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I have two wooden plates with the same dimensions (5 cm thick, 50 cm long and 35 cm wide).

sketch of plate orientation

The distance between plates must be at least 10 cm. Plate P1 is fixed but P2 rotates about the y-axis. Angle alpha can go from 0 degrees (when the plates are parallel) to at least 90 degrees.

sketch of distance between plates

How can I realize this design in practice? Which mechanical elements should I use? It must be strong, there will be load of max. 30 kg hanging on plate P2. There must be some mechanism that will connect these two plates and enable P2 to rotate but when one sets a desired angle between plates, the mechanism must hold the angle constant.

sketch of angle between plates

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My First thought is to use a standard hinge, with the hinge itself on the intersecting lines. The plates can mounted with an offset to create your desired gap. Secondly, you need a positioning mechanism. You can use a rotary detent mechanism, for example two disks with radial grooves that interlock in each other when bolted together and can rotate when the bolt is loosened up.

I would not choose a friction mechanism at the rotation axis. The load is large, which creates a strong moment.

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I think that easiest way to solve the problem of rotating of plate P2 will be using a mechanism like this:

hinge mechanism

To use it, join plate P1 to an additional plate with length of 10 cm (height and width depends on the dimensions of mechanism) like this:

sketch of additional plate

After join of "unknown element" with P1 and after placing P2 on "unknown element", construction will look like this:

sketch of linkage between plates

I still need to find way to prevent plate P2 from falling, I don't think that screws will be enough to attach this mechanism to the plates.

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