The spatial RPRP linkage is a closed-loop linkage composed of two revolute and two prismatic joints. It is an overconstrained linkage, which does not obey the Gru¨bler criteria. This paper investigates the finite displacement of the RPRP linkage and shows that all possible finite displacement screws of the coupler link form a screw system of the second order. This paper explores two configurations of the RPRP linkages, folded and unfolded. The screw systems for both types of RPRP linkage are obtained by intersecting two 3-systems corresponding to the RP and PR dyads. A numerical example is provided to verify the result.

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