X-axis progress

Now that we have the new spindle on our mill, and the linear rail+ballscrew conversion for the Z-axis have been working for a while, it's time to upgrade the X and Y axes.

Jari has made some good progress on the table/X-axis. The IKO 15 mm linear rails are mounted, we've machined and attached the bearing holders for the ballscrew, made a motor mount for the servo, and also worked on the steel saddle plates. The new talbe is much bigger than the old one, and will allow about 500mm of X-axis movement. That's going to be enough to machine fin and bulb moulds for an IOM in one go - something that we can't do right now.

Here's a close-up of the motor mount, all parts machined from aluminium using our own mill. There's room for a coupler between the 12mm motor shaft and the 8mm ballscrew end. The motors we are using are 1.6 Nm continuous torque DC brush motors from Camtronics. Keeping to the KISS principle, we are hoping the motors are strong enough to work in direct-drive (no belt reduction or gears).

This photo shows the ballscrew (16mm diameter, 2.5mm pitch, from metallstore.de), the ball-nut, and the X-saddle plate with some steel bars under it to make room for the ballnut. Next up is a similar assembly for the Y-axis. That's going to be a bit more complicated since the parts will eventually have to be mounted on the very mill we are making them with! Hopefully not too many iterations of disassembly/assembly will be required...

Jari has also made a new tool-holder:

Micro Magic

Timo brought along his latest toy, a Micro Magic, to our annual radiosailing winter meeting. This thing really is small compared to a Marblehead or an IOM! It's an all 'plastic-fantastic' ABS moulded boat, but you do have to glue the deck to the hull in this Racing version of the kit. The vitals are LOA=554 mm, Beam=178 mm, Weight=980 g, Height=980 mm.

The fin and rudder are made of ABS plastic, and the bulb is lead. There are different sized bits that can be inserted fore and aft of the fin in the finbox to adjust the position of the fin for different conditions.

An arm-winch controls both sails, the mainsheet on the left side of the boat and the jibsheet on the right. Timo is using a micro-servo for the rudder, but I understand standard sized ones are used too.

There's one central hatch with a rubber seal, but I doubt it's watertight enough to be used without tape on top.

The standard carbon mast is 5 mm in diameter, and comes with two sidestays, but Timo has made some more rigs using 6/4 mm carbon tube and intends to use these rigs without sidestays. A bit surprisingly rule-writers around the world have usually not put an upper limit to the number of rigs, so I understand some skippers have made up to 5 or 6 different rigs! (the smaller ones all fit within the biggest one)

In terms of number of boats/skippers the Micro Magic is a definite success with ca 1000 or more boats registered in both Germany and the Netherlands. It makes you think that the traditional international radio sailing classes (IOM, M, 10R, A) have somehow failed since they have not as far as I know attained similar popularity. Marketing wisdom tells us that this must be because of the five Ps: Product, Place, Price, Packaging, Promotion. (I'm leaving 'Product' last in my ramblings below, since I have the most doubts about this P)

Price: the Micro Magic wins hands down over an IOM or any other international radio sailing class. The whole MicroMagic kit with the tall rig, a basic two channel radio, and everything you need to go sailing costs about the same (300 EUR) as three suits of sails for an IOM. By comparison, I estimate a competitive IOM with three rigs and radio from a commercial builder costs about 2000 EUR. Home building a boat to the same standard and performance is not much cheaper.

So does price really matter? Die-hard radio sailors usually say no: travelling to events, staying in hotels, spending all that leisure time racing etc. constitutes a much bigger investment than the price of the boat. For someone who travels internationally every year and to all big events nationally it probably doesn't matter if the boat costs 500 eur, 1000 eur or 2000 eur. But for the beginner it does matter! I see very few newcomers to competitive IOM racing in Finland - maybe that's because of the high price tag? To really get into the class you need a competitive, watertight, and fully functional secondhand, or almost completely built new boat, and that's going to cost you about 2000 eur...

Place: go to the local hobby store, hand them your credit card, and within 1-2 days you will be on the water sailing this boat. Depending on your country, getting an IOM is either a lot harder or just a bit harder. There are no industrial builders (The Robbe Windstar is not really a competitive IOM), so you can't buy an IOM from a hobby store, and the salesperson in the shop is not likely to even know there exists such a thing as an IOM class. All manufacturers are small, most amateur hobbyists and a handful of professionals, and usually sell boats in kit-form to keep down the cost. In countries where there are no commercial builders the situation is even worse. The seasoned radio-sailors do know the international suppliers, some personally, but a newcomer is quite unlikely to send a big amount of money to an unknown builder in a foreign country (and wait the usual 4-12 weeks delivery time).

Packaging/Promotion: Probably about equal between an IOM and a MicroMagic. Promotion will largely depend on what class your local club sails I guess.

Product: Here's where my doubts are. When moving from a Marblehead (4-5 kg weight, 1.3 m length) down to an IOM, the boat felt very nervous, unstable, and hard to sail in the beginning. An IOM is also definitely harder to trim for neutral balance. This was a move down in length from 1.3 m to 1 m, and in weight from about 4.5-5 kg to 4 kg. I haven't sailed a MicroMagic yet, but we must be talking about a completely different behaviour at 55 cm overall length and < 1 kg displacement.

