Gear generator

Matthias Wandel is a woodworker who has created a wonderful, interactive wooden gear template generator. I'd love to port some of these ideas to a MEL script within Maya so I can automate 3D gear creation.

Il volo instrumentale

This is a wooden kit made by The Imagination Factory that I'd like to build. There are other kits for different da Vinci machines out there, but this one seems to be in a class of its own.

More coiling rope

I liked the results of the bend deformer, so I applied it to my rope geometry. I then created a sort of "if-then" statement that makes the rotation of the ratchet wheel cause the rope to move upwards. It looked good, but I needed to keep the rope end on the axle from slipping. I added a second condition that moves the rope out, away from the center as it winds onto the axle.

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Rope coil test

Another bit of rigging I need to think about is coiling the rope. This is a test I did moving a curve up into a bend deformer. I'm a big fan of pushing curves and meshes into deformers. Think of the deformer as a sort of distorted space (like a black hole) sitting there waiting to bend things that enter it.

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Rigid body dynamics simulation

I'm using a rigid body dynamics simulation to get the pawl to react properly when the ratchet rotates clockwise.

Here's what I did:

• I turned the ratchet into a passive rigid body, meaning it collides with active rigid bodies, but it is unaffected by external forces.
• I turned the pawl into an active rigid body, so that it reacts to forces (such as gravity) and collisions (the ratchet bumping into it). This would normally send it flying off into space, like a baseball being hit by a bat, so on to the next step.
• I added a hinge constraint to the pawl rigid body. I moved this constraint to the center of the pawl's rod end. This prevents the pawl from moving, and forces it to rotate about a single axis. I also created a gravity field to pull the pawl back down once it's bounced up a bit.
  

Attention to detail

My friend Phil Zucco, an awesome 3D modeler and all-around great guy, pointed out to me that I'd modeled my ratchet with too few teeth, compared to the da Vinci sketch. I have no idea what I was thinking and how I managed to do that. My intention was to count the teeth and build a cylinder with twice the number of spans as teeth. I wasn't even close!
So, here's a the new, correct (I hope) ratchet.

Ratchet and pawl

Here is a description of the ratchet and pawl, from Cornell University's wonderful Kinematic Models for Design Digital Library:

The ratchet and pawl mechanism allows motion in one direction but locks it in the other direction. In this sense it acts in the same way as a diode in an electrical circuit or a check value in a water pipe. The ratchet and pawl was often used with a winch or windlass, a horizontal drum with a rope or cable attached, which allowed the rope to be wound onto the cylinder but prevented the cylinder from unwinding the rope. Reuleaux was fascinated with ratchet mechanisms and designed several different models to illustrate the different motions and uses of the ratchet. In his machine design book The Constructor (1893), he defined the ratchet in the similar way as Leonardo da Vinci; "The object of the ratchet is to check the action of certain portions of a machine and so modify an otherwise continuous motion into some intermittent form." (Page 150). The use of control valves in steam engines and internal combustion engines in the 19th century to regulate speed represented the beginnings of automatic control of machines. Reuleaux recognized the importance of control but did not have the mathematical concepts to describe it. He saw instead the special digital nature of ratchet mechanisms, on or off, as having special significance in machine regulation and created several models to express the role of ratchets in machine control devices.

Ratchet UVs

I've applied a checkerboard texture to each piece of the model. At first, the checkers look stretched out. After correcting the UV mapping coordinates on each model they look much more uniform.

If you're new to the concept of UV mapping, you'll probably still remember this one from school: how do you wrap a flat map around a globe, and vice versa? That's the same sort of problem as UV mapping. The answers lie in various types of projections. I used a mix of planar and cylindrical projections, along with some automatic layout tools and a bit of manual editing.

Once each object has reasonably good UV mappings, I'll be able to create materials for them, such as wood, rope, and iron.

Ratchet working file

Here is the current working file of the 3D ratchet model, in case anyone wants to use it. I'm hosting it on a free service called MediaFire. Later, I'll put stuff up on TurboSquid, which is an online model shop.

I'm placing all of my work under Creative Commons attribution licensing, which means you can use it for anything you feel like, including commercial purposes, so long as you give credit to the original creator (me!).

Ratchet modeling continues

I've beveled all of the edges and added a couple of parts. I think this is meant to have a central hub around which the rope wraps. Starting to think about rigging, too. Rope is not straightforward in rigging, so I may end up rebuilding the rope model in a straight line, and then using the rig I build to coil it over the hub.

Ratchet bevel

Here is the beveled version of the ratchet wheel. Perfectly sharp edges give CG models a kind of unrealistic perfection. By rounding out all the edges, I've introduced a little bit of an organic, realistic quality.

Ratchet model proportions

I've used some simple polygonal objects (cube, cylinder, torus) and pushed around some of their vertices to mass out these forms. I may need to go back and add beveled edges later so that they look nice when rendered.

Ratchet wheel image plane

One way to get the proportions of the 3D model is to import a drawing into your 3D modeling software. I'm using Maya, so this is what it looks like with the da Vinci sketch imported as an image plane. This just serves as a guide for me as I build the model. I'll eyeball the proportions to match, even though the drawing isn't perfectly flat (orthographic).

Ratchet wheel translation

For the sake of having fun with this, I'm going to avoid existing research as much as possible and just try to see what the da Vinci notes and sketches themselves reveal.

In order to do this, I've convinced my Mom (who is Italian, with a degree from the University of Rome) to see what she can translate from these notes.

I've flipped the notes to "un-mirror" them, since Leonardo wrote many of his notes in a mirrored script. I think I read once that this was probably to avoid smearing the ink, since he was a lefty.

Ratchet wheel design

This is the first simple mechanism I plan to create. It is taken from Codex Milan I.

Transmission

Here is an example of Leonardo's notes from Codex Atlanticus, and the type of system I'll be reproducing using Maya.