While blogging away on the 'X Marks the Spot' series over the past week, I have been working away slowly and carefully on the wood for the dining table. A few revisions took place in the drawing as well, which I'll explain soon enough. There didn't seem to be much point photographing the wood as I brought it down to size by way of repeated jointing and planing sessions, as not much visibly changes.

Earlier this week, however, I had at last reached the point where the bubinga was straight, square and at dimension, or very slightly above, as with the main frame rails:

The extra 1/32" of material over the 2.5" target is due to the fact I'll be running one face through the shaper in a few days.

One of the boards sliced up for the table top has been wanting to cup, so I've been massaging it back to straightness again with a combination of moisture, heat, and weighting:

It's is like a dance with that piece of wood, but it will follow along with my prodding.

The main frame rails will have 0.75" of material removed from their inner faces along 80% of their length, and I have had some concerns about what the wood might do as a result of the removal of so much stock. Movement from moisture changes and/or the release of stresses by cutting could cause problems, so I tried an approach of doing things gradually. The first step, intended to allow the piece to equalize to moisture changes from inside to outside, was to perforate the side with a long session at the drill press, using a 1" Forstner bit:

A closer view:

The holes allow for any moisture to move in/out, and yet retain the bulk of the stick's cross section without severing completely across the fibers, which should help it stay straight. it's really little more than an experiment, but so far, several days later, there has been no appreciable movement in the wood. The housings that you see in the pieces are for the battens (on the long rails), and the center rib (on the short rails). I then routed these housings down exactly 0.745", which is a couple of scrapes shy of the target 0.75" depth.

Then I started rouging out some pieces which are involved in the locking mechanism to secure the legs to the frame rails (aprons). It was a chance to work on getting the shaper set up as well, which needed some minor tuning of its fences:

And I've started constructing some jigs to work the apron/rail joinery, starting with this little number:

Last, but not least, I promised a photo of the planing beam I had set up, so here ya go:

The needed shaper tooling should be in my hands early next week so it will be time to, uh, plunge right in once I have them. It's cool to have a shop space set up again after a few years, the last couple of which, as regular readers are well aware, were in my kitchen on saw horses. My wife seems pleased with the change too! It was tough moving from Canada to the US right after the economy plummeted and made the process of getting established all the more difficult. I will continue my efforts to promote the art of Japanese carpentry, at least as I practice it, and look forward to see what unfolds.

That then is my final post of the Carpentry blog here on the last day of the first decade of the 21st century. I look forward to 2011 and whatever it may bring, and plan to keep blogging away. I hope readers will keep returning to see what sort of trouble I can get into.

I wish my readers and fellow woodworkers out there all the best in your ventures for 2011. May it be a year of bounty and success, and challenges surmounted. Ganbatte kudasai!

## Friday, December 31, 2010

## Wednesday, December 29, 2010

### X Marks the Spot (VII)

After the previous post in this series, the reader may have begun to notice the rapidly multiplying profusion of lines. Well, don't worry about that, as it is only going to get worse from here, and the truth, er, is plane to see.

A couple of readers have commented about having problems rendering or using the arcs I show in the drawing - welcome my friends to SketchUp, and the problem it has with representing curves and attaching lines to curves. It's frankly one of the shortcomings of the drawing program, and has given me my share of hair-pulling moments of frustration at times.

In SU, there are two ways to draw a circular line - either one uses the 'arc' tool or one uses the circle tool and then chops the circle up into the required arc portion required. Either way, SU is representing that circle as a series of facets. If, at the tangent point to the arc, there happens to be a facet arris, then the point is slightly further out than where it ought to be. If one is, on the other hand, connecting to a facet more closely to the midpoint of a facet, then the point is further in than where it ought to be. One can specify that either the circle or the arc tool have more facets, up to 1000 facets I think, but then it is still hard to know where the tangent point of the circle is located. One can download plug-ins to deal with this, like True Tangent, but in the end, it really is simpler and easier to draw an arc with an old-fashioned drawing compass than SU. Shocking, I know.

On this charpente problem drawing I am presenting in this series, while I am using SketchUp, I am not presuming that the reader is also using it - in fact I am presenting the material in such a way that the reader with pencil, straightedge, compass and rule can accomplish the drawings. Readers who are following along with SketchUp, and who are unfamiliar with its peccadilloes in terms of arcs and circles may run into little errors when trying to connect to arcs. The arcs on my drawing are in fact only representational, and the lines that purport to connect to them, actually do no exactly connect to them. Its fiction actually. I figured out the positions of the lines using a little bit of math.

Here, I'll show you what I mean - in this next picture, I have placed a large arrow pointing to the intersection of an arc and the line which it is supposed to delineate:

Now I'll zoom right in on that arrow, and you can see that the faceted arc does not exactly meet the line:

In the above picture it almost looks like the facet arris of the arc actually does meet the line a little lower down from where the arrow points, however if you zoom right in you will see it does not in fact intersect:

The line's position is determined not by the arc, which I know to be wrong, but by using a little math. The cross sections of the sticks, which are square, each measure 20 cm on a side. The diagonal of that square is √2 times longer, that is 20√2, which equals 28.2842712474619... or thereabouts. The distance therefore of the bottom line of the stick (in the elevation view) from the top line of the stick is 28.2842712474619... and the line in the middle is 1/2 of that, or 14.142135623731... roughly. That's how I spaced the lines on the elevation view of the stick, not by using the arcs on SketchUp.

