Guidance

Linkage Fundamentals, the nine parts from class, then how to turn a linkage into a robot and how to document it. Keep this page open while you're in the simulator, in Onshape, and at the bench.

One motor, one circle, one footstep

Your walker gets a single TT motor. It can only spin a crank in a circle. The linkage has to turn that circle into a step: flat along the floor, then up and back for the next one.

A Theo Jansen walking leg. The crank is labeled motor, the chassis is ground, and the foot traces a dashed path with a flat bottom — A Theo Jansen leg, drawn from his published link lengths. The dashed curve is the foot path: flat on the bottom (foot on the floor) and arched on top (foot lifting and returning).

By the end of the unit you can answer nine questions about any linkage:

Vocabulary. What are the parts called?
Coupler curves. What paths can a linkage draw?
Degrees of freedom. Can one motor drive it?
Grashof condition. Will the crank turn all the way?
Kinematic inversion. What if another link is ground?
Transmission angle. Will the motor bog down?
Time ratio. How long is the foot down?
Assembly modes. Which way did it go together?
Scaling. How big should it be?

Then: the design checks, building it, the TT motor, gears, wiring the switch, the build log, and the gallery walk.

The design process

Same six steps as every project. Steps 4 and 5 are a loop, and on this project the loop has two places to happen: the simulator first, then the wood.

Model it, build it, run it for 15 seconds, fix it, run it again. Record every pass through that loop.

Define the problem. Read the brief. In your notebook, write the goal and every rule in your own words.
Research and brainstorm. Look at real walkers. Sketch several leg ideas and build them in the Linkage Designer.
Pick a solution. Run the design checks on your best ideas and compare them against the hook: distance in 15 seconds.
Prototype. Model it in Onshape, then cut and build it. See building it.
Test and evaluate. Run it, find what fails, fix it, and record it. See change tracking.
Communicate. Your build log and the gallery walk.

1 · Vocabulary: links, joints, and the ground

A link is a rigid body

A binary link with 2 joints, a ternary triangle link with 3 joints, and a quaternary link with 4 joints — We assume a link never bends or stretches. Only its joints let it move. Links are named by how many joints they carry: binary = 2, ternary = 3, quaternary = 4. The triangles in a Jansen leg are ternary links.

Shape doesn't matter. Joint locations do.

A triangle, a bent bar, and a plate with holes, all with pins at the same three points — All three links have pins at the same three points (dashed triangle), so they move identically.

Design freedom: bend or reshape a link to clear another part or the motor.
Save material: lightening holes cut weight and laser time without changing the motion.

Joints connect links and allow specific motion

A revolute pin joint, a prismatic slider joint, and a cam with a point contact — **Lower pairs** have surface contact: pins and sliders. Each allows exactly 1 motion. **Higher pairs** have point or line contact: cams and gear teeth. They often allow rolling and sliding. Almost every joint on your walker will be a pin.

Ground is a link too

Left, a loop of four links floating freely. Right, three links on two fixed pivots, with the dashed distance between the pivots as the fourth link — A chain becomes a mechanism once one link is fixed to ground.

Ground (frame) is the link that doesn't move. On your walker, it's the chassis.
The fourth bar of a four-bar is the distance between its two fixed pivots (the dashed line). Most people count three bars. Count four.

The four-bar linkage: named roles

A four-bar linkage with the crank, coupler, rocker and ground labeled, and a coupler point tracing a dashed loop — The coupler point (red dot) is a point on the coupler plate, not on the line between its pins. Its path is the dashed curve. On a walker, the foot is almost always a coupler point.

Role	What it does
Crank	Rotates a full 360°. The motor drives it.
Coupler	The floating link. Never touches ground.
Rocker	Swings back and forth (oscillates).
Ground	Fixed frame between the pivots.

Input = the driven link. Output = the link doing useful work.

Walker connection

On every walking leg	is the
Chassis	Ground
Motor shaft	Crank
Foot	A point on a coupler, or on a link further down the chain

A Jansen leg is just several four-bar loops chained together. Understand one four-bar and you can read any leg, one loop at a time.

