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The URDF format does not support closed loops of links so cannot represent a four bar linkage such as your gripper.

There is a solution though. URDF models can describe mimic joints where the angle of one joint is defined to have a linear relationship to the angle of another joint. In your case one of the four revolute joints on each side of your gripper would be a normal joint, two others would be mimic joints, and the final joint wouldn't need adding at all. This is not an ideal solution and only works for parallel four bar linkages, but it will work in your case.

Here's an example of this being used in a URDF model.