Alright, on with the fun - in the last blog entry in this series we formed a large plane off of one of the surfaces of stick 'a', like this:

We then noted how that plane meets the floor and forms a line emanating from the foot of the stick, and with a few magic tricks we produced the following lines on the elevation view of stick 'b', showing where the plane from stick 'a' intersects it:

Today we are going to do pretty much the exact same procedure, this time with another plane. The simplest one to consider is the plane formed by the surface of stick 'a' which is parallel to the surface we already played around with. That surface can also be extended into a plane, just as we did before, and this time I'll make that plane light green in color:

It may not be clear that the green plane formed by that rear face of stick 'a' even intersects with stick 'b', however if we swing around to look at things from the other side, it is clear that is does intersect:

So, just like we did in the previous post, I'll disappear that green plane, only to leave its trace upon the floor, a line which runs roughshod over the plan view of stick 'b' at slope:

And, just like with the work we did on the orange plane's ground trace previously, here we not the intersections of the green plane's trace line with stick 'b''s plan, and mark those points as 5, 6, and 7:

Moreover, from 5, 6, and 7, we then project square to the axis of stick 'b''s plan, traveling over to the ground line of stick 'b' in elevation view. We label these intersections 5', 6', and 7' respectively.

Now, since this green plane is parallel to the orange plane we used in the previous blog post, one would think that all lines generated from the green plane's trace would also run in parallel to the lines from the orange plane's face, no? Therefore, if this is true we can run lines up from 5', 6', and 7' up parallel to those lines previously marked out for the orange plane, that the lines that gave us the points 1", 2", and 3":

You can see in the above illustration that from our points 5', 6', and 7', we have run lines parallel to those previously generated, to form new points of intersection, namely 5", 6", and 7". If you're a little confused as to why 5", 6", and 7" are points that require marking, and not other places where the lines cross, take a look again at which lines in the plan view of stick 'b' we crossed originally, giving those first points of 5, 6, and 7.

Here's a closer view showing our new points, the entire point of today's drawing exercise, 5", 6", and 7", formed in much the same pattern as 1", 2", and 3":

Just as before, since the line crossed in plan where we obtained the crossing point labeled 6 was actually the top and bottom arris of the stick, it should come as no surprise that when this line is projected across the elevation view of the stick we would obtain two points of intersection, one on the bottom arris and one on the top.

Now then, in case the reader might not be sure of my assertion that these lines we have generated to points 5', 6', and 7' are to run parallel to the lines we obtained from points 1', 2', and 3', let's just confirm that geometry. You may recall that the way we obtained the slope line crossing the elevation view of stick 'b' was produced by two points. The one at the bottom was the intersection with the trace at point 3, which projected to give point 3', and the point at the other end was found by projecting a line from the top cut view of the stick and meeting the same arris as 3 was marking further down. We should be able to replicate that exact procedure, no?

Here's the projection then of the other side of the top cut of stick 'a':

Notice on the right side is that projection line which met the arris of stick 'b' (plan view) at point 4. We have now projected a line from the other side of that white diamond indicating the top cut, and this meets the arris of stick 'b's plan at point 8.

That line at point 8 then projects at a 90˚ angle to the plan axis of stick 'b', and travel up to the line representing the plane of the top cut of the stick, in elevation, to give us point 8':

Notice that at point 8', the line from point 7, via 7' and 7" drops right in to say hello. Thus we confirm the geometry of that slope, and know that in future we needn't bother with such confirmations when parallel faces are involved.

So, another fine mess we have created here:

Where's it all going? If we look at a view from the rear side, we can hopefully gain some clarity about what has been accomplished so far:

Today we merely repeated what we had done in the previous post, and by using a face which was parallel to the one dealt with earlier we made this pretty much a paint by numbers session. In the next post, we will move yet closer to our objective as we deal with the remaining two planes on stick 'a'. Enterprising readers may wish to forge ahead on their own if they feel confident as to the methodology.

And if you are thoroughly confused, swimming in lines that have lost all relevance or meaning, well, sorry if I managed to confuse anyone. I'm trying to be as clear as I can in my explanation, but I'm sure it could always be improved. As you learn, I learn.

All I can say, is if you feel like you're stuck in the muck, simply start a new drawing and work through the steps again in this series - and again if necessary - until simply be rote copying of what I have illustrated thus far you produce the same drawing. You will find that each time you re-draw you will gain a clearer understanding, if not basic familiarity with what is going on.

Thanks for dropping by the Carpentry Way today. --> go to post 8

A couple of readers have commented about having problems rendering or using the arcs I show in the drawing - welcome my friends to SketchUp, and the problem it has with representing curves and attaching lines to curves. It's frankly one of the shortcomings of the drawing program, and has given me my share of hair-pulling moments of frustration at times.

In SU, there are two ways to draw a circular line - either one uses the 'arc' tool or one uses the circle tool and then chops the circle up into the required arc portion required. Either way, SU is representing that circle as a series of facets. If, at the tangent point to the arc, there happens to be a facet arris, then the point is slightly further out than where it ought to be. If one is, on the other hand, connecting to a facet more closely to the midpoint of a facet, then the point is further in than where it ought to be. One can specify that either the circle or the arc tool have more facets, up to 1000 facets I think, but then it is still hard to know where the tangent point of the circle is located. One can download plug-ins to deal with this, like True Tangent, but in the end, it really is simpler and easier to draw an arc with an old-fashioned drawing compass than SU. Shocking, I know.

On this charpente problem drawing I am presenting in this series, while I am using SketchUp, I am not presuming that the reader is also using it - in fact I am presenting the material in such a way that the reader with pencil, straightedge, compass and rule can accomplish the drawings. Readers who are following along with SketchUp, and who are unfamiliar with its peccadilloes in terms of arcs and circles may run into little errors when trying to connect to arcs. The arcs on my drawing are in fact only representational, and the lines that purport to connect to them, actually do no exactly connect to them. Its fiction actually. I figured out the positions of the lines using a little bit of math.

