Abstract
parametric robots into four classes. The classification criterion is the spherical rank of the robot, which is the number of independent directions of revolute joints axes. Robots of the spherical rank 1 are robots whose axes of revolute joints are mutually parallel and different. The main aim of the paper is to introduce asymptotic robot motions. The notion of asymptotic motions is connected with the theory of connections. On a pseudo-Riemannian manifold ( (3) E has pseudo-Riemannian structure), there is a canonical connection called the Levi-
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