# A different linear transmission mechanism

Thinking about Babbage's mechanism for transmitting linear motion from one place to another, I realized that the extent of motion is multiplied based on the proportional lengths of the arms. However, I want the extent of motion to be exactly the same on both ends, which limits the flexibility of the arms-on-an-axle mechanism.

Instead, I came up with a different mechanism which has the flexibility to have whatever routing is desired, in whatever direction is desired.

Here we see two horizontal rods. Assume the left rod is the driven rod, while the right rod is the following rod. The two vertical things are levers with slots cut in the bottom which allow the lever to move. The pivots on the lever are spaced apart the same distance as the ends of the rods, so that a line drawn from the ends of the rods, through the levers, and through pivots forms a parallelogram. The levers are also the same size, and their pivots are at the same distance along the levers.

When we push the left rod, it pushes the left lever which pivots, pulling on the wire. The wire in turn pulls on the right lever. Because the wire, levers, and pivots form a parallelogram, the right rod is forced to move the same distance and direction as the left rod.

The spring on the right is required because when the left rod is pulled back, the wire cannot be pushed by the lever. I use the spring to tension the wire and pull back the right lever.

The force on the wire depends on the mechanical advantage of the lever, and the angle of the wire relative to the lever. Ideally, the wire should leave perpendicularly to each lever.

If it is not practical to route a wire directly from point to point, we can wind the wire around pulleys like so:

The pulleys can be placed close to or far away from the levers, and again the wire should ideally leave the levers perpendicularly. We can even place more pulleys if multiple changes in direction are required.

In place of the lever pivot, we could use a fixed pulley, so that the wire can leave at any angle desired.

The wire could be made of steel, stainless steel, copper, or brass. I'm pretty sure mid-19th century engineers had access to such metallic wire.

Some possibilities for wire (from McMaster-Carr):

 Alloy Diameter (0.001 in) Min. Tensile Strengh* (1000 lb/sq in) Price, 1/4 lb spool, per foot Yield Force (lb) 260 Brass 20 50 \$ 0.041 15.7 25 50 \$ 0.060 24.5 32 50 \$ 0.095 40.2 1006 Steel 14 60 \$ 0.008 9.24 23 60 \$ 0.019 24.9 29 60 \$ 0.027 39.6 35 60 \$ 0.039 57.7 302 Stainless Steel 7 75 \$ 0.015 2.89 10 75 \$ 0.026 5.89 25 75 \$ 0.047 36.8 32 75 \$ 0.074 60.3 99.99% Copper 6 34 \$0.003 0.961 10 34 \$0.008 2.67 20 34 \$0.027 10.7 25 34 \$0.042 16.7 32 34 \$0.066 27.3

*There are different tensile strengths. I've tried to use yield strength, since that is the point after which permanent elongation of the material occurs, which is a Bad Thing. If I couldn't find the yield strength, I just used whatever was listed as tensile strength. Keep in mind that yield strength could be as little as on the order of around 1/2 that of ultimate strength, so a wide safety margin is a good idea.

I tried to choose the softest alloy, since I think softness and flexibility would go together. It wouldn't be very good to choose a wire used to form springs (i.e. a hard alloy) for a wire that goes around pulleys. Also, the thicker a wire is, the less flexibility it has.

With flexibility, though, comes a price: the wire will break and deform more easily. I haven't done any experiments yet to see if using wire is a good idea.

In terms of price, we have 1006 Steel < 99.99% Copper < 302 Stainless Steel < 260 Brass, and in terms of strength we have 99.99% Copper < 1006 Steel < 302 Stainless Steel < 260 Brass.

So it seems that the 99.99% Copper and 1006 Steel alloy wires are possibilities, the other alloys being too expensive and too stiff.

Another possibility instead of metals is to use fiber. Catgut (which is not from cats, although it is made from intestines!) was known for hundreds of years prior to the 19th century, and was, and still is, used in musical instruments, badminton and tennis racquets, hunting bows, and as surgical sutures. All of these require high tensile strength (being required in sutures for knot-tying).

However, since I wouldn't need the special harmonic or dissolving properties of catgut, I think I can safely substitute a modern synthetic fiber without calling it cheating. And, of course, that means nylon line. Nylon monofilament line has a tensile strength of about 75000 psi, and I can get 0.014 inch diameter line (12 pounds breaking strength) for a crazy \$0.0015 per foot from any fishing supply. This is as strong as the strongest metal wire, more flexible than any, and cheaper than any.

Nylon it is!