Here, I'll show you what I mean - in this next picture, I have placed a large arrow pointing to the intersection of an arc and the line which it is supposed to delineate:

Now I'll zoom right in on that arrow, and you can see that the faceted arc does not exactly meet the line:

In the above picture it almost looks like the facet arris of the arc actually does meet the line a little lower down from where the arrow points, however if you zoom right in you will see it does not in fact intersect:

The line's position is determined not by the arc, which I know to be wrong, but by using a little math. The cross sections of the sticks, which are square, each measure 20 cm on a side. The diagonal of that square is √2 times longer, that is 20√2, which equals 28.2842712474619... or thereabouts. The distance therefore of the bottom line of the stick (in the elevation view) from the top line of the stick is 28.2842712474619... and the line in the middle is 1/2 of that, or 14.142135623731... roughly. That's how I spaced the lines on the elevation view of the stick, not by using the arcs on SketchUp.

Alright, on with the fun - in the last blog entry in this series we formed a large plane off of one of the surfaces of stick 'a', like this:

We then noted how that plane meets the floor and forms a line emanating from the foot of the stick, and with a few magic tricks we produced the following lines on the elevation view of stick 'b', showing where the plane from stick 'a' intersects it:

Today we are going to do pretty much the exact same procedure, this time with another plane. The simplest one to consider is the plane formed by the surface of stick 'a' which is parallel to the surface we already played around with. That surface can also be extended into a plane, just as we did before, and this time I'll make that plane light green in color:

It may not be clear that the green plane formed by that rear face of stick 'a' even intersects with stick 'b', however if we swing around to look at things from the other side, it is clear that is does intersect:

So, just like we did in the previous post, I'll disappear that green plane, only to leave its trace upon the floor, a line which runs roughshod over the plan view of stick 'b' at slope:

And, just like with the work we did on the orange plane's ground trace previously, here we not the intersections of the green plane's trace line with stick 'b''s plan, and mark those points as 5, 6, and 7:

Moreover, from 5, 6, and 7, we then project square to the axis of stick 'b''s plan, traveling over to the ground line of stick 'b' in elevation view. We label these intersections 5', 6', and 7' respectively.

Now, since this green plane is parallel to the orange plane we used in the previous blog post, one would think that all lines generated from the green plane's trace would also run in parallel to the lines from the orange plane's face, no? Therefore, if this is true we can run lines up from 5', 6', and 7' up parallel to those lines previously marked out for the orange plane, that the lines that gave us the points 1", 2", and 3":

You can see in the above illustration that from our points 5', 6', and 7', we have run lines parallel to those previously generated, to form new points of intersection, namely 5", 6", and 7". If you're a little confused as to why 5", 6", and 7" are points that require marking, and not other places where the lines cross, take a look again at which lines in the plan view of stick 'b' we crossed originally, giving those first points of 5, 6, and 7.

Here's a closer view showing our new points, the entire point of today's drawing exercise, 5", 6", and 7", formed in much the same pattern as 1", 2", and 3":

Just as before, since the line crossed in plan where we obtained the crossing point labeled 6 was actually the top and bottom arris of the stick, it should come as no surprise that when this line is projected across the elevation view of the stick we would obtain two points of intersection, one on the bottom arris and one on the top.

Now then, in case the reader might not be sure of my assertion that these lines we have generated to points 5', 6', and 7' are to run parallel to the lines we obtained from points 1', 2', and 3', let's just confirm that geometry. You may recall that the way we obtained the slope line crossing the elevation view of stick 'b' was produced by two points. The one at the bottom was the intersection with the trace at point 3, which projected to give point 3', and the point at the other end was found by projecting a line from the top cut view of the stick and meeting the same arris as 3 was marking further down. We should be able to replicate that exact procedure, no?

Here's the projection then of the other side of the top cut of stick 'a':

Notice on the right side is that projection line which met the arris of stick 'b' (plan view) at point 4. We have now projected a line from the other side of that white diamond indicating the top cut, and this meets the arris of stick 'b's plan at point 8.

That line at point 8 then projects at a 90˚ angle to the plan axis of stick 'b', and travel up to the line representing the plane of the top cut of the stick, in elevation, to give us point 8':

Notice that at point 8', the line from point 7, via 7' and 7" drops right in to say hello. Thus we confirm the geometry of that slope, and know that in future we needn't bother with such confirmations when parallel faces are involved.

So, another fine mess we have created here:

Where's it all going? If we look at a view from the rear side, we can hopefully gain some clarity about what has been accomplished so far:

Today we merely repeated what we had done in the previous post, and by using a face which was parallel to the one dealt with earlier we made this pretty much a paint by numbers session. In the next post, we will move yet closer to our objective as we deal with the remaining two planes on stick 'a'. Enterprising readers may wish to forge ahead on their own if they feel confident as to the methodology.

And if you are thoroughly confused, swimming in lines that have lost all relevance or meaning, well, sorry if I managed to confuse anyone. I'm trying to be as clear as I can in my explanation, but I'm sure it could always be improved. As you learn, I learn.

All I can say, is if you feel like you're stuck in the muck, simply start a new drawing and work through the steps again in this series - and again if necessary - until simply be rote copying of what I have illustrated thus far you produce the same drawing. You will find that each time you re-draw you will gain a clearer understanding, if not basic familiarity with what is going on.

