You may see http://188.8.131.52/moodle/file.php/2/Transitional_Expressions.doc.I put the information there.In fact, the three you mentioned are all used in comparison. However, there are slight differences among them.(1) on the other hand: It is used when you are comparing two different facts or two opposite ways of thinking about a situation.(2)on the contrary: It is used to show that you think or feel the opposite of what has just been stated.(3)in contrast or by contrast: It is used to show an obvious difference between two or more things.