When a rigid body is in contact with another rigid body, which is fixed in the frame of reference, its motion becomes constrained (i.e., restricted) and the number of degrees of freedom associated with its motion is reduced. This restriction of the motion depends on the type of contact. When the body is in contact with several other bodies, its motion is even more restricted, and it can become immoveable. In this chapter, our goal is to present the basic mathematical description of the contacts between rigid bodies, to study the effects of several types of contacts on the constraints of the body’s motion, and to determine the requirements for the modeling of a single robot contact. As the mathematical tool appropriate for a description of the contacts we use the screw representation, which relates the velocities and forces, occurring before and during the contact, with the contact normal.
KeywordsDirection Cosine Planar Contact Friction Cone Screw Representation Coulomb Friction Model
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