Thanks for dropping by the Carpentry Way today. --> go to post 8

## Thursday, December 23, 2010

### X Marks the Spot (VI)

Back at this gem of a French charpente drawing problem. This exercise was sent to me by a reader who in turn received it from his teacher at the American College of the Building Arts, Bruno Sutter. This is the 6th post in the series, with previous entries archived to the right side of the page.

Where we last left off, the work of marking out the basic configuration of the crossing sticks had been established in a 2D format:

Now the more challenging part of the drawing begins, which is the process of using the information we already have on our 2D to determine how the pieces intersect one another. At the end of this process we will have a drawing which we can directly measure and take angles off of, or, from which we could, if the drawing were done full scale, superimpose our pieces of wood upon the drawing and transfer the marks directly to the wood from the drawing to give our cut lines.

Let's just refresh the memory in terms of the basic layout issue here, with the 3D sticks -note that on one stick, piece 'a', I have colored the face we will work on today a different color than the rest, in the interest of clarity:

In the next drawing, I have taken that orange-colored face and extended it into a much bigger plane:

While the plane can run into infinity to the left and right, it is bounded at the bottom by the floor, where the stick terminates, and by the line of cut at the top of the stick. The line along the floor coincided of course with one side of the footprint of the stick, and the line at the top coincides with one edge of the top cut of the stick. Those lines, along the floor and along the top cut, are also parallel to one another and in complete alignment.

Next I have, presto!, disappeared the orange plane and left only the lines which defined it. We are most interested initially in the plane's trace line which runs along the floor:

Obviously, looking at the place where the sticks cross, you can see the lines of intersection formed between the orange face and two of the faces on piece 'b'. The line along the floor from the footprint of piece 'a' also crosses the plan view of piece 'b'.

Let's take a closer look at how that line, the lower trace from the orange plane, and observe how it intersects the lines defining the plan of stick 'b':

Remember that you can click on these pictures to make them larger- in fact, to have any hope of getting a handle on the drawing development as it becomes more complex with each step, you'll want to enlarge every picture. Note in the above picture that I have marked the crossing points of the trace and the plan lines for piece 'b' with small blue circles, numbered 1, 2 and 3. Note that point 2 is in fact crossing two lines which happen to be in the exact same place, as the center line represents the arris of the stick on top and on the bottom.

Now, I'll zoom in a little closer on those crossing point, as I make a departure for new pastures:

You can see that I've extended lines from points 1, 2, and 3 up to the baseline of the elevation view of stick 'b'. Like the lines which produced the elevation view of piece 'b' in the first place, these lines from points 1, 2, and 3 run at a 90˚ angle to the plan of piece 'b'. Where these three lines run into the ground line for piece 'b', I have marked 3 new blue circles, denoted as 1', 2', and 3'.

Let's pan back a little, with no changes to the drawing so you can be sure where we are:

It's very important when you start adding and intersecting lines in these sort of descriptive geometry exercises to be crystal clear about each line, what it does and at which point it is intersecting and why. The three points, 1, 2, and 3, are the points of intersection between the plane, as it traces along the ground, and the plan lines for stick 'b'. Our new points, 1', 2', and 3', are formed as we transfer from the plan view of stick 'b' to the elevation view of stick 'b'. My aim here is to produce a line on the elevation of stick 'b' which depicts that orange plane we saw a few pictures back, to show it crossing stick 'b' in other words. To produce that line, or any line, we need two points to connect. We have already produced three points, 1', 2', and 3', however they are all at the same end so it is not those points we will be connecting. Not quite yet at least. We now need to produce a point on the other end of the plane. Having used the ground trace of the plane already, you might guess that we will now use the trace formed by the plane at the top of piece 'a'.

We'll start by first putting that orange plane, presto!, back into the scene:

Notice again the line which defines the top of the plane, and that it defines a cut line on the the top of the stick at the same time.

If I wanted to relate this upper line to the ground somehow, the most direct way would be to drop a pair of plumb lines down from the top corners of the orange plane:

You can see that where these two plumb lines meet the ground I have indicated it with large blue circles. Like a stone falling into a pond, plop!

Now, if we connect the two encircled blue points we just made, we would have this:

Here's a view from a slightly different vantage point:

The main thing to understand here is that the line we just formed happens to run right through the white diamond defining the top cut of stick 'b'. This line is the trace for the top of the plane, which is also the upper end of the stick.

Now, if you think back to the first few steps we took with the lower trace line in intersecting it with the plan lines for stick 'b', you might expect something similar, process-wise. Your assumption would be correct, however all I'm going to do is deal with one point of intersection between that upper trace and the plan lines of stick 'b':

If you look right in the middle of the above picture, following to the right along the trace line from the white diamond, you will see a small blue circle, marked 4, denoting the point of intersection. This is the point where the upper trace line meets the side arris of stick 'b'.

Again, just as was done with the lower trace points of intersection, where we projected up at 90˚ from the axis of the stick in plan, to form points 1', 2', and 3', we now project point 4 up 90˚ to form point 4':

Now for the grand finale - we connect point 4' at the top of the stick 'b' elevation view, with the point on the bottom of the elevation which corresponds with it. Point 4 and 4' relate the top trace of the plane and the right side arris of the same stick in plan view. Which of the points on the bottom, out of 1', 2', and 3' represents the same arris?

Let's look again at the detail of the intersections down at the foot:

You can see clearly that it is point 3 which intersects the same arris as point 4 does, and therefore it is point 3' which must connect with point 4':

As I have written directly on the above drawing, the line formed between 3' and 4' defines that orange plane of stick 'a' as it slices through piece 'b' in elevation view. How about them apples?