Vocabulary in the MIT Linkage Designer

In the tool	What it is
Ground node	Fixed pivot attached to the chassis
Simple node	Revolute joint (pin)
Linkage	Link (rigid bar between nodes)
Select motor	Marks the crank: the input link
Select target	The point whose path is traced (the foot)
DOF readout	Mobility of your mechanism (part 3)

Try it. Build the four-bar above. Ground two nodes, link them up, select the crank as motor and a coupler point as target, then press Simulate. decode.mit.edu/links

Check: name the parts

A slider-crank: a short crank on a fixed pivot, a long connecting rod, and a block sliding on a rail — Slider-crank (engine or pump).

Which link is ground?
Which link is the crank?
Which link is the coupler?
What kind of joint connects the block to the rail?
Is that joint a lower pair or a higher pair?

2 · Coupler curves: the paths a linkage can draw

Every point traces a path

A four-bar where a crank point traces a circle, a rocker point traces an arc, and a coupler point traces a complex closed curve — **Crank points** trace circles. **Rocker points** trace arcs. **Coupler points** trace complex closed curves: teardrops, figure-eights, near-straight lines. The coupler is the only link that both moves and turns, which is why the foot goes on it.

Where you put the foot changes everything

One four-bar with three different points on its coupler plate, each tracing a different curve — **Same linkage:** same four link lengths, same crank. Only the point on the coupler plate changes. **Different paths:** moving the point a short distance can turn a loop into a figure-eight. In the simulator, Select target lets you try many points fast.

An atlas of curves

A grid of nine different coupler curves, all from four-bar linkages — All nine curves come from four-bars. In 1951, Hrones and Nelson published an atlas of thousands of them, and designers paged through it to find the shape they needed. The teal curve has a nearly straight edge: Chebyshev's lambda linkage, below. Your job in the simulator: search for a curve that looks like a footstep.

Straight-line linkages become footsteps

Chebyshev's lambda linkage. Its coupler point traces a curve with a long straight edge (stance) and an arch (swing) — Chebyshev's lambda linkage: crank 1, ground 2, rocker 2.5, coupler 5, with the rocker pinned at the coupler's middle.

Stance: the nearly straight edge. The foot moves level along the floor without bobbing.
Swing: the arch. The foot lifts, clears the floor, and returns for the next step.

Chebyshev's 1878 walking machine hung its feet below a frame carried by this point, so the flat edge became the step on the floor.

3 · Degrees of freedom: can one motor drive it?

Degree of freedom (DOF)

The number of independent inputs needed to fully define a mechanism's position. Count what's left after the joints, and you know how many motors it needs.

A single link lying in a plane with arrows for sliding in x, sliding in y, and rotating — A free rigid body in a plane has 3 DOF: slide in x, slide in y, rotate by θ. Every joint you add takes some of that away.

Joints remove freedom

Joint	Allows	Removes	Counts as
Pin (revolute)	1	2	j₁ (full joint)
Slider (prismatic)	1	2	j₁ (full joint)
Cam / rolling + sliding	2	1	j₂ (half joint)

Grübler's equation

Planar mobility

M = 3(n − 1) − 2j₁ − j₂

M = mobility (degrees of freedom). n = number of links, including ground. j₁ = full joints (pins and sliders). j₂ = half joints (cam-type contacts).

3(n − 1): every moving link starts with 3 freedoms. Ground is fixed, so subtract it. Then each full joint removes 2 and each half joint removes 1.

Worked examples

Four mechanisms side by side: a triangle, a four-bar, a five-bar, and a six-bar — Count the links and joints on each picture before you read the table.

Mechanism	n	j₁	M	What it means
Triangle	3	3	3(2) − 6 = 0	A structure. Nothing moves.
Four-bar	4	4	3(3) − 8 = 1	One input controls it. What we want.
Five-bar	5	5	3(4) − 10 = 2	Needs two inputs. With one motor, part of it flops.
Six-bar	6	7	3(5) − 14 = 1	Back to one input, with richer motion.

What M tells you

M	Name	What happens
M < 0	Over-constrained	Statically indeterminate. Binds unless dimensions are perfect.
M = 0	Structure	Nothing moves. Good for a rigid frame. The motor stalls.
M = 1	Your target	One motor fully controls the mechanism.
M ≥ 2	Under-constrained	With one motor, part of it hangs loose and flops.

