Finding 3d space area where IK target can be placed

How can i make a script which calculate the area/volume of possible positions where the end target of a chain of multiple hinge joints can be placed by an IK component with respects of each joint angle limits? I want to draw the shape of this area on editor so it can be easier to visualize foot placement positions for my insect legs(not mine, the player) real time when editing joints limits. Trying to image the possible area increase in complexity with every next joint in chain: for one hinge joint target area represent a piece of circumference/arc, for two joints the area extends to a 2d space, for three joints, every point situated on the previous 2d space will create its own 2d space extending to a 3d volume space and so on. For one or two joints seems easier to determinate the area and draw it's shape in editor but it becomes really confusing when i have to deal with 5 or more joints.