Move object perfectly to a plane surface

I would like to know if there is an easy way to move an
object on a plane surface.

Context: I create some toys for my children and I like to “assemble”
with SU the different parts to see the final result in a 3D view. That means
that at the end I have some blocks titled in a strange position.

To realize the toy, I need to draw a flat template on paper,
the paper is glued and with a jigsaw, I cut plywood. I’m wondering if there is
a plug-in or a best practice to move all the objects on a plan surface
(sometimes, when I move manually, the objects are not exactly “glue” to the plane surface).

Here’s one way to accomplish what you want: When you have designed the toy, select each component in turn and move it away from the others. Rotate each component until its most important side faces you. Don’t worry about their position along the green axis; just spread them out along the red and blue axes. Switch to the Front standard view (Camera>Standard Views>Front). Then switch to the Parallel Projection view (Camera>Parallel Projection). All the components will appear as 2D shapes as if they are on one plane, although they are still 3D and probably not on the same plane. You can then print the parallel projection view for the cutting pattern you need.
Hope this helps.


Knowledge of how the Move and Rotate tools work will help.
Practice will soon make your difficulties a thing of the past.

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You question is getting complicated enough you should post the skp model if you have one because without seeing it is probably going to lead to a number of answers perhaps not germane to the issue.
For example, if you want to assemble the cuts I am guessing you may be dealing with some compound miter cuts ( just because of the finite thickness of the plywood) but, the template and jigsaw should avoid this type of case.
You should make each of the cuts a component so you are not struggling with self intersecting geometry. When you do that you can set the “glue to attribute” to help with moving. You can also use the on face inference lock when moving.
You should watch the you tube Sketchup videos to get some quick knowledge on its tool etc.

Import DWG into Sketchup
Export it back as a 2D drawings
Import the 2D drawings into Sketchup again
All objects will be on the same one plane