Single Point Contact of Planar Bodies

1 DAE formulation for Single Point Contact of Planar Bodies 

We consider two planar bodies with arbitrary shapes. Body 0 and Body 1. For simplicity we assume that the body fixed reference system of Body 0 is the reference system in which all motions are expressed. With respect to that coordinate system the reference point of Body 1 is given by the two coordinates x and y (cf. Fig. 5.10). 

Assume that the surfaces of the bodies are described by the functions ro,ri, respectively a surface point of Body 0 is given by its two coordinates ro(r/o), o and one of Body 1 by ri(7/i),r/i.  

The distance vector d between two arbitrary points of the surfaces is given as 

In a contact point we obtain from d = 0 by eliminating r/o = + y the contact 

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