In this paper we shall classify and explicitly describe all 5-parametric closed kinematic chains consisting of rotational pairs which have one degree of freedom. We shall prove that beside the so-called Goldberg linkages we obtain another class of 5R closed kinematic chains with one degree of freedom. Similarly as in the case of Goldberg linkages the new class is also closely connected with the Bennett's mechanism, but linkages have non-zero offsets. Because of the complexity of the problem, all computations were performed on a work station using Mathematica. For one example from the new class of movable 5R closed kinematic chains we give explicit formulas for joint angles that allow verification of the movability of the closed kinematic chain on a computer.
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