Mechanisms, Mobility & Motion Conversion

The machine

This course designs and builds one machine: a treadle lathe, the foot-powered lathe that turned chair parts and tool handles in shops before electric motors. You stand at it, rock a long treadle with one foot, and a pitman (a connecting rod) turns a crank on a heavy flywheel; a belt from the flywheel spins the spindle fast. It’s a good teaching machine because every topic in machine design shows up in it, and the whole thing can be built in a home shop from oak, ash, a few bearings, and a shaft.

Start by writing what it has to do, before drawing any parts:

Turn a comfortable foot stroke of about 9 inches at about 100 strokes a minute into continuous rotation, store enough energy to carry through cuts and dead points, and drive a spindle at roughly 400 to 750 rpm.

Then compare ways to do it: a spring-pole lathe (a cord around the work, a springy pole overhead) cuts only on the down-stroke and reverses every stroke; a crank and flywheel turns continuously. Continuous rotation wins for spindle turning, so the drive is a crank, which makes it a four-bar linkage.

Four links

Look at the drive from the side and count the parts that move relative to each other:

1. the frame, fixed: the line from the treadle pivot to the flywheel shaft, about 28.8 inches;
2. the crank on the flywheel shaft: 3 inches from shaft to pin;
3. the pitman: 16 inches, from the crank pin down to the treadle;
4. the treadle: pivoted at the back near the floor, with the pitman attached 24 inches out and the foot pad at 36 inches.

Count the freedom

For a planar linkage, Kutzbach’s equation counts degrees of freedom: M = 3(n − 1) − 2j₁ − j₂, where n is the number of links including the frame, j₁ the one-freedom joints (pins), and j₂ the two-freedom joints. Four links and four pins give M = 3(3) − 8 = 1: one input, the foot, sets the position of everything. It’s a screening count: odd geometry can still bind, which is why the next check matters.

Is it a crank-rocker?

Grashof’s criterion decides whether any link can turn all the way around. Call the shortest link s, the longest l, and the other two p and q. If s + l ≤ p + q, at least one link rotates fully; which one depends on where the shortest link sits ¹:

• shortest link is a side link (pinned to the frame): crank-rocker, with the shortest link as the crank;
• shortest link is the frame: double crank;
• shortest link is the coupler: double rocker;
• s + l > p + q: every link only rocks ¹.

Here s = 3 (crank), l = 28.8 (frame), p + q = 16 + 24 = 40. Since 3 + 28.8 = 31.8 ≤ 40 and the crank is pinned to the frame, it’s a crank-rocker: the crank goes all the way around while the treadle rocks. If you’d made the crank 13 inches, the sum would pass 40 and the flywheel could never complete a turn.

Stroke

Solving the geometry through a full turn: the treadle swings about 14°, the pitman pin moves 6 inches up and down (twice the crank), and a foot pad 36 inches from the pivot moves about 9 inches, the stroke in the requirement. A longer crank gives more stroke and more torque per push but a bigger swing; a shorter one, the reverse. The crank length is how you tune it to a leg.

The transmission angle, between the pitman and the treadle, stays between about 78° and 104°, close to the 90° that transmits force best ¹. That matters because forces through the pitman act along it; near 90° they turn things instead of just squeezing the pins.

The dead points

Here’s the catch. A crank-rocker is usually driven from the crank. A treadle drives it backward, from the rocker, and that creates dead points: when the crank and pitman line up, at the top and bottom of the crank’s circle, a push from the pitman only squeezes or stretches the crank along its length, and can’t turn it ¹. Stop the lathe there and no amount of pushing on the treadle will start it.

There are two standard answers: inertia carries the crank through, or the dead point is avoided by arrangement ¹. A treadle lathe uses the first: a heavy flywheel stores enough energy to coast through each dead point and through the cut, and you start it by giving the wheel a pull by hand. The next lesson sizes it.

What to take from this

Write the motion requirement first, then compare mechanisms. The treadle drive is a four-bar with one degree of freedom (Kutzbach M = 1). Grashof (3 + 28.8 ≤ 16 + 24, shortest link a side link) makes it a crank-rocker. The crank length sets the stroke: 3 inches gives a 6-inch pin stroke and about 9 inches at the foot. Driving from the treadle creates two dead points, so the design needs a flywheel.