Abstract
Combinatorics We study a robot hand model in the framework of the theory of expansions in non-integer bases. We investigate the reachable workspace and we study some configurations enjoying form closure properties. Keywords: Robot hand, discrete control, expansions in non-integer bases, expansions in complex bases
Highlights
Aim of this paper is to give a model of a robot’s hand based on the theory of expansions in non-integer bases
In our model the robot hand is composed by H fingers, every finger has an arbitrary number of phalanxes
A point x = (x, y, z) ∈ R3 belongs to reachable workspace of the h-th finger if there exists a couple of control vectors u =kj=1 and v =kj=1 such that x = x(h)(u, v)
Summary
Aim of this paper is to give a model of a robot’s hand based on the theory of expansions in non-integer bases. Our model includes two binary control parameters on every phalanx of every finger of the robot hand. In particular the sub-configurations can be looked at as scaled miniatures with constant ratio ρ, named scaling factor, of the whole structure. This is the key idea underlying our model and our main tool of investigation. We establish a connection between our model and the theory of iterated function systems and the theory of expansions in non-integer bases This yields several results describing the reachable workspace, some conditions on the parameters in order to avoid self-intersecting configurations and a description of a class of configurations satisfying a form closure condition
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