Abstract
The problem of contact between objects and object manipulation is reduced to the simplest yet fundamental case of a body moving on a surface in Cartesian space. Certain smoothness assumptions are made such that the body and the surface have the properties of submanifolds embedded in Cartesian space. The configuration space of the body constrained to move on the surface is constructed as a submanifold of the Cartesian product of the six-dimensional configuration space of the free body and the two-dimensional submanifold of the body itself. This is done considering initially the motion of “general sliding”. Consequently “rolling” motion is considered as an additional kinematic constraint. Certain mathematical properties are proved and algebraic relations derived from the contact conditions are interpreted in the context of the physics of the problem. In this work we developed the foundations for the investigation of the dynamics and control of contacting bodies.
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