Once we have established the line of the orange plane through stick 'b', we can add a few more lines. As the points 1' and 2' which projected parallel to the line 3~3', they must continue in parallel to the line formed between 3' and 4':

Looking closely at the drawing, you can see that with these new projection lines, from points 1', 2', and 3', we also find new points of intersection with the plan view, at 1", 2", and 3". Recall that earlier in the post I mentioned that where point 2 was formed, at the place where the lower trace crosses the central plan line of the stick, that 2 arrises are represented by that plan line; in the elevation view development above, you can see that there are two points marked with 2", one for each arris, the top and the bottom. The plan view's central line also is representing two arrises, these two being exactly 90˚ rotated from the arris we crossed in plan at point 2.

Well, that's quite enough excitement for one day. In the next post in this series we'll look at what sort of useful fun we can have with the three lines we have just formed upon the elevation of stick 'b' in a drive to define the cut lines needed on stick 'b'.

Thanks for dropping by today, and your outraged comments, or whimpers for mercy, as the case may be, are of course welcome as always. Hope you're having fun with this drawing - I am!

Where we last left off, the work of marking out the basic configuration of the crossing sticks had been established in a 2D format:

Now the more challenging part of the drawing begins, which is the process of using the information we already have on our 2D to determine how the pieces intersect one another. At the end of this process we will have a drawing which we can directly measure and take angles off of, or, from which we could, if the drawing were done full scale, superimpose our pieces of wood upon the drawing and transfer the marks directly to the wood from the drawing to give our cut lines.

Let's just refresh the memory in terms of the basic layout issue here, with the 3D sticks -note that on one stick, piece 'a', I have colored the face we will work on today a different color than the rest, in the interest of clarity:

In the next drawing, I have taken that orange-colored face and extended it into a much bigger plane:

While the plane can run into infinity to the left and right, it is bounded at the bottom by the floor, where the stick terminates, and by the line of cut at the top of the stick. The line along the floor coincided of course with one side of the footprint of the stick, and the line at the top coincides with one edge of the top cut of the stick. Those lines, along the floor and along the top cut, are also parallel to one another and in complete alignment.

Next I have, presto!, disappeared the orange plane and left only the lines which defined it. We are most interested initially in the plane's trace line which runs along the floor:

Obviously, looking at the place where the sticks cross, you can see the lines of intersection formed between the orange face and two of the faces on piece 'b'. The line along the floor from the footprint of piece 'a' also crosses the plan view of piece 'b'.

Let's take a closer look at how that line, the lower trace from the orange plane, and observe how it intersects the lines defining the plan of stick 'b':

Remember that you can click on these pictures to make them larger- in fact, to have any hope of getting a handle on the drawing development as it becomes more complex with each step, you'll want to enlarge every picture. Note in the above picture that I have marked the crossing points of the trace and the plan lines for piece 'b' with small blue circles, numbered 1, 2 and 3. Note that point 2 is in fact crossing two lines which happen to be in the exact same place, as the center line represents the arris of the stick on top and on the bottom.

Now, I'll zoom in a little closer on those crossing point, as I make a departure for new pastures:

You can see that I've extended lines from points 1, 2, and 3 up to the baseline of the elevation view of stick 'b'. Like the lines which produced the elevation view of piece 'b' in the first place, these lines from points 1, 2, and 3 run at a 90˚ angle to the plan of piece 'b'. Where these three lines run into the ground line for piece 'b', I have marked 3 new blue circles, denoted as 1', 2', and 3'.

Let's pan back a little, with no changes to the drawing so you can be sure where we are:

It's very important when you start adding and intersecting lines in these sort of descriptive geometry exercises to be crystal clear about each line, what it does and at which point it is intersecting and why. The three points, 1, 2, and 3, are the points of intersection between the plane, as it traces along the ground, and the plan lines for stick 'b'. Our new points, 1', 2', and 3', are formed as we transfer from the plan view of stick 'b' to the elevation view of stick 'b'. My aim here is to produce a line on the elevation of stick 'b' which depicts that orange plane we saw a few pictures back, to show it crossing stick 'b' in other words. To produce that line, or any line, we need two points to connect. We have already produced three points, 1', 2', and 3', however they are all at the same end so it is not those points we will be connecting. Not quite yet at least. We now need to produce a point on the other end of the plane. Having used the ground trace of the plane already, you might guess that we will now use the trace formed by the plane at the top of piece 'a'.

We'll start by first putting that orange plane, presto!, back into the scene:

Notice again the line which defines the top of the plane, and that it defines a cut line on the the top of the stick at the same time.

If I wanted to relate this upper line to the ground somehow, the most direct way would be to drop a pair of plumb lines down from the top corners of the orange plane:

You can see that where these two plumb lines meet the ground I have indicated it with large blue circles. Like a stone falling into a pond, plop!

Now, if we connect the two encircled blue points we just made, we would have this:

Here's a view from a slightly different vantage point:

The main thing to understand here is that the line we just formed happens to run right through the white diamond defining the top cut of stick 'b'. This line is the trace for the top of the plane, which is also the upper end of the stick.

Now, if you think back to the first few steps we took with the lower trace line in intersecting it with the plan lines for stick 'b', you might expect something similar, process-wise. Your assumption would be correct, however all I'm going to do is deal with one point of intersection between that upper trace and the plan lines of stick 'b':

If you look right in the middle of the above picture, following to the right along the trace line from the white diamond, you will see a small blue circle, marked 4, denoting the point of intersection. This is the point where the upper trace line meets the side arris of stick 'b'.

