# Pendulum Wave Derivation and Bill of Materials I posted a while ago that I had worked out some of the math for a pendulum wave. Attached are PDF files detailing the derivation of my specific variation of the pendulum wave and the corresponding bill of materials.

Pendulum Wave Tutorial (PDF)

Pendulum Wave Bill of Materials (PDF)

There is small problem with the bill of materials. On page 6 (arm dimensions), I have only one of the two arm types shown. Looking from the assembly drawing on the first page, it should be clear that the cut and grooved side of the arm alternates for each pendulum. The first and last arms should have inward-facing grooves.

## Screeching Billy

### Image This is a small project that I hope to finish before too long. I still need to fix his brain and put his body together. When finished, he will screech very shrilly, then plot what he hears in spherical coordinates.

# Origami Buckyball

I’ve begun work on a rather largish buckyball. Below is a section that will end up composing about 1/12 of the finished thing. There will be 12 sections of 4 colors (yellow, blue, green and red), or 3 sections of each color. I’m not exactly sure how I will connect these sections; I suppose I’ll find out when/if the time comes. Yes, that is an Escher in the background.

# Spherical Configuration of Rounded Gears – A Derivation

Introduction

While sitting at my desk one day, I wondered how to model a spherical configuration of rounded gears (SCORG). Where does each gear need to be positioned? How should each gear be sized in such a way as to share the same diametral pitch with all other gears? How does the size of each gear affect the overall dimensions? Crappy sketches

## Pendulum Wave Demonstration With Matlab

### Video

I’ve decided to build a pendulum wave and write an Instructable to document the process.

In the meantime, here’s a matlab demonstration showing how I hope it will behave. Matlab function is posted after the video.

``` %Created by Eric Cox - https://ericboy.wordpress.com - 5/17/2012```

function [] = PWT(n,f,df,t)

%This function plots pendulum wave motion as seen from the top view.
%
% n is the number of pendulums, f is the frequency of the first pendulum
% in the wave, df is the incremental change in frequency between pendulums
% (added), t is the time to display the animation

%set initial time to zero.
t_n=0;

%preallocate lengths of matrices.
y=(1:n);
x=(1:n);

while (t>t_n)

%for each value in x,y matrices, populate with value at current t.
for j=1:n
x(j)=j;
y(j)=sin(2*pi*(f+(j)*df)*t_n+pi/2);
end

%Plot pendulum wave
plot(x,y,’o’,’MarkerEdgeColor’,’k’,…
‘LineWidth’,2,…
‘MarkerFaceColor’,’b’,…
‘MarkerSize’,11);

%Define axis
axis([0 n+1 -1.5 1.5]);

%Increment loop time
t_n=t_n+1/30;

%Animation delay
pause(1/30);

end

# Spherical Gear Configuration

7/27/12 – Update: I have posted the process and calculations for creating a spherical gear configuration here.

For a while now, I’ve thought about how awesome it would be to have a spherical configuration of bevel gears with a surface radius of curvature equal to that of the sphere composed. I have made great progress in figuring out the math. If I find time, I might post the calculations in the next month or so. I haven’t added the teeth yet, but that will come sometime after finals.

I spoke to the dean of mechanical engineering at my school, and he gave me permission to build a solid model using the department’s rapid prototyping facilities. So, solid model coming summer 2012! 🙂

Here is the rendering I have so far: 