A single-motor walker must be M = 1. Check this before you cut a single part.

Gotcha 1: several links on one pin

Three links sharing one pin, counted as two joints — A pin joining m links counts as m − 1 joints. This shows up at the crank pin of most walkers, where two or three links ride on the same pin. Miss it and your M will be wrong.

Gotcha 2: the equation counts topology, not geometry

Left, an exact parallelogram with a redundant middle link that still moves. Right, a slightly-off version that binds — **Special geometry:** n = 5, j₁ = 6 gives M = 0, yet the exact parallelogram moves. The middle link is redundant. **Shop lesson:** a design that only works with perfect dimensions will bind once laser kerf or hole slop gets in. Avoid it.

Worked example: a full Jansen leg

Jansen leg

n = 8 · j₁ = 10 · M = 3(8 − 1) − 2(10) = 21 − 20 = 1

Links (8): ground, crank, 2 triangles, 4 bars. Joints (10): 1 + 2 + 2 + 1 + 2 + 1 + 1. Three pins each carry three links, so each counts as 2 joints. Miss that and you get M = 7.

More legs, same motor

Add a second Jansen leg to the same crank and the same frame:

6 new links × 3 freedoms each +18

9 new joints × 2 freedoms each −18

Net change in M 0

Each extra leg shares the crank and the frame, so its links and joints cancel out. The whole robot stays at M = 1, which is exactly why one TT motor can drive every leg.

In the simulator: check the DOF counter

Sketch a linkage on paper and compute M by hand.
Build it in the Linkage Designer.
Compare your M with the DOF readout. If they disagree, recount.
Now build a linkage with DOF = 0 on purpose. Try to simulate it.
Then build one with DOF = 2. What happens when you drive it?

Notebook. Record each linkage's n, j₁ and M, and a screenshot of the DOF readout. Note any case where your count and the tool disagreed, and why.

Practice: find M

Practice A: a slider-crank — A. Slider-crank

Practice B: a four-bar with an extra diagonal link — B. Four-bar + diagonal

Practice C: a six-bar with two triangle links — C. Six-bar (two triangles)

For each one: count n (include ground), count j₁ (watch shared pins), then compute M. We go over the answers in class.

4 · The Grashof condition: will the crank turn all the way?

A Jansen leg with one four-bar loop colored in: crank, coupler, rocker and ground. The rest of the leg is faded — The four-bar is the simplest linkage with M = 1 that uses only pins. The colored links on this Jansen leg form one four-bar. Check each loop, and you've checked the leg.

First question for every loop: can the crank turn a full 360°? A motor spins forever, so it has to.

Grashof's condition

s + l < p + q

s = shortest link. l = longest link. p and q = the other two. Count all four links, including ground.

Bars 2 and 6 end to end make 8. Bars 4 and 5 end to end make 9. 8 is less than 9, so Grashof — **Read it like this:** lay the shortest and longest end to end. If that's shorter than the other two end to end, the linkage is Grashof: at least one link can turn all the way around.

Three possible outcomes

Three linkages: a Grashof one whose crank turns a full circle, a non-Grashof one that jams at two red X marks, and a change point that can flip into a crossed shape — Dashed curves show where each crank tip can go. Red X marks are where the non-Grashof crank jams. Your walker needs the first one. A change point (s + l = p + q) does turn, but it can flip into its crossed shape when all four links lie flat.

Which link is shortest?

Three linkages built from bars 6, 2, 5 and 4: a crank-rocker, a double-crank, and a double-rocker — All three pass Grashof. Which link is shortest decides what kind of linkage you get.

The shortest link is…	Type	Motor on a fixed pivot?
Next to ground	Crank-rocker	Yes, on the shortest link
The ground	Double-crank (drag link)	Yes, both side links turn fully
The coupler	Double-rocker	No. Neither link on the ground turns all the way.

