Cubical modular robots

Abstract We study a simple type of modular robot, consisting of a collection of identical d -dimensional cubes in $${\mathbb {R}}^{d}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mrow> <mml:mi>R</mml:mi> </mml:mrow> <mml:mi>d</mml:mi> </mml:msup> </mml:math> , which change position by sliding along each other (parallel to the axes). We describe the configuration space of such a mechanism, and show that it has a dense open smooth submanifold, and that book singularities are generic in its complement.