Cam_(mechanism) - Wikiparency

# Cam (mechanism) A **cam** is a [[Machine_element|machine element]] with a shaped working surface that drives a second element, the [[Cam_follower|follower]], through a prescribed motion as the cam turns or slides. The two touch along a line or at a point rather than over a fitted surface, and that single contact does the work of a whole train of links: one turning shaft can open a valve, index a turret and trip a switch, each at its own moment in the turn, simply because three profiles were cut differently. A cam converts steady rotation into a translation or an oscillation of almost any shape, including motions that no [[Linkage_(mechanical)|linkage]] of fixed bars can produce. What distinguishes cam design from the rest of [[Kinematics|kinematics]] is the order in which the work is done. The designer does not draw a shape and ask what it does; the designer draws the follower's displacement against cam angle — the displacement diagram — and the profile is then whatever curve delivers it.[^b109cam] That order matters because velocity, [[Acceleration|acceleration]] and [[Jerk_(physics)|jerk]] are the first three derivatives of that diagram, multiplied by the shaft speed, its square and its cube. A kink that looks harmless on a hand-drawn rise is an impact at a few thousand revolutions per minute, and the choice of motion law, not the choice of material, is what decides whether the follower stays on the cam. The framework microsim *The cam: the follower's motion is designed first, the profile follows* puts that order in the reader's hands: choose a motion law — harmonic, cycloidal or 3-4-5 polynomial — then set the lift, the rise angle, the dwell and the base radius, and the cam's outline is generated from the choice and turned on screen, while four strips show what the follower feels (displacement, velocity, acceleration and jerk) and a [[Pressure_angle|pressure angle]] readout says whether the cam can push the follower at all. ## Camshaft A [[Camshaft|camshaft]] is a shaft carrying several cams, angularly indexed so that one rotation issues a fixed sequence of events. Its best-known form is in the [[Internal_combustion_engine|internal combustion engine]], where each cylinder's intake and exhaust [[Poppet_valve|poppet valves]] must open once every two [[Crankshaft|crankshaft]] revolutions; the camshaft is therefore geared, belted or chained to turn at exactly half crank speed, and every valve event is quoted in crank degrees, twice the cam figure. Whether the shaft sits in the block and works through pushrods and [[Rocker_arm|rocker arms]] or directly over the valves as an [[Overhead_camshaft_engine|overhead camshaft]] changes the [[Valvetrain|valvetrain]]'s stiffness and moving mass, not the cam's job. The See-also variant *The camshaft: one lobe per valve, timed in cam degrees at half crank speed* builds two roller-[[Tappet|tappet]] lobes 90 degrees of cam apart, each a 3-4-5 polynomial lift of 10 mm over a 60-degree rise and a mirrored 60-degree fall on a 30 mm base circle, and prints the resulting valve event as 120 degrees of cam, 240 degrees of crank.[^engsim-camshaft] The arithmetic behind that note is what makes valve gear hard. At 3,000 crank rpm the camshaft turns at 1,500 rpm, so the whole event lasts about 13 ms, and the 3-4-5 law's peak acceleration, `a = 5.7735 h ω²/β²`, comes to roughly 1.3 km/s² — about 130 times gravity.[^manual27] Every gram of follower, pushrod and valve must be pulled back down against that figure by the [[Spring_(device)|valve spring]] alone, because a plate cam can only push; when the spring cannot, the follower leaves the profile and lands again out of time. Systems that vary the timing or lift while the engine runs ([[Variable_valve_timing|variable valve timing]]), and the [[Desmodromic_valve|desmodromic]] gear that closes the valve with a second cam instead of a spring, are answers to the same number. *Try: step the lift from 5 to 10 mm and watch both tappets rise higher while the base circle stays the size it was; then cut the rise from 60 to 40 degrees and see the acceleration strip grow as the same lift is crammed into two-thirds of the cam angle, while the note line keeps reading the event in crank degrees, twice the cam figure.* ## Displacement diagram The displacement diagram plots follower position `s` against cam angle `θ` for one full turn, divided into a rise, a dwell at full lift, a fall and — in the classical layout — a second dwell at the bottom.[^b109cam] Its rules are derivatives. The fundamental law of cam design requires that `s`, its slope and its curvature be continuous everywhere around the turn, because a jump in slope is an infinite acceleration and a jump in curvature an infinite jerk; two well-behaved pieces joined carelessly at a dwell produce those spikes anyway.