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UNION will connect things that don't touch each other into a single Solid [try it]. If I misunderstood, explain in greater detail.
Kent Cooper, AIA 
@tecnicoKJFRK wrote:... 2 solids (a blade and a support) which need to be unified into a single piece.
...it would require them to be tangent to each other, I guess.
I agree with @Kent1Cooper, if you just want to "unified into a single piece" - as currently shown.
However, because you mentioned "it would require them to be tangent to each other", I think you may want to have the inside radius of the blade (gray) meet exactly with the outer radius of sphere support - unless this is intentional. If you can determine the center of the inside blade, then it can be moved from center to center (without having any gaps between the blade and the support -see image). Otherwise, consider using the SUBTRACT command to redo the inside radius of the blade.
@tecnicoKJFRK My understanding of your goal is to position the blade such that its contact surface is coincident with the spherical surface of the red support. I estimate that the radius of the support's spherical surface to be 100. Is this correct? The center of the blades center should lie on a surface offset by 100. The offset command failed to generate an offset surface of 100. This is understandable as a point surface would be the result. I created an offset surface at 50 and then created lines (with ray) from estimated corresponding points on the blade surface and it offset. These line should intersect at the center of curvature of the blade's spherical surface.
From here all you need to do is move the blade so that its center of curvature point is coincident with the supports center of curvature point.
So.. based on what others are saying, I subtracted the 3 Red Flat Washers.
Then Moved the Red Body with Blade from Center to Center of Purple Body and perfect FLAT FIT.
You don't need the Flat Washers to keep in place if you use your bolt holes.
But you need now to make your Outside of the Red Body larger to make it Smooth Transition to the Purple Body.
See my CAD and Pasted image.
Hope this helps some more!
JRR.
Making the red object flush with the magenta object is easy. Just move it by -101.0055 in Y so that the top of the boss is tangent to the magenta's surface.
After the move.
Now make a copy of the blade on another layer (bladecopy) and work on that layer with the other layers frozen.
Rather than use the offset method I suggested earlier here's another approach. If the blade surface we want to mate with the support (red) is spherical then its center is at the intersection point of three spheres of radius 100 whose centers are on the surface.
Construct three 100 R spheres using osnap nearest at different points along the surface edge. The result should look something like this.
Now do a Boolean subtract of two of the spheres from the third resulting in the following. Place a point at the corner as noted.
This point should be at the center of curvature of the blade's spherical surface.
The white point is the center of the blade and the green point the center of the red support (located 100 to the right of red's surface along its centerline).
Move the blade and point together so the the two points are coincident yielding the following.
Visually examining the result they the two objects look tangent.
Doing a Boolean intersect with no results shows that the do not intersect. You can use rotate3d or 3drotate to reposition the blade to any orientation as long as you use the center point as the base point for the rotations.
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