By a sequence of rollings without slipping or twisting along segments of a straight line of the plane, a spherical ball of unit radius has to be transferred from an initial state to an arbitrary final state taking into account the orientation of the ball. We provide a new proof that with at most 3 moves, we can go from a given initial state to an arbitrary final state. The first proof of this result is due to Hammersley ( 1983). His proof is more algebraic than ours which is more geometric. We also showed that generically no one of the three moves, in any elimination of the spin discrepancy, may have length equal to an integral multiple of 2 pi.MICINN/FEDERAGAURICREA AcademiaFCT (Portugal)Univ Estadual Paulista, BR-04026002 Sao Paulo, BrazilUniv Sao Judas Tadeu, BR-03166000 Sao Paulo, BrazilUniv Autonoma Barcelona, Dept Matemat, E-08193 Barcelona, Catalonia, SpainUniv Tecn Lisboa, CAMGSD, ISR, Inst Super Tecn, P-1049001 Lisbon, PortugalUniv Sao Paulo, Dept Matemat Aplicada, Inst Matemat & Estat, BR-05508900 Sao Paulo, BrazilUniv Estadual Paulista, BR-04026002 Sao Paulo, BrazilMICINN/FEDERMTM 2008-03437AGAUR2009SGR 410FCT (Portugal)POC-TI/FEDERFCT (Portugal)PDCT/MAT/56476/2004