The invention provides a multi-freedom-degree rotation edge pulling head assembly, which comprises an edge pulling head and a joint element in mutual connection, wherein the joint element comprises anexternal joint ball head and an inside inner ring; the inner spherical surface and the outer spherical surface of the joint ball head are parallel; the outer spherical surface of the joint ball headis a third spherical side surface; the inner ring is fixedly sleeved on the left end head part of a driving shaft; on the located arbitrary plane of the axial line of the joint element, the outer spherical surface arch center angle of the inner ring is smaller than the arch center angle of the inner spherical surface of the joint ball head; an inner rotating rail for multi-freedom-degree rotationof the joint element is formed between the outer spherical surface of the inner ring and the inner spherical surface of the joint ball head. The multi-freedom-degree rotation edge pulling head assembly has the advantages that the swinging angle and downwards pressing angle required by the production process can be obtained by the edge pulling head without the integral movement of the edge pullingmachine; the machine body structure of the edge pulling machine is greatly simplified; more edge pulling machines can be arranged in the shaping region with the same tin groove length.