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Page 1 - In which we'll model the outside rim and the spokes of our Mag Wheel.


Step 1 - We're going to start with the outer rim of the mag wheel.  This is the area that the tire attaches to.  First, create a new layer for the rim (right click on the word "default" at the bottom of the screen, the rest should be obvious) and call the layer "Rim".  In the front viewport use the Curve: Interpolate Points {InterpCrv} tool to draw the cross section profile of just the top half of the rim (as illustrated).  The curve should be drawn the radius of the rim away from the centre (green line) and should be open at the bottom.  Line up the bottom 3 point on each end of the curve so that it meets the horizontal axis at exactly 90 degrees.  Make sure snap is on when drawing the first and last points so they snap to the horizontal axis (the line the red x-axis line is on).
Logic - The top and bottom of the rim is essentially symmetric so there's no need to draw the entire profile, we'll mirror it next.  Also, it's probably wise to start with the rim as that defines the shape we'll have to work in to make the central portion of the wheel, it's also the only part we have fixed dimensions for.

Step 2 - Select the curve you just drew (make sure control points are not on, so you can select the whole curve) and then select Transform>Mirror {Mirror} command.  For the start and end points of the mirror plane select any two points along the indicated blue line.  Having snap and ortho on will aid you in drawing a line in the right place.  Notice how it was important to line up the last 3 control points so there is no crease at the point the two curves meet.

Step 3 - Turn on contol points for the curve (Edit>Point Editing>Control Points On {PtOn}) and delete the central ones and move others around to refine the shape to what you desire.
Logic - The less points required to make a curve, the less likely you'll run into problems when you make a surface from it.  Keep everything as simple as you can.  It'll also result in smaller models later.

Step 4 - Now we'll revolve a portion of the rim surface.  Make sure control points are off.  Join the two curves together with Edit>Join {Join}.  Now that they are a single curve, select this curve, then choose Surface>Revolve {Revolve}.  When prompted for the revolve axis select any two points along the vetical Y axis at world centre (along the green line). Having snap and ortho on makes this easier.  In the options box that appears, select Exact and start at 0, end at 72, and check "delete curve to revolve".
Logic - The wheel rim we're making will have 5 spokes.  Since I'm inherently lazy and would like to save needless work, I'm only going to make 1/5 of the wheel (a 72 degree piece of the pie) and then duplicate it accordingly.  This will save multiple steps in filletting and matching angles later.

Step 5 - It'll probably be helpful if we have some guides to work in so we can visualize what the 72 degree wedge looks like.  Create a layer and name it "Guides".  Switch to this layer and use the Curve>Arc>Center, Start, Angle {Arc} tool to draw an arc along the outside of the surface we just made.  Set the first point, using "snap" to centre it, to world centre (green and red intersection), then set the second point to line it up with the x axis at one end of the surface (line extending from red line).  Now type 72 to create a 72 degree arc.  Turn on OSnap End and draw single segment lines from the world centre to the end points of the arc.  Now switch back to the "Rim" layer.

Step 6 - Now we are going to start on the spokes.  Use the Control Point Curve {Curve} tool to draw a sweeping curve, lined up with world centre and extending through the rim surface.  Turn the control points on for the first spoke curve.  Turn on OSnap Point.  Now draw a second curve using the Control Point Curve tool, snapping the first two points to the first two points of the original spoke curve.  It should follow a similar curve to the first spoke curve but be separated at the rim end by a short distance.  It should also extend through the rim surface.
Logic - We want the spokes to appear to branch from a single spoke into two sweeping forks.  By aligning the first two contol points of each of the two spoke curves we can achieve this.

Step 7 - Next we need to give both these curves the same sweep from top to bottom.  With control points on, select the end points of both the spoke curves.  In the front viewport move them up towards the top of the rim and, if not already, into the rim surface itself.

Step 8 - Select the next point of each curve and again, in the front viewport, move them vertically (hold shift down to constrain the motion to vertical only) until they cause the curve to follow a shallow sweep from top to bottom.  Continue to refine the shapes as necessary.  See the final positions I have decided upon for these points in the next step.

Step 9 - Use the ellipse tool Curve>Ellipse>From Centre {Ellipse} to draw the inner (lower) cross-section.  This will be the shape of the spoke near the centre of the hub before the spoke branches.  Next use the ellipse tool to draw a single outer cross-section of the spoke.  This will be the shape of the spoke where it meets the rim.  Copy and Paste this outer cross section so you have one for each spoke curve.