[^b109cam] Three rise laws cover most practice, and they differ exactly as the derivatives predict. With lift `h` over a rise angle `β`, the peak acceleration in cam-angle units is `π²h/(2β²)` for [[Simple_harmonic_motion|simple harmonic motion]], `5.7735h/β²` for the 3-4-5 polynomial and `2πh/β²` for the [[Cycloid|cycloidal]] law — coefficients of 4.93, 5.77 and 6.28.[^manual27] At the microsim's defaults, a 15 mm lift over a 90-degree rise at 300 rpm, the three come to 29.6, 34.6 and 37.7 m/s².[^engsim-cam] The harmonic law wins on peak acceleration and loses everywhere else: its acceleration steps from zero to full value where the rise leaves a dwell, so its jerk there is unbounded and the readout prints `inf` rather than a number. The cycloidal law begins and ends a rise with zero acceleration, joining a dwell smoothly, and pays with the highest peak and a jerk of 4,737 m/s³ at the same settings.[^engsim-cam] The polynomial sits between, which is why it is the usual industrial compromise. Timing follows from the same diagram: at 300 rpm a turn takes 0.2 s, so the default rise occupies 50 ms, the dwell 33 ms and the fall the remaining 210 degrees. On screen the cam turns at a reduced 15 rpm so the motion can be watched, while every readout is computed at the speed the control is set to.[^engsim-cam] The last quantity the diagram fixes is the pressure angle, between the [[Cam_follower|follower]]'s direction of travel and the line along which the cam actually pushes. For a radial roller follower with no offset it is `tan φ = s'/(R_b + s)`, where `s'` is the slope of the displacement diagram and `R_b` the prime-circle radius.[^b109cam] At the defaults the peak is just over 22 degrees. Shrink the base circle to 20 mm and demand 30 mm of lift in a 60-degree rise, and it reaches about 55 degrees: most of the cam's push is then sideways, loading the follower guide and its [[Friction|friction]] rather than lifting anything, and the profile begins to undercut itself, which the sim flags in a caption.[^engsim-cam] The cure is always a larger base circle, a longer rise or less lift, which is why cams grow when their motion is made more demanding. The undercut test, the roller-surface offset and the flat-face contact point are computed in the sim's own hooks from the library's `s`, `s'` and `s''`; the framework's cam module does not yet provide them.[^engsim-cam] *Try: switch the law from harmonic to cycloidal and watch the acceleration strip's square corners round off while its peak grows and the jerk readout turns from `inf` into a number; then drop the base radius from 30 to 20 mm and see the pressure angle climb until the caption warns of undercut.* ## Types by shape Cams are classified first by the geometry that carries the profile, because that choice settles how the follower is held against the cam and how much motion can be had from a given size. A cam that can only push is *force closed*: a [[Spring_(device)|spring]], gravity or an air cylinder returns the follower, and the highest usable speed is set by what that return can accelerate. A cam whose follower runs in a groove is *form closed*, driving in both directions without a spring, at the price of the clearance the roller needs in the groove, which it crosses noisily at every reversal. Cutting across this classification is the follower's own shape — a knife edge, a roller, or a flat face — which decides where the contact point sits and how the contact stress is spread; the same profile drives a roller and a flat face to different motions, and the flat-face follower has its own curvature limit. The families below are the ones a designer chooses between, and the motion laws of the section above apply to all of them unchanged. ### Disc or plate The disc or plate cam is the common case and the microsim's default: a plate whose edge is the working profile, turning on a shaft, with the follower travelling in a line that passes through the axis or is offset from it. Because the plate can only push, the follower is held on by a spring, and everything difficult about high-speed cams follows from that — the spring must supply the entire negative acceleration of the fall, and it is the first component to run out of authority. The base circle is the smallest radius of the profile, and it is the designer's main lever on the pressure angle: a bigger base circle means a gentler push angle and a bigger, heavier cam. Plate cams are cheap to make, easy to inspect with a profile gauge or a coordinate measuring machine, and easy to replace, which is why they survive in engines, presses and [[Textile_manufacturing|textile machinery]] where a groove would be stronger but costlier. ### Cylindrical A cylindrical cam, also called a barrel or drum cam, carries its profile as a groove cut in the surface of a cylinder, and its follower moves parallel to the shaft rather than across it. The groove captures the roller, so the drive is positive in both directions and no return spring is needed. Unwrapped, the groove *is* the displacement diagram, wound once round the cylinder, so the