Again, just as was done with the lower trace points of intersection, where we projected up at 90˚ from the axis of the stick in plan, to form points 1', 2', and 3', we now project point 4 up 90˚ to form point 4':

Now for the grand finale - we connect point 4' at the top of the stick 'b' elevation view, with the point on the bottom of the elevation which corresponds with it. Point 4 and 4' relate the top trace of the plane and the right side arris of the same stick in plan view. Which of the points on the bottom, out of 1', 2', and 3' represents the same arris?

Let's look again at the detail of the intersections down at the foot:

You can see clearly that it is point 3 which intersects the same arris as point 4 does, and therefore it is point 3' which must connect with point 4':

As I have written directly on the above drawing, the line formed between 3' and 4' defines that orange plane of stick 'a' as it slices through piece 'b' in elevation view. How about them apples?

Once we have established the line of the orange plane through stick 'b', we can add a few more lines. As the points 1' and 2' which projected parallel to the line 3~3', they must continue in parallel to the line formed between 3' and 4':

Looking closely at the drawing, you can see that with these new projection lines, from points 1', 2', and 3', we also find new points of intersection with the plan view, at 1", 2", and 3". Recall that earlier in the post I mentioned that where point 2 was formed, at the place where the lower trace crosses the central plan line of the stick, that 2 arrises are represented by that plan line; in the elevation view development above, you can see that there are two points marked with 2", one for each arris, the top and the bottom. The plan view's central line also is representing two arrises, these two being exactly 90˚ rotated from the arris we crossed in plan at point 2.

Well, that's quite enough excitement for one day. In the next post in this series we'll look at what sort of useful fun we can have with the three lines we have just formed upon the elevation of stick 'b' in a drive to define the cut lines needed on stick 'b'.

Thanks for dropping by today, and your outraged comments, or whimpers for mercy, as the case may be, are of course welcome as always. Hope you're having fun with this drawing - I am!

## Tuesday, December 21, 2010

### Ramping Up for New Action, 2

The follow up from yesterday's (er, this morning's) post. I've received emails from people over the past 10 hours wondering about a few points in the sequence that I showed in the previous post depicting the steps to cut a dai to receive a plane blade. Frankly, I wasn't really thinking too much about trying to document every step in the process, and occasionally I simply forget about the camera for a while. So, my apologies if there were a few gaps in the sequence.

At the end of yesterday's post, I had the blade fitted to the dai, nestled in there at a 60˚ angle, sans chip-breaker:

The next steps were to condition the sole of the plane. No pictures, but if readers are interested in a detailed post on how to do that, I'd be happy to oblige at some point in the near future.

Anyway, with the sole conditioned, and the blade sharp, I tried taking a few swipes on some curly bubinga. The result:

No doubt about it, a 60˚ bedding angle means no tear-out in this otherwise recalcitrant material. I could plane in pretty much whatever direction I wanted with no tear out.

Another view:

I then tried to capture a low angle view in flat light to give an idea of the surface quality, but once again my photography skills were not up to the task. I snapped picture after picture and the results were all kinda lame. But what the heck, here's a picture anyhow:

The surface, given the Type 2 shavings produced, is not quite as glassy as can be achieved in some more cooperative plane-friendly woods, but it was nice to have no tear-out and the surface was better, I felt than what I would have produced with a card scraper.

I then grabbed a piece of Canarywood, the material I made that Mazerolle sawhorse from a few months back. I had problems with tear-out at the time. The piece I grabbed had nice straight grain with a slight slope, and seemed about as ideal as possible for regular old planing. So I grabbed my Ichihiro finishing plane, bedded at 37.5˚ or so, and took a pass down one face - it planed perfectly! what could be easier? Then I flipped it over 180˚ and took a pass down the opposite side face, and it tore out - that's Canarywood for you. It's very unpredicatable.

So, I grabbed the new 60˚ plane and cleaned up the tear-out with no issues:

Then I decided to set up a planing beam. I grabbed a chunk of 8/4 Canarywood, and ran it over the jointer and then planed it, finishing out close to 1.8". I set up one end on a window-sill, and then needed to make a stand for the other end. I found a piece of 8" x 8" pine out in the yard, then cleaned it up, jointed it, and then cut the end square. A few swipes with the plane to dress it more tidily:

And it was ready:

Not a perfect surface, but as it rested on the oily floor, I wasn't too bothered.

It was nice to run the plane over some pine after all these pit viper woods the past while, let me tell you!

Here's where I am marking the top of the chunk of pine for the slope of the planing beam:

Time for a little Sawing for Teens:

And that is where I forgot to take more pictures, however I'll be sure to throw in a picture in the next post or so showing the planing beam set up. It works well and the Canarywood is pretty rigid and flat. Nice looking wood too!

Thanks for your visit today!

At the end of yesterday's post, I had the blade fitted to the dai, nestled in there at a 60˚ angle, sans chip-breaker:

The next steps were to condition the sole of the plane. No pictures, but if readers are interested in a detailed post on how to do that, I'd be happy to oblige at some point in the near future.

Anyway, with the sole conditioned, and the blade sharp, I tried taking a few swipes on some curly bubinga. The result:

No doubt about it, a 60˚ bedding angle means no tear-out in this otherwise recalcitrant material. I could plane in pretty much whatever direction I wanted with no tear out.

Another view:

I then tried to capture a low angle view in flat light to give an idea of the surface quality, but once again my photography skills were not up to the task. I snapped picture after picture and the results were all kinda lame. But what the heck, here's a picture anyhow:

The surface, given the Type 2 shavings produced, is not quite as glassy as can be achieved in some more cooperative plane-friendly woods, but it was nice to have no tear-out and the surface was better, I felt than what I would have produced with a card scraper.