Worked example

A: ground 6, crank 2, coupler 5, rocker 4

Sort: 2, 4, 5, 6. So s = 2 and l = 6.
s + l = 2 + 6 = 8
p + q = 4 + 5 = 9
8 < 9 → Grashof
Shortest is the crank, next to ground → crank-rocker ✓

B: shorten the coupler to 3

Sort: 2, 3, 4, 6. So s = 2 and l = 6.
s + l = 2 + 6 = 8
p + q = 3 + 4 = 7
8 > 7 → non-Grashof
Nothing turns all the way. A motor on the crank jams.

Changing one link by 2 units flips the answer. Build both in the simulator: A spins freely, and B's crank stops partway.

Check a real leg: Jansen's crank loop

The Jansen crank loop with lengths 15, 50, 41.5 and 38.8 marked — Lengths from Theo Jansen's published leg dimensions.

Ground	distance between the fixed pivots	√(38² + 7.8²) = 38.8
s + l	crank + coupler	15 + 50 = 65
p + q	rocker + ground	41.5 + 38.8 = 80.3
Result	65 < 80.3 → Grashof. The crank (15) is the shortest link and sits on a fixed pivot: a crank-rocker. ✓

Practice: classify each linkage

	Ground	Side 1	Coupler	Side 2
A	7	2	6	5
B	3	7	8	6
C	7	5	2	6
D	5	3	4	7
E	6	2	6	2
F	6	4	5	2

Side 1 and side 2 are the two links pinned to the ground. Type: crank-rocker, double-crank, double-rocker, non-Grashof, or change point. Bonus: for each crank-rocker, which side gets the motor? We go over the answers in class.

Rule for your walker

A crank-rocker with the motor driving the shortest link, which is pinned to the chassis — The motor drives the shortest link.

Every loop that contains the crank passes Grashof: s + l < p + q (not equal).
The crank must be the shortest link in its loop, or the ground must be.
Most walkers use a crank-rocker: the motor turns the shortest link, which is pinned to the chassis.

In the simulator: if your crank stops partway or snaps to a new shape, check Grashof first.

In the Design Lab: the Four-Bar Analyzer runs the Grashof test on your four lengths, names the type, and marks where the crank jams.

5 · Kinematic inversion: same links, different ground

The same four bars, 6, 2, 5 and 4, shown four times, each time with a different bar fixed to the chassis — Bars 6, 2, 5 and 4, pinned in the same order every time. The only change is which bar is bolted to the chassis (the thick one). Colors follow each bar, not its role: the 2 is always orange.

Why the Grashof table works

One sentence

In a Grashof chain, the shortest link can turn all the way around relative to every other link.

Fix…	What happens	Type
A neighbor of the shortest (the 6 or the 5)	The shortest spins around a fixed pivot.	Crank-rocker
The shortest (the 2)	Both neighbors spin around it.	Double-crank
The link across from it (the 4)	The shortest still spins, but it isn't on the ground.	Double-rocker

Try it: four inversions in the simulator

Build the 6-2-5-4 chain with the 6 as ground and the motor on the 2.
Rebuild with the 2 as ground, then the 5, then the 4.
Each time, put the motor on a link touching the ground and simulate.
Record which links turn all the way and which only rock.

Notebook. Copy this table: Ground · Turns fully · Rocks · Type, with a row for each of 6, 2, 5 and 4. Add a screenshot of each inversion and circle the link the motor drives.

6 · Transmission angle: why a linkage can look great and still stall

The force from the coupler split at the rocker pin into a part that turns the rocker and a part that pushes on the pivot — The coupler can only push or pull along its own length. The part of that force across the rocker turns it. The part along the rocker just loads the pivot.

Definition	μ is the angle between the coupler and the rocker.
Near 90°	Most of the coupler's force turns the rocker.
Near 0° or 180°	The force mostly squeezes the joints. Friction rises and the motor bogs down.

Keep μ between 40° and 140° all the way around.

Same Grashof test, very different μ

Two crank-rockers at their worst position: ground 6, crank 2, coupler 5, rocker 4 with mu 51 degrees, and ground 6, crank 3, coupler 4, rocker 6 with mu 26 degrees — Both pass Grashof. Only the left one keeps μ in the safe range. The simulator shows both moving fine — it doesn't model friction or motor torque. The motor feels the difference.

