**TERMS & DEFINITIONS**

Multi Axis turning is a Field within the Domain of Woodturning. If you think of turning as a tree, single axis turning - to full round - is the trunk of the family tree, with Ornamental Turning, Split Turning, Segmented Turning, Inside Out Turning and Multi Axis Turning being branches on the turning family tree. Each branch / field of turning develops its own vocabulary in order to communicate ideas with others in the field. The development of a vocabulary for Multi Axis turning is particularly important because there are fundamental concepts of Multi Axis turning that are difficult to convey in 2D, or even 2 1/2D (3D objects projected onto a 2D plane) illustrations. WITH an agreed upon vocabulary for the fundamental concepts of this field, it's possible to describe a multi axis piece and convey how it can be turned - with just words. And if you THINK in words, you need words to think in

OK - so lets get to TERMS & DEFINITIONS of multi axis turning, some of which have already been introduced - so we can use them to think about and communicate about multi axis turning - verbally or in writing - without having to include 2 1/2 D illustrations of actual 3D things , in order to share multi axis ideas. Don't worry if some of these terms don't make sense at first or that their definitions don't make sense - yet. Right now just go through them once or twice so when we get to using them and you see them in a virtual 3D model that illustrates them in a multi axis example, they'll be a little familiar.

AIR WOOD / REAL WOOD:When turning a square blank to round, until we've turned the blank to a cylinder, where we can makecontinuous cuts, we're making INTERRUPTED CUTS - the cutting edge contacting and cutting wood (REAL WOOD), then out in air, the cutting edge "cutting" through only the air (AIR WOOD).

When making

continuous cutswe're turning FULL CIRCLES.

When we're makinginterrupted cuts, we can only turn PART OF A CIRCLE - an ARC.

ARC:Part of the circumference of a circle. Until your blank has been turned to round, you can only cut ARCS in its outside surface. So if you're making interrupted cuts, which you usually are when turning a multi axis piece, you're turning ARCS - NOT CIRCLES

AXES- the number of axes for the FORMS used for a multi axis piece. Two axes are only the minimum number of axes - there can be as many axes as you chose to use. Where you place them, relative to each other, will affect how the turned multi axis piece looks.

A

XES CENTERS: Each axis must have two, and only two, centers - one on each end of your blank. You can't see the Axis running through your blank - but you CAN see its centers on the ends of your blank. Keeping track of which center on THIS end goes with which center on THAT end can get confusing when you've got two or more centers on each end of the blank - sowe'll need to to be able to identify which one goes with which one. More about that later,

AXES SEPARATION:The distance between axes anywhere along their length. The Axes Separation affects the size and shape of the OUTCOME'S cross section. The closer the axes are to each other, the rounder the resulting COMMON AREA's cross section. The farther apart the axes are to each other, the more angular and smaller the resulting COMMON AREA's cross section becomes

AXES TYPES: There are only two basic types of axes, but they have variations and the variations affect the OUTCOME

- PARALLELrelative to each other (You've already seen examples of PARALLEL AXES virtual 3D pieces)

- CROSSING: Axes are NOT PARALLEL, they slope or lean in opposite directions. There are two types of CROSSING AXES:

INTERSECTING:If the two axes CROSS / lean in opposite directions - and intersect - anywhere - inside the blank or outside the blank - they're INTERSECTING AXES

NOT INTERSECTING (aka TWISTED AXES) :If the two axes cross / lean in opposite directions - and DO NOT INTERSECT - they're CROSSING BUT NOT INTERSECTING and will result in a TWIST. (The idea of "twisting" will make more sense in just a little bit)As you'll see later, CROSSING AXES affect the OUTCOME's CROSS SECTIONS. When they CROSS BUT DO NOT INTERSECT - the outside surfaces of the resulting piece will TWIST, the direction depending on which direction they cross. For this reason, Non Intersecting crossing axes are

also called TWISTED AXES.You can't actually twist an axis, but you can twist the OUTCOME if you have the axes cross each other - without them actually intersecting. We'll be seeing how that works later. (I know, I keep saying - later. We WILL get to all these laters - later -honest.)

Note that the Crossing Axes can cross anywhere within your blank - or - outside your blank.

CHORD:Any line connecting two points on the circumference of a circle, whose length is less than the diameter of the circle.

COMMON AREA:The AREA shared by two or more overlapping 2D closed shapes. Since we're wood turners, the 2D closed shapes will be circles.

COMMON VOLUME:The VOLUME shared by two or more overlapping 3D FORMS / objects - the 3D equivalent of the 2D COMMON AREA.

With single axis turning, we turn a single profile. The profile can be any combination of just five types of cuts - the PRIMITIVES - a peeling cut to make a straight side, a convex cut (think bead cut), a concave cut (think cove cut), a V cut and a groove cut. That's all we have to play with - five basic cuts. But as a woodturner, you know how many nice ways you can use those cuts or combination of cuts to create beautiful turnings. The same PRIMATIVES can be used on each of two or more axes of a multi axis piece - to turn interesting FORMS / sculptures.

CROSSING AXES:When the axes of piece ARE NOT PARALLEL, they are defined as Crossing Axes

Crossing Axes can either Intersect, within your blank or outside your blank, or cross but NOT intersect

When the centers of the axes to be turned on - are not the same distance apart on the top of the blank as they are on the bottom of the blank, the axes lean towards or away from each other.

