A mounting structure for a rig may include a base configured to support the mounting structure on an operating surface and a plurality of transport systems operatively connected to the base and configured to lift the mounting structure off of the operating surface. An elevated rig platform may be connected to the base by a plurality of support struts, wherein at least some of the support struts comprise a mounting connection that is configured to pivot to lower the elevated rig platform toward the base and place the mounting structure in a partially collapsed state. Additionally, a connecting member may be attached to one or more of the plurality of transport systems, wherein in response to the elevated rig platform being lowered to the partially collapsed state, the connecting member may be configured to displace at least a portion of the one or more transport systems.