I then grabbed a piece of Canarywood, the material I made that Mazerolle sawhorse from a few months back. I had problems with tear-out at the time. The piece I grabbed had nice straight grain with a slight slope, and seemed about as ideal as possible for regular old planing. So I grabbed my Ichihiro finishing plane, bedded at 37.5˚ or so, and took a pass down one face - it planed perfectly! what could be easier? Then I flipped it over 180˚ and took a pass down the opposite side face, and it tore out - that's Canarywood for you. It's very unpredicatable.

So, I grabbed the new 60˚ plane and cleaned up the tear-out with no issues:

Then I decided to set up a planing beam. I grabbed a chunk of 8/4 Canarywood, and ran it over the jointer and then planed it, finishing out close to 1.8". I set up one end on a window-sill, and then needed to make a stand for the other end. I found a piece of 8" x 8" pine out in the yard, then cleaned it up, jointed it, and then cut the end square. A few swipes with the plane to dress it more tidily:

And it was ready:

Not a perfect surface, but as it rested on the oily floor, I wasn't too bothered.

It was nice to run the plane over some pine after all these pit viper woods the past while, let me tell you!

Here's where I am marking the top of the chunk of pine for the slope of the planing beam:

Time for a little Sawing for Teens:

And that is where I forgot to take more pictures, however I'll be sure to throw in a picture in the next post or so showing the planing beam set up. It works well and the Canarywood is pretty rigid and flat. Nice looking wood too!

Thanks for your visit today!

### Ramping Up for New Action

In order to have a shot at working the curly bubinga for the current Ming-inspired table project, I anticipated I would be doing a lot of scraping. With a card scraper, and the acreage of wood needing surfacing, my thumbs were facing a nightmarish scenario. While it wasn't keeping me up at night, or giving me thoughts of skipping town, I was looking into alternatives. So, taking another tack, I was thinking of obtaining a scraping plane, say one made by Lie Neilsen or Lee Valley, but before going that route I decided it would be worthwhile making a plane dai to bed one of my existing plane blades at a steeper angle. If that did the trick, then I wouldn't need to bother with the scraping plane.

Now, I'm not entirely sure exactly what the magic number, in terms of angle, I need to set the plane blade at so as to have no tear out with curly bubinga. To be on the safe side, given that I would be chopping into a carefully hoarded 30-year seasoned piece of Japanese white oak, shirogashi, for the plane's block, I decided to place the blade at a 60˚ angle. I figured that would likely work - if i could pull the 70 mm plane in such a set up.

Now as all those math-heads and battle-scarred SAT veterans know, a 60˚ angle, which is part of a 30-60-90 right-angled triangle, is formed by a right angle with a rise of 1, a hypotenuse of 2, and a run of √3. In a post (<-- a link) way, way back in time, I described how that special 30-60-90 right triangle is found using the compass and the vesica piscis. In this case, cutting to the chase, I used some trig, taking the tangent of a 30˚ angle, and then measuring out a large right triangle using that obtained measure and so produced a 60˚ angle. Then I set my bevel gauge to that angle:

And, with the aid of a try square, transferred the 60˚ line to my precious piece of white oak:

Now, I took way too many photographs today. Over-indulged, you might say, so in the interest of keeping the post to less than 30 photographs, I have to cut out the odd step. Sorry about that.

Once the lines for the plane blade were laid out on the dai, I took it over to the hollow chisel mortiser and made a start on the excavation:

Then, out comes a bench chisel:

A few minutes later, I was digging that proverbial hole to China:

As I got closer to the bottom of the block, I flipped it over and made some preliminary chops on the mouth opening:

A while later, after some vicious kickboxing, I had punched a hole through the mouth:

A view from the other side:

Then I started tidying up the mouth a little bit, using a paring block set at the angle I wanted, which was 80˚:

Then I returned my attention to the top of the dai, and began paring the sidewalls, using a gauging block and, well, would ya lookit that! - the jointer table comes in handy!:

With the side walls of the opening in plane with the sides of the dai -- oh, did I mention that this all began with a dai that was straight and square? -- little details, I know, but an important one, with the side walls ready, I laid out the lines for the side trenches which hold the blade and got out the detail saw:

These little ramps are quite critical parts of the set up and its important to be fussy and get them right.

Once the saw cuts were made, two for each ramp, out comes a skinny paring chisel:

Here's the resulting rough-cut dai:

So all the above hacking and stumbling went fairly quickly, maybe an hour. The next part took quite a while longer - fitting the blade to the mouth.

Attempt 1:

Now, to gauge the fit, what you have to do is find a way to transfer marks from the spots that the blade rubs on. I've tried using pencil/graphite, and I've tried using camelia oil. What I find works the most effectively, however, is neither of those: it is both of them combined together. I rub the blade with a carpentry pencil, then put a few drops of camelia oil on and rub it around, then fit the blade. It works like a charm. At the first attempt, the blade barely fits and there was but one small area of contact:

And then the process is repeated, and repeated, and...well, here's the scene a few steps further along:

Now you can see that the blade is now at least on speaking terms with the dai:

A while later, and they're starting to get real friendly, like:

You could say this is the beginning of a beautiful friendship, though things are definitely touch and go:

Now, in the early stages of fitting the blade, I use a chisel to slice the points of contact down. That allows the blade to move down in a reasonable amount of time. but as one gets closer and closer to the final fit, just like with joinery work, it is the time to slow down and do a little less with each round of material removal. some people like to use a file, or a file with a burr rolled on one end, however I like to use a bottom-scraping chisel or soko-zarai nomi, to make those fine adjustments in the final hour or so of fitting:

You can tell you're getting closer, not only by how far down the blade goes, but by how completely the surface is blackened by the blade rubbing on the wood:

A while (or was it a lifetime?) later I had the blade within a millimeter of peeping out:

This is the view at that point inside the mouth:

If the blade were driven down much further, it would run into the escapement, and if I wasn't paying attention might split the wood out. Not a great thing to have happen. I made a second paring pass on that 80˚escapement using the paring block, just to make a little room. I want the mouth to be fairly tight, but I'm not obsessive about that. The tightness of the mouth opening plays a role in getting good results, but I haven't found it to be extremely critical.

