We are interested in wire-driven parallel robot with four wires and at least two distinct attachment points on the end-effector. Such type of robot is non redundant, it exhibits 4 d.o.f. and can be used as a crane. This paper addresses the inverse and forward kinematics problem, taking into account the mechanical equilibrium equations. We show that surprisingly the forward kinematics can be solved, either for determining all solutions or in a real-time context, but that the inverse kinematics is still an open issue.