles one each at a time by choice of the opperator. Actually I would like to investigate when a gimbal lock will appear with 2 and/or 3 circles in different experiments.

The gimbal lock on my humble oppinion is a constrain of the gimbal toolls at all. The equasions of the so called gimbal lock and detailed explanation of this phenomenon are given at the following sites ordered by importance:

http://en.wikipedia.org/wiki/Gimbal_lock

http://www.edharriss.com/tutorials/tutorial_xsi_gimbal/xsi_gimbal.html

http://www.anticz.com/eularqua.htm

Please excuse me that I can not give you a physics model and other constraint mathematics but I am a medical doctor and have only basic knowledge on that matter obtaining from the Internet sites. That is the reason of my request because I can not make such an applet by myself despite the EJS. I can just opperate it.
Here are my answers of you questions below:
1/,The dimension of the system shoud be in degrees not in radians or arbitrary units
2/. Yes all 3 circles Yaw, Roll and Pitch should rotate in their one axis without moving the other one i.e. when I rotate the Pitch the Jaw and Roll should not move. Then I will need to rotate the othe 2 one at a time with changin the position of the rest circles. The axes should be perpendicular each other.
3/. This static applett is OK with my work.
4/. The left hand picture is my gimbal (the blue one). The animated one is not correct for my purposes.

Thanking you very much again  for your time and efforts I am,
With kindest regards,
Evgeni.

Let me make sure one thing:

1. Dimension of the system (at least r1,r2,r3)
2. Does the outer most one can only rotate in YAW AXIS?
3. Is it a static system, only need to be able to set the angle for Pitch, Roll and Yaw angle?
Or there is(are) initial angualr velocity for a dynamic system? What are those values? What are the differential equations according constraints for your system.

Because I have never play with such device before, I do not have any ideas about the physics model (constraints) for the system. I need physics model to create the simulation.

The rotation axes for the following two images are not the same. Which one is similar to your gimbal?