Build a 3D Pull-up Rig Configurator Game/Tool with Unity 3d

I want a 3D game/tool that will allow the user to build a simple steel frame pull up rig structure with 3D drag and drop/join construction. My preference for this is Unity3d so it can be ported to PC and IPad. I already have 3d solidworks models for all of the components. The rigs will all need to follow some basic rules for how the parts connect to each other. See attached image for example. A user will be able to select from a menu of components on the side of the screen and drag them onto a canvas. Starting with a single Upright component. From here they can attach a cross bar on any side of the upright, followed by another upright etc. Once the frame is built there will be some accessories that can be attached. The user should be able to navigate around the rig as they build. If possible I would like the tool to generate a list of the components used. As well as an image of the finished rig.