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• A bar between two midpoints
• A circle costs one term
• A demand that is an equation
• A parallelogram carries an angle, and only so far
• Doubling is cheaper than adding
• Every curve is a sum of cosines
• Exact costs more than close
• Five bars for a line, four hundred for a quintic
• Four bars that add two angles
• The machine, compiled
• The proof drew more than the curve
• What universality is worth
• Where the machine stops being the function
• A compiled machine and its own scale
• The price is on the equation
• Two circles for the price of one

• A cam is a conjugate pair
• A follower needs a face
• A profile is an envelope
• Prescribing motion
• Stopping thirty times a second
• The cam that cannot be cut
• The law that costs least is not the smoothest
• A lift is a size and a law is a shape
• An offset trades the rise for the return
• A flat face asks for a convex cam
• A cam that holds its follower both ways
• An arm is an offset that grows with the lift
• A roller in a groove changes walls with the speed
• A flat face on an arm is worse
• The time a crossover takes

• A catalogue is a search space
• A machine with one dyad in it
• Deciding that two chains are one
• Eight ways to drive it, and one machine
• Eleven assortments and four that are empty
• Four that a compass cannot reach
• Right until the size nobody checked
• Same links, same pins, different machines
• The candidates a search throws away
• The chain has no lengths
• The mechanism is the graph
• What a count cannot see
• What has to be solved together
• Which link to bolt down
• A graph has no numbers at all
• A slide turns nothing

• A chain is not a strand
• A member with no length of its own
• A ratio that is a derivative of a length
• One strand over many joints
• The drum that is not round
• The radius a winch works at
• The strand that is slack
• The taut path has more than one answer
• The tensioner is the unknown
• The wraps add up to a turn
• Where a strand leaves a body
• Where a strand stops touching
• A drum is a size, a wrap is a shape
• The wrap that walks along the axis
• A strand in a tube
• Which walls a strand is held by

• A chain multiplies
• A higher pair has no group
• A joint is a surface that slides on itself
• Almost nothing is a group
• Compose two positions and see where you land
• Four joints that give a group, and four that do not
• Legs intersect
• Six, and no others
• The block in the guide has a length
• The count cannot tell a pin from a slide
• The instrument that is not a derivative
• Twelve kinds of freedom
• Two planes meeting in a line
• What a point sees
• A coupling that only translates

• A circle for the first millimetre
• A constraint that takes nothing away
• Every axis through one point
• How many wiggles
• One bracket, two subjects
• One character apart
• Parking is an exponent
• The angle that doubles
• The ball that remembers where it has been
• The motion left over by going nowhere
• The path a towed wheel takes
• The road a wheel carries with it
• The wheel that forbids nothing
• Which way did the bicycle go
• A wheel that cannot report its radius
• A bearing is a planetary with no teeth

• A clearance inside a tolerance box
• A clearance is a link
• A length is a range
• Exactness a micron destroys
• Fragility has a direction
• How far the crank turns first
• Seven lengths and a hundred corners
• Taking up the play
• The error that is an integral
• The error that is repeated
• The four lengths do not matter equally
• The pair a catalogue sells
• The ratio that has a tolerance
• Tolerancing the holes
• Two routes to a sensitivity
• What a drop cannot be smaller than
• What is still outside
• Where a stack-up stops working
• Where the boundary moved
• Where the shortest loops are
• Which pin to buy
• Why a hinge works
• Worst case and the square root
• A band with a direction in it
• Where the boundary moved again
• A piano hinge is not forty door hinges

• A clock is a factorisation
• A tooth flank is an unwound strand
• Backlash is an allowance
• Epicyclic ratios, two ways
• Moving the cutter out
• One rack and every wheel
• Two flanks, one law
• Undercutting, and the seventeen-tooth rule
• What happens in a mesh
• Which tooth meets which
• Why a tooth is an involute
• The module is a size, the ratio is a shape
• The angle the standard left free
• A tooth that lives on a sphere
• The mesh with one curvature reversed
• Contact that runs along the tooth

• A constraint that has been said already
• A stack that has to fit
• Each one moves, and together they do not
• Every vertex is a spherical linkage
• It moves to first order and not at all
• Many loops, one freedom
• One input at one end
• The cell that repeats for ever
• The freedom that survives repetition
• The loops are in the graph
• The ring that closes at every size
• What a pattern has to satisfy
• Where the branches meet
• Which diagonal rigidifies a grid
• The count says how many and not where