DEPTH OF CUT:With multi axis turning, on any given axis, you begin turning making interrupted cuts - your cutting edge in air then in wood and in air again. At any given point along the axis on which you are turning, until you've turned deep enough to make a continuous cut, you are cutting only PART OF A CIRCLE - an ARC.

When you're turning AIR WOOD, you're turning an ARC in the blank.

Once you are turning REAL WOOD, your are turning CIRCLES in the blank.Look at the following illustration. For the axis shown in the left diagrams, the right diagrams show what you'd see on the lathe as the blank is spinning. The YELLOW and BLUE areas are AIR WOOD, where you can only cut ARCS. The GREEN area is the SOLID WOOD, where you can only turn to rull round, CIRCULAR CROSS SECTIONS. As you can see, depending on where you're turing along the axis, you have to make shallower or deeper cuts to get through the AIR WOOD and begin turning Circles in the REAL WOOD. Until you turn all the way through the Air Wood, you're turning ARCS, only part of a circle.

DIRECTIONALITY:Unlike single axis, turned to round pieces, multi axis pieces can have directionality because their horizontal cross sections ARE NOT ROUND.

THIS IS A KEY CONCEPT OF MULTI AXIS TURNING.

IT FREES YOU FROM "JUST ROUND"

AND LETS YOU SCULPT ANYWHERE IN YOUR BLANKHere are several different views of a piece I did that uses multi axis directionality, a stylized Masai Herdsman. I did do some carving to get the hair separated from the face, but other than that, it was all turned. The head was turned on three PARALLEL AXES to get a TRIANGULAR horizontal CROSS SECTION and the torso was turned on two PARALLEL AXESE to get a LENS SHAPED horizontal CROSS SECTION

The neck and legs were turning to full round on the blank's center axis.. As you can see, the piece has a definite Front, Sides and Back

Here's another example of using directionality that multi axis turning allows you to do - this one inspired by my grand daughter at age 6.

EDGES (VERTICAL):Unlike single axis, single profile, turned to round cross sections, turnings - multi axis turnings can have edges where parts of each axis' profile intersect. The line of intersection can be straight, though it DOESN'T HAVE TO BE A STRAIGHT VERTICAL LINE - and - edges may TWIST.

OUTCOME:The piece that results from turning on multiple axes. This is the same as the Common Volume of overlapping 3D turned forms.

In the examples above, two "bead"forms are overlapped, the bead on one axis offsect vertically by half a bead. In the middle, a bead form on one axis, overlapping a cove form, offset vertically by half a cove. On the right, two iverlapping cove forms, one offset vertically by half a cove.

OVERLAPPING FORMS:When SOMEof two or more 3D forms, each with its own profile and axis around which the profile is generated, occupy the same 3D space, and their 3D forms overlap, they create a COMMON VOLUME, bounded by parts of each 3D form.

PLAIN OF CLOSEST PROXIMITY:When two or more axes cross but DO NOT INTERSECT (TWISTED), the horizontal plane in which they are closest together is the PLANE OF CLOSEST PROXIMITY. It's at this horizontal plane that the resulting cross section of the multi axis piece can be closest to round - but not actually round.

POINT OF INTERSECTION:When two or more axes INTERSECT, they intersect at a point - their POINT OF INTERSECTION. WHERE they intersect the horizontal cross section will be ROUND - just like it is any where down the axis of a single axis piece . Above and below the Point of Intersection, the horizontal cross section WILL NOT BE ROUND, unless you turn away all of the AIR WOOD..

PRIMITIVE CUTS:On any given axis, at least when turning between centers, there are only five types of cuts you can makePeeling Cuts

Bead Cuts (

Cove Cuts )

V Cuts (V)

Groove Cuts

PRIMITIVE FORMS: With these basic PRIMITVE CUTS, we can turn PRIMITIVE FORMS. We can also combine them in a lot of ways to create all sorts of interesting turned objects.

PROFILES ALIGNMENT:When turning on two or more axes, each axis with its own profile, how the profiles align both horizontally and vertically, relative to each other, affects the look of the results / OUTCOME - or preclude getting ANY results / OUTCOME - at all.

TRANSITIONS:When turning a multi axis piece to FULL ROUND (ie Round Cross Sections) on each axis, where the shapes turned on two or more axes come together, the resulting COMMON VOLUME is neither that of the adjacent rounde cross sections of what's above or below that space, but rather a comibination of parts of what's above and below.(this definition needs a lot more work and probably more illustrations)

TWISTED: "Twisted" refers to the outside surfaces of a multi axis turning - the OUTCOME - that twists around the center axis

The TWIST is the result of the axes CROSSING BUT NOT INTERSECTING. Up to, but not including, a 180 degree / half twist is possible

TWISTED AXES:When the axes lean in opposite directions (cross each other) and DO NOT INTERSECT, the OUTCOME's outside surfaces will TWIST. Though the axes DO NOT and cannot TWIST, because the OUTCOME is twisted, we'll refer to this axes orientation type as TWISTED AXES

VERTICAL EDGE(s):where arcs intersect in an Arc Type turning, they create a vertical edge down the side of the piecee