Difference between rigid body mechanic , deformable
body mechanic and theid mechanics?

A rigid body is one for which all the parts maintain the same positions relative to one another. I cannot deform or change shape in any way. It can only translate and rotate. It is an idealization. There is no such thing as a perfectly rigid body.

A deformable body is one that can distort. It would normally refer to a solid object so that as it deforms, it sort of deforms in a way that it could return to its starting shape if all the external forces were removed that caused it to deform. I don’t think of a blob liquid as being a deformable body even though a liquid can clearly deform. An object made of rubber is the idea that I have in mind for a deformable body.

You need to be more specific.  i really don't know what a "motion map" is.you can draw a graph of an object's position, distance, displacement, speed,velocity, or acceleration versus time, or you can draw a graph of the object's x-position versus its y-position and not give any information about time at all.if the graph presents position or displacement against time,  then constant velocity is a straight line . . i.e. a line that has  constant slope.if the graph shows speed against time, then constant velocityis a horizontal piece of line.if the graph shows acceleration against time, then constant  velocity is a piece of line that lies on the x-axis . . it's value is zero. 

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