• A constraint that only pushes
• Four in the plane and seven in space
• Free at every instant and going nowhere
• Held is not located
• Neither part comes out first
• Six hold nothing
• The contact that is free not to touch
• The escape is a place
• The test is a program, not a rank
• What one contact forbids
• Where the jaws put it
• Which contact to make accurately
• Which way it comes out
• A cone has no size
• Free to turn and unable to
• The hold is in the corners

• A construction with no arithmetic in it
• Every point has a centre
• Exact because two circles roll
• Four positions brought together
• How long a pivot stands in for a linkage
• The circle a point stays on longest
• The circle of points going straight
• The mechanism drops out
• The other pole
• The straightest point there is
• Where a curve has a corner
• Where the curvature stands still
• A curvature is a size with a minus sign
• The linkage, put back from two curves
• The two numbers are the curves' own
• The frame seen from the coupler

• A defect that is not kinematic
• Choosing the chain before the lengths
• Five positions, and what is left
• How many points may be prescribed
• Prescribing a curve rather than points
• The linkage that is only nearly right
• The problem the other way round
• Three linkages, one curve
• Three positions, and a circumcentre
• Three problems called synthesis
• What the fourth position costs
• Where an optimiser starts
• Where the precision points go
• What a synthesis assumes it knows
• Where a pin becomes a slide

• A dwell made from a curve
• Grashof, predicted and then swept
• One chain, four mechanisms
• Six bars, and what the extra dyad buys
• Four bars and four pins
• The return stroke is quicker
• The slider-crank
• The transmission angle
• Grashof is a shape test
• Eight kinds of four-bar
• A swing and a time ratio
• A drag link ahead of a crank-rocker
• Four kinds of slider-crank
• Three rotations, and four benches
• A quick return that cuts evenly

• A gap is a number
• A gap with corners in it
• A link that takes up room
• A pin is not a point
• A plane is a colour
• A shape with a dent in it
• A sweep that missed nothing
• Free space comes in pieces
• The crank that cannot turn all the way
• The hole the machine needs
• The room a machine sweeps
• Two bars that have to cross
• A body is all size
• The gap is a straight line in the metal
• The regions overlap and the parts never meet
• A link may be bent

• A hundred to one from a difference of one
• A ratio is a null space
• A ratio with no steps in it
• Four speeds from two numbers
• Holding a member chooses the ratio
• One wheel on ice
• The lever that is the gearset
• The reductions a planetary cannot give
• The steps are not free
• Three mechanisms, one subtraction
• Two inputs and one output
• Two shafts that must be in line
• The transmission angle has no size
• A bounded ratio made unbounded
• Sliding the travel across the pole
• The power that goes round twice

• A joint that works one way
• Detached, and safe while detached
• One piece, and still not reachable
• One test, three mechanisms
• The angle that holds the lock
• The arc that is concentric with the pivot
• The gear with its teeth cut away
• The mechanism that waits
• The resolution is the pitch
• The wheel that goes backwards
• Where the input stops deciding
• Where the tooth lets go
• Two pins and no dwell at all
• A ratchet with no teeth
• When the index law becomes a choice
• The disc decides the pin count

• A name for each overconstraint
• The smallest screw system has a shape
• Bennett, and the condition that moves it
• In space there is one chain
• When the link lengths are angles
• Sarrus, and the straight line that is exact
• Six freedoms, not three
• What a mechanism cannot do
• The joint that is not constant velocity
• Twelve bars and a symmetry
• Two ways to be overconstrained
• Every motion is a screw
• Bennett's condition is a ratio
• What a leg of three joints leaves free
• The lines a leg turns about and the lines it is pushed along

• An arm is a tree
• A straight line at constant speed
• Eight ways to hold the same tool
• Four numbers or a screw
• Pin the tool and it is a loop
• The arm that hits itself
• The arm that is a group
• The chain that does not close
• The distance between two poses
• The freedom that does nothing
• The space of configurations
• The wrist is three joints and one point
• Two routes to a Jacobian
• What a calibration cannot see
• Where an error at the shoulder ends up
• Where the arm loses a direction
• Where the hand can go
• An arm's parameters and its poses
• Branches were components all along

