# Twin Elliptic Pendulum Harmonograph Drawings

### Ratios Larger Than 1:1

The Twin Elliptic Pendulum Harmonograph combines two separate conical motions around a single axis by suspending a “deflector” pendulum below the main pendulum. There are several different ways to configure a Twin Elliptic Pendulum, but they are usually comprised of a moving drawing table with a pen arm that floats up and down vertically from a separate fixed support.

**Interesting Properties of the Twin Elliptic Pendulum**** **

With the Twin Elliptic Pendulum, a **1:1** ratio cannot be achieved. The nicest drawings are produced when the ratios are higher, such as with a **3:1** or **5:3 **ratio. It can be demonstrated that when both pendulums are rotated in the same direction (*concurrent *motion) at a ratio of **X:Y,** the drawings produce **X-Y** cusps (or loops); and if the pendulums are rotated in opposite directions (*counter-current* motion), then a ratio of **X+Y** cusps is produced. When the **X** and **Y** are both odd, symmetrical drawings are produced in both *concurrent* and *counter-current *pendulum motion (examples: **3:1** or **5:3** ratios). The **2:1** motion produces a *deltoid* figure and the **3:1** produces the *asteroid*; with more complex hypocycloids created at other ratios.

**Motion and Ratio Adjustments**** **

It takes a bit of practice to achieve *counter-current* motion with the Twin Elliptic Pendulum. It also takes some practice (and a bit of trial and error) to produce a perfect “tuning” of the pendulum periods so that precise ratio’s of motion can be achieved. As a simple rule of thumb: You *increase* the ratio by either raising (or lightening) the upper pendulum; or lowering (or adding weight) to the lower deflector pendulum. Note that frictional dampening becomes more apparent as the **x** and **y** are increased.

*Click on the drawings below to see them full sized.*