P
ar
allel robots enjoy enh
anced mech
anic
al ch
ar
acteristics th
at h
ave to be contr
asted with
a more complic
ated design. In p
articul
ar, they often h
ave p
ar
allel singul
arities
at some poses,
and the robots m
ay become uncontroll
able,
and could even be d
am
aged, in such configur
ations. The comput
ation of the connected components in the set of nonsingul
ar re
ach
able configur
ations, c
alled gener
alized
aspects, is therefore
a key issue in their design.
This paper introduces a new method, based on numerical constraint programming, to compute a certified enclosure of the generalized aspects. Though this method does not allow counting their number rigorously, it constructs inner approximations of the nonsingular workspace that allow commanding parallel robots safely. It also provides a lower-bound on the exact number of generalized aspects. It is moreover the first general method able to handle any parallel robot in theory, though its computational complexity currently restricts its usage to robots with three degrees of freedom. Finally, the constraint programming paradigm it relies on makes it possible to consider various additional constraints (e.g., collision avoidance), making it suitable for practical considerations.