Step 10 - Next we need to align these cross-sections to the appropriate points on the curve.  Rhino has some nice controls to do this.  Use the Transform>Orient>Perpendicular to Curve {OrientPerpToCrv} command.  Turn on Osnap Centre.  Now move the mouse near the edge of the smaller, inner cross-section ellipse.  The crosshair will jump to the centre of the curve.  When prompted, click on either spoke curve (this is the orientation curve).  Move to the inner end of the curve and click to deposit the cross-section ellipse.

Step 11 - Repeat the previous step, orienting each of the two outer (larger) cross-section ellipses to the other ends of the spoke curves.  These end cross sections should not extend out through the inner wall of the rim surface.  It is ok if they do extend out through the outer edge of the rim, though.
Logic - To create cross-sections of curves that are not on an easily definable plane, it is often easier to just draw the cross-sections on an orthogonal view and then orient them on the curves using Rhinos various Orient commands.  It will become apparent in later steps why the end of the curve and the associated cross-section should pass completely throught the wall of the rim.

Step 12 - Now to give the spokes some surface.  Use the Surface>Sweep 1 Rail {Sweep1} command.  Choose one of the spoke curves as the rail and each of the ellipses at it's ends as the two cross-sections.  The result should be as illustrated.  Shade the perspective viewport and rotate it around to inspect the point that the spokes intersect with the rim.  The entire surface of the spoke should pass into the surface of the rim.
Logic - Note how both rail sweeps use the same ellipse as a cross-section at the inner end.  They also end in copies of the same ellipse.  As a result they already appear to be one object at the inner end in the shade preview.  It is also important that they fully intersect the inner surface of the rim as it will allow us to make a smooth join between the spokes and rim.

Step 13 - So let's make the junction between the spokes and rim a little smoother.  Use the Surface>Fillet {FilletSrf} command.  Set the radius to a value that gives pleasing results (in this case, given my scale, I typed in 0.75), and Extend and Trim should both be set to "Yes".  Click the spoke for the first surface and the inner surface of the rim for the second surface (or the other way around, it doesn't seem to matter in this case).  This creates smooth fillets at the intersection of the spoke and rim.  If it doesn't work, undo, then try again with a different radius.
Logic - This command is very useful for making smooth joins between two surfaces.  Note how it also trims off the part of the spoke that was protruding through the rim.  Very handy!  It was important that the spoke completely intersected the rim, otherwise the fillet would not have been made where we wanted it to.  It can get pretty ugly!

Step 14 - Right now we have two separate spokes, that join abruptly in the centre, not seeming to really flow from each other.  To remedy this, we'll have to go through a couple of extra steps.  First we'll define the place where they join.  Turn on the control points for one of the spoke curves.  Do NOT use OSnap to Point, but just draw a new control point curve in the top viewport.  Place the first point near the inner-most point of the spoke curve's control points, but a little past it toward world centre.  The second point should lie directly overtop the second point of the spoke curve.  The third point should be placed in the space between the two spoke surfaces.

Step 15 - Use the Surface>Extrude>Straight {Extrude} command to turn this curve into a surface that intersects the spokes.
Logic - In many instances trimming operations with a curve do not work, but will work with a surface.  Out of habit I just go ahead and extrude a surface to use in trimming operations to save having it fail.

Step 16 - Copy and paste this surface so we have two to work with.  Move them both slightly away from where you drew the original curve, in different directions, creating a small gap between them.  Make sure that both ends of both cuves are outside the actual surfaces of the spokes.

Step 17 - We'll now use these two surfaces to trim the spoke surfaces.  Select the Edit>Trim {Trim} command, where the curved surfaces are the cutting edges and the spokes are the items to be trimmed.  Use the front surface to trim the back off the front spoke.  Use the back one to trim the front off the back spoke.  If that didn't make much sense check out the image above.  You should have been left with a slight gap between the two spokes.  You may find that you have to trim one of the spokes twice.  It just depends on where the spokes seam happened to lie.

Step 18 - Delete the curved surfaces you used for trimming.  Now to create the surface betweent he two spokes we'll use Surface>Blend {BlendSrf}.  When prompted to select the first set of edges, make sure you select every edge around the opening we just created with the trim on one of the spokes (there may be several edge segments), then hit enter.  For the second set select all the edges on the opposite spoke around the area we trimmed.  Once you hit enter again you should see a nice new surface fill the gap between the two spokes.  Looks a little more natural now!

Step 19 - Yes, there is no image for this step!  Since we've more-or-less made most of the spoke, it's time for a little cleaning up.  I like to get all the curves and lines out of the way so I can better see what I'm doing.  Go to Edit>Select>Curves and hit the delete key.  We won't be needing them anymore.

Next page we'll be working on the central hub and getting to the point that this will actually look like a Mag Wheel!

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