μ all the way around

Graph of transmission angle against crank angle. The 6-2-5-4 linkage stays inside the 40 to 140 degree band. The 6-3-4-6 linkage drops below 40 near 0 and 360 degrees — Shaded band: the 40°–140° guideline. Orange fill: where the 6-3-4-6 linkage drops below it.

Worst positions: μ is smallest and largest when the crank lines up with the ground, at 0° and 180°.
Shortcut: you don't need the whole graph. Check those two positions.

Worked example: find the worst μ

A four-bar with the triangle formed by the coupler b, the rocker c, and the diagonal L from the crank tip to the rocker pivot — Linkage: crank a = 2, coupler b = 5, rocker c = 4, ground d = 6.

Law of cosines

cos μ = (b² + c² − L²) ÷ (2bc)

L is the diagonal from the crank tip to the rocker pivot. At 0°, L = d − a. At 180°, L = d + a. Calculator in degree mode.

	Crank at 0°	Crank at 180°
L	6 − 2 = 4	6 + 2 = 8
cos μ	(25 + 16 − 16) ÷ 40 = 0.625	(25 + 16 − 64) ÷ 40 = −0.575
μ	51.3°	125.1°

51° to 125°: inside 40°–140° ✓. Your turn: ground 6, crank 3, coupler 4, rocker 6.

Toggle positions

Motor drives the crank: the rocker just reverses at each toggle. No problem.
If the rocker drove: crank and coupler line up, so pushing can't turn the crank. It locks. That's why the motor always drives the crank, and why a hand-turned prototype can catch at the same spot every turn.

In the Design Lab: the Four-Bar Analyzer plots μ all the way around the turn, shows the two toggle positions, and tells you how many degrees fall outside 40° to 140°.

7 · Time ratio: slow stroke, quick return

A crank-rocker with ground 7, crank 2, coupler 5, rocker 7, and its crank circle split into a 197.6 degree slow stroke and a 162.4 degree fast stroke — Linkage: ground 7, crank 2, coupler 5, rocker 7. The toggle positions split each crank turn into two unequal parts. The motor turns at a steady speed, so the angle ratio is the time ratio.

Time ratio

Q = slow angle ÷ fast angle = 197.6° ÷ 162.4° = 1.22

Reverse the motor and the slow swing goes the other direction.

Worked example: find Q

The triangle formed at the extended toggle and the triangle formed at the folded toggle — At each toggle, the crank and coupler form one straight side of a triangle, so the law of cosines gives the crank angle directly.

Crank angle at a toggle

cos φ = (d² + side² − c²) ÷ (2 · d · side)

side = a + b when extended, b − a when folded.

Extended: side = 7. cos φ₁ = (49 + 49 − 49) ÷ 98 = 0.5, so φ₁ = 60.0°
Folded: side = 3. cos φ₂ = (49 + 9 − 49) ÷ 42 = 0.214, so φ₂ = 77.6°
The folded crank points the other way: 77.6° + 180° = 257.6°
Slow = 257.6° − 60.0° = 197.6°. Fast = 360° − 197.6° = 162.4°
Q = 197.6 ÷ 162.4 = 1.22

Compare: the 6-2-5-4 linkage has Q = 1.02, almost even.

Walker connection: duty factor

The Chebyshev foot path beside its crank circle, split into a 239 degree stance and a 121 degree swing — Same idea as the time ratio, applied to the foot instead of the rocker. In the simulator, note the crank angle when the foot reaches the flat part of its path and when it leaves.

Duty factor

duty factor = stance angle ÷ 360° = 239° ÷ 360° ≈ 0.66

The Chebyshev foot is on the floor for about two thirds of every crank turn.

Why stance should be more than half

Two timelines of two legs 180 degrees apart. With 66 percent stance the bars overlap. With 40 percent stance there are gaps with no foot down — Each row is one leg on the same side, driven by the same crank, 180° out of phase.

Stance over 50%: with two legs 180° apart, at least one foot is always down.
Stance under 50%: there are moments with no foot down. The body drops or drags. This is also why Jansen uses three legs per side, 120° apart.

In the Design Lab: Leg and Foot Path finds your leg's stance angle and duty factor, and tells you whether a foot is always down. It splits the foot path a little differently from the slide, so it gives 248° for the Chebyshev leg, not 239°. Either is fine.