• Any shape has a partner
• A ratio that is a function of the angle
• A rotor nobody drew
• Eleven lobes from twelve pins
• Rolling at one point only
• The cutter takes back the tooth
• The demand that cannot be met
• The second shape is not a choice
• The shape that does not mind where the shafts are
• The tool is the definition
• Three chambers and a constant
• Where two shapes stop touching
• Rotors that mesh and cannot drive each other
• The clearance that is the seal
• A twist steadies what it cannot tighten
• What a second contact is for

• A ratio that is a count
• A roll centre is not a point
• A roller is not a slider
• Holding an axle still
• Locked on purpose
• Six points and no more
• The cam is not the valve
• The chain is a polygon
• The number on the box
• The seventh contact
• The steering that is never right
• The wheel is the coupler
• Where a hinge pin can go
• Where the pad touches
• Which numbers survived

• Counting and measuring mobility
• One freedom and four hundred links
• The count was right and the name was wrong
• The freedom that is a set
• The mechanism Grübler says cannot move
• The formula is repaired by the thing it replaced
• What decides whether it moves
• What each joint takes away
• The count that counts the wrong thing
• One freedom, and a motion that never repeats
• A parallelogram a micron wrong
• Nine bars that ought to be rigid
• A length error is undone by its own size
• The right angle as a tolerance
• Every change point lies flat

• Exactly right, and unbuildable
• Not unreachable, only expensive
• Six things a body is not
• Six things a centre is not
• Six things a chain is not
• Six things a compiled linkage is not
• Six things a hold is not
• Six things a joint is not
• Six things a network is not
• Six things a shape is not
• Six things a strand is not
• The escapement that could not alternate
• The gearset that could not be assembled
• The ratio that is not a number
• The solver was refusing a quarter of the sweep
• Two things called jamming
• Six things a measurement cannot tell you

• Following a root from a problem already solved
• The count that does not move
• The paths that leave
• The search that was right
• Twenty-eight, not forty
• Two circles, four answers
• Two to the power of the dyads
• The equation a four-bar satisfies
• The curve nobody eliminates
• Never three circuits
• A degree counted on a line
• Nine times through each circular point
• Every rational gear ratio has a degree
• The mesh inside keeps the half
• Where a slide puts the rest of the degree

• Locked, and still moving
• Six legs and a square root
• The easy problem and the hard one change places
• Three legs and one plane
• Why the platform stays flat
• A platform that measures itself
• One command, six answers
• The workspace is not a shape you choose
• What a fourth leg buys
• The smallest parallel robot
• A yaw that is singular everywhere
• Round a cusp into another assembly
• Two orientations no position can rescue
• One placement of every placement
• The dead yaw is a design choice
• Tilted, near the dead yaw

• Peaucellier and the exact answer
• The straight-line problem
• What a coupler point draws
• Where the coupler is turning
• The curve the other assembly draws
• A sextic that comes apart
• Three linkages, one equation
• A symmetric curve from a lopsided machine
• A point the machine never reaches
• The area a coupler point encloses
• The flattest dwell is not the longest
• A null space of fifteen is not noise
• Where three machines keep one area
• The kind is decided before the lengths are
• The dip that buys the dwell

• A count is neither
• A dimension is a measurement
• A machine that measures itself
• A number that runs away
• A parameter the model has not got
• A ruler and a protractor
• Every length wrong, every reading right
• Four indices, four answers
• How many poses are enough
• Nine parameters, two of them invisible
• One set of lengths, two machines
• Reading a residual
• Six per joint is two too many
• The chart breaks, the machine does not
• The common normal, and where it is
• The coordinates the site already had
• The direction no protractor can see
• The instrument's error, multiplied
• The matrix a calibration inverts
• The pose the machine cannot reach
• The same part, dimensioned twice
• Three machines, one curve
• Two instruments disagree about the worst
• What a model is allowed to change
• What another measurement is worth
• What this field cannot measure
• Where a calibration should measure
• Where the two analyses cross
• Which numbers have a size
• Where a length comes from
• Which feature to hold tight
• A calibration is a synthesis with more equations