same motion laws and the same fundamental law apply, with the lift now an axial travel. Cylindrical cams feed tools on automatic [[Lathe|lathes]] and [[Screw_machine|screw machines]], traverse thread on winding machines, and index [[Machine_tool|machine tool]] turrets. Their cost is the clearance that lets the roller turn in the groove: at each reversal the roller crosses from one flank to the other, and that crossover is felt as a knock and paid for in [[Wear|wear]] at exactly the moments the motion changes direction. ### Face A face cam cuts the groove into the flat face of a disc instead of the rim of a cylinder, so the follower moves radially across the disc while the drive remains positive in both directions. It buys the same freedom from a return spring in a package that is short along the shaft and large across it — the opposite trade to the barrel cam. Face cams are used where a spring would be unreliable or where the return stroke itself does work, for instance in feed mechanisms that must pull as well as push, and in indexing tables where the follower must be held in place rather than merely pressed there. The same flank clearance applies, and because the groove's radius from the axis varies along the profile, the roller's rubbing speed varies with it, so a face cam's groove wears unevenly unless the roller is free to spin on a good [[Bearing_(mechanical)|bearing]]. The profile is also harder to inspect than a plate cam's open edge, since a gauge cannot simply be laid against it. ### Heart shaped The heart cam is a profile of constant velocity out and constant velocity back, so named for the outline that results. Its property is that a follower pressed against it will always be driven to the same datum position, whatever angle the cam starts from. The best-known use is in a [[Chronograph|chronograph]], where a hammer falling on heart pieces snaps the timing hands back to zero in one motion; the same shape guides thread evenly across a bobbin on a winding machine, where constant velocity is exactly what lays an even wrap. The constant-velocity law breaks the fundamental law at both ends of its stroke: velocity reverses in a corner, so the acceleration there is impulsive. That is tolerable, and even wanted, where the motion is a snap or is driven slowly by hand, and unacceptable at speed — which is why the heart shape is common in instruments and winding gear and absent from valve trains. ### Snail drop A snail cam rises gradually through most of a turn and then falls off a step, giving a slow advance and a sudden return. The best-known example is in [[Striking_clock|striking clocks]], where the snail's stepped radius sets how far the rack falls and so how many blows the hour receives; the same shape gives a quick return in machine tools and a rapid release in trip mechanisms. The drop is a deliberate discontinuity: at the step the follower is unsupported and falls until it lands, so the whole family belongs to slow-running machines where the landing energy is small, and a stepped snail can be made with several radii so that one cam issues several different returns. A snail cam is the clearest case of the rule that the fundamental law is a rule about speed, not a rule about taste — breaking it is a design decision with a cost that can be stated and paid. ### Linear A linear cam translates instead of turning: a wedge, a shaped bar or a plate that slides past its follower, lifting it according to the profile cut along its length. Because the cam does not return to its start by turning, the profile is drawn at full size and read once per pass, and there is no wrap-around condition to satisfy at the end of the diagram. The everyday example is a key for a [[Pin_tumbler_lock|pin tumbler lock]]: the bitting is a linear cam whose steps lift each pin exactly to the shear line as the key slides in. Industrially, linear cams appear as feed wedges in presses, as ramps that lift guards and covers, and as the moving jaws of [[Simple_machine|simple machines]] built to hold a part in one position while another mechanism works on it. A linear cam is also the easiest form in which to see what a cam is: the profile and the motion it produces are the same drawing at the same scale, with no polar transformation between them. ## History The cam is one of the oldest mechanisms that is not a [[Simple_machine|simple machine]], and it arrived with the first power sources that turned continuously. Once a [[Water_wheel|water wheel]] delivered steady rotation, pegs set into its shaft could lift and drop a [[Trip_hammer|trip hammer]], lift and fall by lift and fall, all day — a cam in its simplest form, a peg that turns rotation into a repeated blow. The Hellenistic automatic theatres attributed to [[Hero_of_Alexandria|Hero of Alexandria]] used pegged rotating cylinders to sequence a series of movements, the ancestor of the barrel cam and of every drum-programmed machine after it.