8 · Assembly modes: two ways to put the same links together

The same 6-2-5-4 linkage assembled open and assembled crossed, with completely different coupler curves — The red curves are the paths of the same coupler point in each mode: completely different.

Same lengths: same crank angle, different shape and foot path.
Can't switch: you'd have to take it apart to change modes. It only happens if parts get pinned together the wrong way.
Check it: compare your build to your drawing before you blame the design.

In the simulator, editing a length can make the solver pick the other mode. It looks like the linkage suddenly flipped.

9 · Scaling: bigger stride, bigger load

The Chebyshev linkage at full size with a stride of 4.7, and scaled 1.5 times with a stride of 7.0 — Multiply every link by k and the foot path keeps its shape. The stride grows by k: 4.7 × 1.5 = 7.0. Angles don't change, so μ, the time ratio, and the duty factor all stay the same.

Design move: find the shape you like in the simulator first, then scale it to the stride you want.

The trade-off

Scale every link by k, and…	changes by
Stride	× k
Foot speed at the same crank speed	× k
Motor torque for the same load	× k
Weight	heavier: longer links weigh more

Walking speed

speed ≈ stride × crank turns per second

Each crank turn moves the robot about one stride, as long as the feet don't slip. Multiply by 15 for your distance.

	Speed	In 15 s
Original	4 cm × 1.5 turns/s = 6 cm/s	90 cm
Scaled 1.5×, motor slows a little	6 cm × 1.2 turns/s = 7.2 cm/s	108 cm
Scaled 1.5×, motor slows a lot	6 cm × 0.9 turns/s = 5.4 cm/s	81 cm

A closer estimate. One stride per turn is right for a single leg. With two or more legs sharing the work, a foot is always pushing, so each turn moves the robot about stride ÷ duty factor. That's more than one stride. Motor and Speed in the Design Lab works it out for your leg and your motor.

Made-up crank speeds — you'll measure real ones in the Motor Lab. See the TT motor for the datasheet numbers. A TT motor slows down as its load goes up. A bigger walker is only faster if the motor doesn't slow down by more than the stride grows.

The design checks

Run every one on paper or in the simulator before you cut a single part. Show the work in your notebook. These are what Research and Brainstorm is scored on.

M = 1. Count ground, and count shared pins as (links − 1) joints. Part 3.
Grashof on every loop that contains the crank: s + l < p + q, not equal. Part 4.
The motor drives the shortest link in its loop (or the ground is shortest). Part 4.
Worst transmission angle between 40° and 140°. Check the crank at 0° and 180°. Part 6.
Stance more than half a turn, or legs phased so a foot is always down. Part 7.
No design that only works with perfect dimensions. Kerf and hole slop will make it bind. Part 3, gotcha 2.
Your build matches your drawing. Same assembly mode. Part 8.

Check your answers · Design Lab

Four-Bar Analyzer: Grashof, transmission angle, toggle positions, and time ratio.
Leg and Foot Path: stride, duty factor, body bob, and the torque it takes to lift the robot.
Motor and Speed: the Motor Lab, then a prediction of how far your robot walks in 15 seconds.

The lab checks your math. It doesn't replace it. Your notebook still has to show every step by hand.

Building it: from the simulator to wood

Hole centers are your link lengths. The distance between two holes on a link is the length from the simulator. Everything else about the shape is yours to change — see shape doesn't matter.
Put link lengths in Onshape variables (for example #crank, #coupler) and use them for every hole spacing. When a check fails, you change one number instead of redrawing the part.
Every pin is a standoff or a bolt. Threaded standoffs, or spacers with a bolt through. A moving link has to turn freely on its pin without wobbling off it. Test the fit on scrap wood before you cut every link.
Plan the stack. Links that cross each other sit on different layers. Spacers keep them from rubbing. The crank pin usually carries two or three links — that's gotcha 1 in real life.
The chassis is ground. The fixed pivots and the motor all mount to it, so the distance between fixed pivots on the chassis is a link length too.
Shoes. Rubber bands, hot glue, or anything else with grip on the feet. Every slipped step is distance you don't get.

