It sounds like you're looking for framerate-independent animation. If you're using a faster machine and your animations hang around for a certain number of frames, they'll appear to be moving faster. If your animations however are set to last for a certain number of milliseconds (framerate independent) then everything should appear the same on each machine.
There are exceptions to this, such as if the machine is very slow and the cycle time is longer than the expected duration of more than one frame in the animation, you may need to skip frames which can make things look not so nice.
Some searching revealed this example. Of note is the prototype for the Animation class, where the update function takes a time delta since the previous frame.
This framerate independent approach should be applied to all other concepts in the game as well such as character movement. Consider your standard walking speed to be in terms of pixels (at the current resolution) per second rather than pixels per frame.