On the computation of the direct kinematics of parallel spherical mechanisms using Bernstein polynomials

Solving the direct kinematics of parallel spherical mechanisms with l legs boils down to solving systems of l 1 second-order multinomials. This paper presents a recurrent expression for the control points of these multinomials when expressed in Bernstein form. This result allows us to propose a technique for solving the direct kinematics of these mechanisms that takes advantage of the subdivision and convex hull properties of polynomials in Bernstein form. Contrary to other numerical approaches, the one presented here is clearly less involved and, although it can be classi ed within the same category as interval-based techniques, it does not require any interval arithmetic computation.