Read Making Parts before you send anything to the laser cutter or the printer.

The TT motor

The blue TT motor is two things in one: a small DC motor that spins very fast, and a 1:90 gearbox that slows it down. The output shaft turns once for every 90 turns of the motor inside. You lose speed and gain torque.

These numbers come from the manufacturer's datasheet.

From the datasheet	Value	What it means for you
Gear ratio	1:90	Already geared down. Your own gears add to this.
Voltage	3 to 6 V DC	Your 4.8 V pack is inside the range.
Starting voltage	1.2 V (1.6 V max)	The least voltage that gets it turning with no load.
Direction	Either way	Swap the two wires to reverse it.
Mounting	Any position	Upright, sideways, or upside down all work.
No load, at 3 V	130 rpm · 0.10 A	Its top speed at 3 V, with nothing attached.
Stalled, at 3 V	0 rpm · about 1.0 A	Jammed: ten times the current, and no motion.

Converting speed

turns per second = rpm ÷ 60

130 rpm ÷ 60 ≈ 2.2 turns per second. That's the number that goes into speed ≈ stride × crank turns per second.

Load slows it down

The datasheet's motor curve at 3 volts. A blue speed line falls straight from 130 rpm with no load to 0 at stall. A straight black current line rises. A pink power hump peaks in the middle, and a dashed efficiency hump peaks to the left — From the datasheet, tested at 3 V. Load (torque) increases to the right. **Blue line:** speed, falling straight from 130 rpm to 0 at stall (left scale). **Straight black line:** current, climbing from 0.10 A to about 1.0 A. **Pink hump:** power out, highest in the middle, where the speed is about 65 rpm. **Dashed hump:** efficiency, highest at 99 rpm. The humps use the right-hand scale.

Every bit of drag is load. Weight, binding joints, rubbing links, and a bad transmission angle all slow the crank. That's why a bigger walker is only faster if the motor doesn't slow down more than the stride grows (part 9).
Aim for the left half of the graph, between best efficiency (99 rpm at 3 V) and most power (about 65 rpm). If your crank is crawling, you're close to stall. Cut the load (lighter links, fix binding, better μ) or add a gear reduction (below).
Stalled is bad for everything. It pulls about ten times the no-load current, drains the batteries, and heats the motor. If the robot jams, switch it off right away.
Your pack is 4.8 V, not 3 V, so it turns faster than these numbers. A DC motor's speed rises roughly with voltage, so expect somewhere near 200 rpm with no load, and less with legs attached. That's an estimate. Measure your real motor in the Motor Lab.

Sizes for your CAD

The datasheet's dimension drawing of the TT motor, top view and side view, in millimeters: 64.4 long overall, gearbox 37 long, 22.4 wide and 18.6 thick, shaft 5.4 across with flats 3.7 apart sticking out 8.7, and a peg 4 across and 1.92 tall — From the datasheet. All sizes in mm. The 9 and 20 are measured from the mounting hole. This drawing is the single-shaft version, so check your biaxial motor with calipers before you cut.

The shaft is a double D: 5.4 mm across, with two flats 3.7 mm apart. Cut that exact shape into your crank or gear, so it grips the flats and can't spin on the shaft.
The shaft sticks out 8.7 mm. That's all the length your crank or gear has to grab, so keep the parts on it thin.
The locating peg is 4 mm across, 1.9 mm tall, and 11 mm from the shaft, on the same face. Give it a hole in the chassis, or the motor will rock.
The gearbox is 37 × 22.4 × 18.6 mm, and the whole motor is 64.4 mm long. Leave room for it, and for the wires on the motor end.
Mounting holes: bolt through the holes in the gearbox. The datasheet doesn't give their size, so measure them.

One motor, every leg: gears

The blue TT motor is biaxial: its output shaft comes out both sides. That gives you a crank on each side of the chassis for free. Legs that ride on the same crank pin share its timing.

To reach a crank farther away — front legs and back legs, for example — you need gears. Laser cut them or 3D print them.

One way to reach two cranks from one motor. Both crank gears mesh with the motor gear, so they turn the same way at the same speed, and their crank pins stay locked 180° apart. The dashed circles are the pitch circles: they touch where the gears mesh.

