Which connection type allows for movement between elements but does not provide fixed support?

The correct choice is the pinned connection because it is specifically designed to allow movement between structural elements while not providing fixed support. This type of connection permits rotation and translation, which can accommodate changes in position due to thermal expansion, structural loads, or other external factors.

Pinned connections do not constrain the members they connect in the same way that rigid connections do, allowing for flexibility in how elements interact with one another. In contrast, a rigid connection fully restrains both rotation and translation, resulting in fixed support and preventing any relative movement between the connected components.

When considering the other options, gravity connections rely on the weight of the components to maintain their position, which may not provide ample flexibility or accommodate movement adequately. A stable connection, while not a commonly used term in engineering, typically suggests a design that resists movement, effectively providing more support rather than allowing for the necessary flexibility between elements. Thus, the pinned connection is the most suitable choice that meets the criteria of permitting movement while lacking fixed support.