On the other hand, do skippers want a boat that sails and handles gracefully, like a full-scale boat, or are most skippers just looking for a level playing field where they can have fun racing the boats? If the latter is most important, then there must be a bright future for boats like the MicroMagic. In reality very few people have time to design and build their own boat, so I don't think this argument against industrially produced boats really holds.

All of this seems to indicate smaller and industrially produced is better. But there must also be some kind of scale effect: If I show my IOM to someone on the street I'm sure most people would recognize it as more than a toy, capable of racing in widely varying conditions etc. Show the same people a MicroMagic and they will definitely think 'toy'.

This is an interesting topic, so I'd love to hear some thougs from my readers:

  1. I clearly haven't done my homework well enough, so could someone fill me in on the numbers of boats in the big countries for the various 'industrially' made classes: MicroMagic, RC-Laser, Victoria, etc.
  2. How does the MicroMagic sail in different conditions? preferably from people who have a solid background in Marblehead or IOM racing! How does it compare to an RC-Laser?
  3. If you have some deep thoughts on how to make a radio sailing class really succeed I'm also interested.

Offset Ellipse

Continuing with some random thoughts on CAM algorithms, here's a diagram I drew in response to a question on offset ellipses posed by Julian Todd.

(click image for high-resolution version)
The task is to find an offset ellipse to a given ellipse (magenta). The offset ellipse (blue) should lie a distance T, measured along the normal to the ellipse (I've drawn one normal of length T in green), from the original ellipse. Drawing the offset ellipse is simple, but it's a bit harder to find a point on the offset for a given x-coordinate x=k. I've marked this point with a circle, and its coordinates are (k, E(k)), so E(k) is a function that returns the sought y-coordinate.

I took Julian's advice of using a numerical method with respect to the geometry (not neccessarily cartesian coordinates), and parametrized the ellipse as a function of an angle t. So points along the ellipse lie at:

ex=a*cos(t)
ey=b*sin(t)

Where a and b are the major and minor axes of the ellipse, and t is an angle between 0 and 2pi. At every point there's a normal vector

nx = b*cos(t)
ny = a*sin(t)

To find points on the sought offset ellipse, we need to scale this normal so it's length is T. Each normal has a length

l=sqrt(nx^2 + ny^2)

So the sought normal vector is

nx_T = (nx/l)*T
ny_T = (ny/l)*T

or more explicitly

nx_T = ( b*cos(t) / sqrt((b*cos(t) )^2 + (a*sin(t))^2) ) * T
ny_T = ( a*sin(t) / sqrt((b*cos(t) )^2 + (a*sin(t))^2) ) * T

Now, points on the offset ellipse lie at

oe_x = ex + nx_T
oe_y = ey + ny_T

and we need to find the particular t angle which results in a point (oe_x, oe_y) for which oe_x = k holds. Inserting the above expressions, this happens when:

(a+T*b/sqrt( ( b*cost(t) )^2 + ( a*sin(t) )^2 ))*cos(t) -k = 0

I haven't looked for an analytic solution to this equation, but plotting it for a few test cases seems to indicate that it's fairly 'benign', and Matlab's fzero function finds a solution very quickly. If we call the solution to this equation tk, the sought point on the offset ellipse is

E(k) = oe_y(tk)

Here are two Matlab scripts I used to plot this figure: ellipsetest.m is the main program, and oe.m is used when solving the equation.

Defining a milling cutter

Some discussion over at the freesteel blog about defining a general purpose milling cutter shape in a CAM program.

I made this diagram (which hereby is in the public domain) to make it all clear in my head:

(click image for svg file)

It shows one half of the cross-section of the cutter (the axis of rotation is at the right edge of the image). There's a cylindrical part of height ha with radius a, a conical part of height hc that tapers down to radius c, and finally toroidal part of height hf.

The idea is that by writing all CAM algorithms to deal with this tool shape, nothing has to be changed when locating cylindrical, conical, ball-end, or bullnose cutters against the model. All these cutter shapes are different variants of this general shape.

A general purpose CAM program would test this cutter shape against a triangulated model. There are four surfaces on the tool, s1, s2, s3, and s4. These all need to be tested agains the model. There are also three edges (e1, e2, and e3), but only e1 needs to be separately checked against the model since if e2 or e3 were touching the model, so would the adjecent surface.

Compression strut for Gooseneck

Two new parts for the gooseneck: a compression strut from Sails ETC, and a DIY mast-ram.

The compression strut fits the lower end of the gooseneck (bottom left), and if you bend it a little bit, it will fit a Sails ETC eyebolt too (far right) - which I plan to use on the boom. The mast-ram consists of a plastic fitting (Maritim) that grabs the mast, a stainless steel M4 bolt (I need to open the plastic fitting a little so the head of the bolt sinks into the plastic). A brass M4 thumbwheel (Ruuvikulma) provides adjustment.