How do linkages make walking legs? Trace a foot path and build a walker

A linkage is a set of beams joined by pins so they move together. Turn one beam round and the others swing, slide or tilt in a fixed pattern. A walking leg is a linkage where one point on a moving beam (the foot) draws a path with a long flat bottom and a lift on the way back. Turn the crank, and the foot steps.

You don't need many parts to see this. Four beams in a loop already draw surprising shapes, and walking machines like the Klann linkage simply add more beams to shape the step.

Start with four bars

The simplest useful linkage has four bars in a loop. One bar is fixed to the frame: the ground. The crank turns all the way round on one end of the ground. The rocker swings back and forth on the other end. The coupler joins the tips of the crank and the rocker.

The crank pin only draws a circle and the rocker tip only draws an arc. The coupler is the interesting one: it slides and tilts at the same time, so any point on it, or on a plate fixed to it, draws a closed loop called a coupler curve. Pick the right point and that loop has a flat side. That flat side is a foot pushing along the floor.

The linkage idea page explains pins, beams and loops with more examples.

Will it turn all the way round?

Not every set of four bars works as a crank. There is a simple check, named after the engineer Franz Grashof. Add the shortest and the longest bar. If that is less than the other two added together, the shortest bar can turn all the way round. If it is more, nothing turns fully and the "crank" can only rock. If one bar is as long as the other three together, the loop cannot even join up.

For a walker you want a crank-rocker: the Grashof sum holds and the crank is the shortest bar.

Trace a foot path

Try it below. Start with the step-like preset, guess the shape the foot will draw, then turn the crank and watch the red pen. After one full turn the whole path appears as a dashed line with dots placed every 10° of crank. Where the dots bunch up, the foot is moving slowly. Where they spread out, it is moving fast. Walker designers look for an even stride on the floor, because a foot that slows and speeds up makes the machine lurch.

Then go for the walking-leg goals. Change one bar at a time and watch the Grashof readout: you will find lengths that stop the crank, lengths that make a figure of eight, and a few that make a proper step. Try the "Chebyshev-ish straight line" preset to see a famous linkage where the middle of the coupler moves almost straight, and notice that its crank can only rock.

Linkages you can hold: the Lazy-Tongs Grabber

The Lazy-Tongs Grabber is a level 2 build of about 20 minutes and a friendly first linkage. It is a chain of X shapes on smooth pins. Squeeze the handles and the criss-cross arms shoot out to grab things far away. It shows the key linkage idea with no crank at all: change the angle at one joint and every other joint follows.

The Scissor Lift (level 3, about 45 minutes) uses the same X shapes stood on end. A crank and worm drive a rack, the rack squeezes the scissor legs, and the platform climbs straight up.

From turning to pushing: the Twin-Piston Engine

The Twin-Piston Engine (level 3, about 40 minutes) is a crank-slider: a four-bar linkage where the rocker has been swapped for a piston sliding in a guide. Turn the crankshaft by hand and round-and-round becomes up-and-down. The two crank pins sit on opposite sides, so the pistons move in turns. The crank-slider page shows the same linkage in car engines and pumps.

A four-bar at work: the Nodding-Donkey Pump Jack

The Nodding-Donkey Pump Jack is a level 3 build of about 45 minutes, and its instructions name the loop directly: base, crank, pitman arm and walking beam make a four-bar linkage. A motor turns a worm, the worm turns a 24-tooth gear 24 times slower, and the short crank on that gear rocks the long beam. A wheel on the back end acts as a counterweight, so the motor only has to nudge the beam. Load the "Pump jack nod" preset in the lab to see the same short-crank, long-beam idea.

Legs: the Klann Walking Spider

The Klann Walking Spider is the big one: level 4 and about 60 minutes. One L motor drives an 8-tooth gear, a 40-tooth gear and a 24-tooth gear on the crankshaft, so the crankshaft turns three times slower than the motor. Eight beams turn the spinning crankshaft into steps. Its instructions suggest turning the crankshaft by hand first: the feet draw a flat line on the floor, then lift and swing back. The two cranks point opposite ways, so diagonal feet step together and the spider always has feet on the ground.

The Klann leg has more than four bars, but each extra bar does the job you practised in the lab: it reshapes the path so the flat part is longer and the lift is higher.

The spider lists the motor buggy and the XL Power Crane as earlier builds, so check those first if you are new to motors. More moving machines live in the machines collection.

Check yourself