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Coming from a background in engineering, I have used software such as solidwords and Pro-E where you create each part and then combine them in assemblies with mates. Everything I have been able to find tutorial-wise for Blender is all about manually positioning things so that they "look good" from the angle of them camera (which I have found frequently breaks down if you move the camera). What is this even called in 3D art software (since as far as I can tell the term "mate" is exclusive to engineering modeling), and how does one achieve similar results in Blender, ie positioning multiple objects relative to each other in order to make things out of different movable parts or to ensure that things are actually touching rather than going through each other or floating? Tutorial video links welcome.

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You can do this with my addon, Mesh Align Plus (mating, relative movement/positioning, and other abstract precision transformations are its specialties).

To mate an object (or a group of objects) to another, just grab a source and a destination plane, then hit apply (to the selected objects). The GIF below shows relative positioning of 4 separate bracket objects, along with some uniform-spacing after the mate operation:

[alt text][3]

You can think of the "Source" and "Destination" planes as 3-dimensional guides for your alignment. You can grab these guides from anywhere: a real face, or 3 disconnected verts (or from separate meshes, or the 3d cursor in the advanced tools).

You can apply operators to object(s), or to mesh parts. And, you can apply an operator to completely separate/unrelated objects also (this is what makes multi-object editing/relative positioning in the GIF work).

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I am not really that familiar with Blender but from a quick look at the docs, it looks like maybe you want Groups and Hooks. Have a look at this:

Is it possible to assign a parent to a control point of a curve using animall?

You can also change the pivot point of an object: Setting the pivot point of an object

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