[^hero] In 1206 the Artuqid engineer [[Ismail_al-Jazari|al-Jazari]] described camshafts in his water-raising machines and [[Automaton|automata]], where one turning shaft worked several devices in a fixed order.[^jazari] The cam's industrial career came with machines that had to repeat an operation exactly. Barrel cams and pinned cylinders programmed music boxes and automatic looms; cam-driven [[Screw_machine|screw machines]] and turret lathes turned out identical parts by the thousand, with a bank of cams on a single shaft replacing an operator's sequence of movements; and the [[Four-stroke_engine|four-stroke engine]] made the camshaft a component that almost every household would own without ever seeing it. Where the [[Jacquard_machine|Jacquard machine]] carried its program on punched cards, the automatic lathe carried it as metal, and changing the product meant cutting new cams. That is also why the cam has receded. A profile is a program written in steel: cheap to repeat, expensive to change. [[Computer_numerical_control|Computer numerical control]] and [[Servomechanism|servo]] drives now implement the same displacement diagrams in software — electronic camming, in which a [[Motion_control|motion controller]] follows a stored table of follower position against master angle — so the diagram survives while the metal does not. Cams remain where the motion is fixed for the life of the machine and the duty is hard: valve gear, presses, packaging machinery, and any place where a single shaft turning is a more dependable timing signal than a controller that can lose power. ## See also - [[Cam_follower]] - [[Camshaft]] - [[Crank_(mechanism)]] - [[Eccentric_(mechanism)]] - [[Reciprocating_motion]] - [[Swashplate]] - [[Cam_engine]] - [[Four-bar_linkage]] (section 10) - [[Belt_(mechanical)]] (section 12) ## References [^b109cam]: Jensen (Portal Book 109). *Introduction to Mechanical Design and Manufacturing*, pp. 220–222, "Cams": the follower's motion is specified first, the rise–dwell–fall–dwell displacement diagram (the book's 20°/40°/300° split, carried in the framework as `design.cam.BOOK_SPLIT`), the fundamental law that displacement, velocity and acceleration carry no jumps, and the pressure angle. [^manual27]: Wikitube MICROSIM_GUIDE sub-manual `12_design_mfg`, §2.7 "Cams": the harmonic, cycloidal and 3-4-5 polynomial rise laws with peak accelerations `π²h/(2β²)`, `2πh/β²` and `5.7735h/β²`, implemented as `design.cam.rise` and `design.cam.peakAccel`. [^engsim-cam]: Engineering portal microsim spec `specs/sims/Cam_(mechanism).json` and its build report (job E-D, `reports_engrun_2026-09-18.md`, September 18, 2026). Motion by `design.cam.cycle` sampled every degree; peaks by `design.cam.peakAccel` and `peakJerk` in time units (`a = ω²s''`, `j = ω³s'''`); pressure angle by `design.cam.pressureAngle(s', s, R_b)` swept over the turn. Hand check: cycloidal, h = 15 mm, β = 90°, 300 rpm gives a peak acceleration of 37.7 m/s² and a peak jerk of 4,737 m/s³, both matching the readouts; `peakJerk` returns infinity for the harmonic law and the readout prints `inf`. Recorded library gap: `design.cam` provides no roller-surface offset, no flat-face contact point and no undercut check, so the sim computes all three in its hooks from the library's `s`, `s'` and `s''`. The report records no ILLUSTRATIVE quantity in this sim; the on-screen turning rate of 15 rpm is stated on the machine sheet, and the readouts are computed at the set speed. [^engsim-camshaft]: See-also variant `Camshaft` of the same spec (job E-D, September 18, 2026): two roller-tappet lobes 90° of cam apart, a 3-4-5 lift of 10 mm over a 60° rise and a mirrored 60° fall on a 30 mm base circle with a bottom dwell, the note line printing the 120° cam event as 240° of crank. [^hero]: Hero of Alexandria (first century AD). *Automata* (Περὶ αὐτοματοποιητικῆς). The pegged rotating cylinder that sequences the movements of Hero's automatic theatre is described in the treatise and in standard histories of mechanism. (Edition and translation not pinned for this article; a modern critical edition would settle the detail of the attribution.) [^jazari]: al-Jazari, Ismāʿīl (1206). *The Book of Knowledge of Ingenious Mechanical Devices* (Kitāb fī maʿrifat al-ḥiyal al-handasiyya). Translated and annotated by Donald R. Hill, Dordrecht: D. Reidel (1974). (Translation and publisher as recalled; the 1206 date of the treatise is standard in histories of mechanism.)  **Microsim — three.js (Wikitube framework):** *Cam (mechanism)* <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/engineering/Cam_(mechanism).html" data-title="Cam (mechanism)"></div> *Built from `MICROSIM_GUIDE/specs/sims/Cam_(mechanism).json`; part of the [[PORTAL_Engineering|Engineering portal]] spine (section sims and See-also variants).*  ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Cam_(mechanism)) : [Wikitube](https://en.wikitube.io/wiki/Cam_(mechanism)) - skeleton pinned to revision 1372398156 (2026-09-18).