Once I made a few more tweaks, the blade was down. What I aim for is a fit where the blade fits snugly all the way around the lower end of the back of the blade, just before the blade bevel begins. You can see the dark even mark formed by that area of the blade in this picture:

Okay, well there it is, a 60˚ version of a 70 mm Funahiro Tenkei:

The working surface, prior to tuning:

As for how/if it works, well, stay tuned for a follow-up post.

Thanks for taking the time out to check in on things here, and I hope to see you again soon. --> go to post 2

Now, I'm not entirely sure exactly what the magic number, in terms of angle, I need to set the plane blade at so as to have no tear out with curly bubinga. To be on the safe side, given that I would be chopping into a carefully hoarded 30-year seasoned piece of Japanese white oak, shirogashi, for the plane's block, I decided to place the blade at a 60˚ angle. I figured that would likely work - if i could pull the 70 mm plane in such a set up.

Now as all those math-heads and battle-scarred SAT veterans know, a 60˚ angle, which is part of a 30-60-90 right-angled triangle, is formed by a right angle with a rise of 1, a hypotenuse of 2, and a run of √3. In a post (<-- a link) way, way back in time, I described how that special 30-60-90 right triangle is found using the compass and the vesica piscis. In this case, cutting to the chase, I used some trig, taking the tangent of a 30˚ angle, and then measuring out a large right triangle using that obtained measure and so produced a 60˚ angle. Then I set my bevel gauge to that angle:

And, with the aid of a try square, transferred the 60˚ line to my precious piece of white oak:

Now, I took way too many photographs today. Over-indulged, you might say, so in the interest of keeping the post to less than 30 photographs, I have to cut out the odd step. Sorry about that.

Once the lines for the plane blade were laid out on the dai, I took it over to the hollow chisel mortiser and made a start on the excavation:

Then, out comes a bench chisel:

A few minutes later, I was digging that proverbial hole to China:

As I got closer to the bottom of the block, I flipped it over and made some preliminary chops on the mouth opening:

A while later, after some vicious kickboxing, I had punched a hole through the mouth:

A view from the other side:

Then I started tidying up the mouth a little bit, using a paring block set at the angle I wanted, which was 80˚:

Then I returned my attention to the top of the dai, and began paring the sidewalls, using a gauging block and, well, would ya lookit that! - the jointer table comes in handy!:

With the side walls of the opening in plane with the sides of the dai -- oh, did I mention that this all began with a dai that was straight and square? -- little details, I know, but an important one, with the side walls ready, I laid out the lines for the side trenches which hold the blade and got out the detail saw:

These little ramps are quite critical parts of the set up and its important to be fussy and get them right.

Once the saw cuts were made, two for each ramp, out comes a skinny paring chisel:

Here's the resulting rough-cut dai:

So all the above hacking and stumbling went fairly quickly, maybe an hour. The next part took quite a while longer - fitting the blade to the mouth.

Attempt 1:

Now, to gauge the fit, what you have to do is find a way to transfer marks from the spots that the blade rubs on. I've tried using pencil/graphite, and I've tried using camelia oil. What I find works the most effectively, however, is neither of those: it is both of them combined together. I rub the blade with a carpentry pencil, then put a few drops of camelia oil on and rub it around, then fit the blade. It works like a charm. At the first attempt, the blade barely fits and there was but one small area of contact:

And then the process is repeated, and repeated, and...well, here's the scene a few steps further along:

Now you can see that the blade is now at least on speaking terms with the dai:

A while later, and they're starting to get real friendly, like:

You could say this is the beginning of a beautiful friendship, though things are definitely touch and go:

Now, in the early stages of fitting the blade, I use a chisel to slice the points of contact down. That allows the blade to move down in a reasonable amount of time. but as one gets closer and closer to the final fit, just like with joinery work, it is the time to slow down and do a little less with each round of material removal. some people like to use a file, or a file with a burr rolled on one end, however I like to use a bottom-scraping chisel or soko-zarai nomi, to make those fine adjustments in the final hour or so of fitting:

You can tell you're getting closer, not only by how far down the blade goes, but by how completely the surface is blackened by the blade rubbing on the wood:

A while (or was it a lifetime?) later I had the blade within a millimeter of peeping out:

This is the view at that point inside the mouth:

If the blade were driven down much further, it would run into the escapement, and if I wasn't paying attention might split the wood out. Not a great thing to have happen. I made a second paring pass on that 80˚escapement using the paring block, just to make a little room. I want the mouth to be fairly tight, but I'm not obsessive about that. The tightness of the mouth opening plays a role in getting good results, but I haven't found it to be extremely critical.

Once I made a few more tweaks, the blade was down. What I aim for is a fit where the blade fits snugly all the way around the lower end of the back of the blade, just before the blade bevel begins. You can see the dark even mark formed by that area of the blade in this picture:

Okay, well there it is, a 60˚ version of a 70 mm Funahiro Tenkei:

The working surface, prior to tuning:

As for how/if it works, well, stay tuned for a follow-up post.

Thanks for taking the time out to check in on things here, and I hope to see you again soon. --> go to post 2

Subscribe to:
Posts (Atom)