Gear ratio

ratio = driven teeth ÷ driver teeth

Crank turns per second = motor turns per second ÷ ratio. Plug that into speed ≈ stride × crank turns per second. A bigger ratio gives more torque but a slower crank, so it only helps if the motor was bogging down.

Gears only mesh if their teeth are the same size. Make every gear in your train with the same tooth size, and set the center distance so the pitch circles just touch.
Set the phase when you mesh them. Turn each crank to where you want it, then slide the gears together. Write the phase angles in your notebook — two legs 180° apart, three legs 120° apart.
Gear teeth are a higher pair. If you add gears to your Grübler count, each mesh is a j₂ joint. The cranks still have to come out at M = 1.

Wiring the switch

The switch goes in one of the two wires, in series with the motor. Off opens the loop, so no current flows. If the robot walks backward, swap the two wires at the motor.

Mount the switch where you can reach it without grabbing a leg. On test day, the clock starts when it goes on.
Strain-relieve the wires. Tape or tie them to the chassis so a moving link can't catch one and rip it off a motor tab.
Charge your batteries before test day. Tired batteries mean a slower crank and a shorter walk.

The build log

There's no formal presentation on this project. Instead your team makes a build log: one Google Slides deck, attached to the Google Classroom assignment, that tells the story of your robot in pictures. It's open on a laptop at your station during the gallery walk, and it's where stages 1–4 of the rubric are scored from.

Build it as you go. Photos taken the night before can't show a prototype you already took apart.

What goes in it, in order

The problem. The goal and every rule in your own words, and which rule limits you most.
Notebook pages: brainstorms. Photos of your leg sketches and research, and screenshots of the foot paths you tried in the simulator.
Notebook pages: the computations. Your degrees of freedom (M = 1), Grashof, and transmission angle work for the leg you picked, every step shown, and why you picked it. Add a screenshot of the leg in the MIT Linkage Designer.
CAD screenshots. The links, gears, and chassis in Onshape, and the assembly. Show the variables you used for link lengths.
Prototype versions and change tracking. A photo of every version, and its entry in the change-tracking table below.
Final build. Photos of the finished robot from the side and from above, and your best 15-second distance.

A notebook page with a sketched leg linkage and its mobility count — A notebook page: sketch, link lengths, and the M count beside it.

An Onshape assembly of a walking robot — A CAD screenshot: the assembly, with link lengths as variables.

An early walking robot prototype on the bench — A prototype photo: version 1, before it worked.

Change tracking

One row for every version. Write your guess at the cause before you fix it, even if it turns out wrong. Make one change per version when you can, so you know what made the difference. Give the Onshape parts the same version numbers: coupler_v3.

Version	What failed	Our guess at the cause	What we changed	Distance in 15 s
v1	Curved left. Back legs dragged.	Rear crank was 90° off the front one, not 180°.	Re-meshed the rear gear so the cranks sit 180° apart.	31 cm
v2	Bogged down at the same spot every turn.	Transmission angle too small. Worst μ was 26° at crank 0°.	Rebuilt the loop as 6-2-5-4, scaled 1.5×. Worst μ now 51°.	40 cm
v3	Feet slipped on the tile.	Bare wood has no grip.	Rubber band shoes on every foot.	72 cm

An example, not a real team's log. Yours will have more rows.

The gallery walk

Like an art gallery opening, not a presentation. Every team sets up a station: the robot, ready to run, and the build log open on a laptop. People wander from station to station, try the robots, and ask questions. You talk them through your project in a normal conversation.

Part of the time you're at your station explaining. Part of the time you're the visitor at other stations. Each of you is scored on your own, so everyone on the team needs to be able to explain the whole robot — not just the part they built.

Be ready to answer

How does one motor drive every leg? Point to the crank, coupler, rocker, and ground.
What's your M? Show the count.
Does your crank loop pass Grashof? What's your worst transmission angle?
What's your gear ratio, and how are the legs phased?
What broke, what did you change, and what did the distance do?
What would you change next?

When you're the visitor, run their robot, and ask at least one real question. "What was your worst μ?" gets a better conversation than "cool robot."