Ames Watt and His Linkages

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G E N E R A L   ARTICLE Jam es W att and his L inkages

Sangam esh R D eepak and G K Ananthasuresh

Jam es Watt’s nam e is synonym ous w ith steam engines but there is another equally im pressive facet to his technical accom plishm ents in the areas of design and m anufacture of m achines. In this article, w e highlight his contributions to the design of linkages, w hich are assem blies of rigid bodies that (left) Sangam esh R D eepak is a P hD student in the perform intricate m echanical m otions. T he linkages described D epartm ent of M echanical here range from the ones that can draw a straight line to those E ngineering, IISc, that can replicate three-dim ensional objects through purely B angalore. H is specific m echanical m ovem ents. interest is the design of innovative m echanism s W e use a com pass to draw a circle and a scale (a r u l e r a s i t i s using deform able bodies that can be held in static som etim es called) for a straight line. W e g e n e r a t e a circle w ith equilibrium in m ultiple the help of a com pass w hereas w e c o p y a straight line from a scale. configurations. If the scale is not straight, so w ill be the line w e copy. It is difficult (right) G K A nanthasuresh and expensive to m ake a perfectly straight scale. It w as m ore so teaches in the departm ent of M echanical E ngineer- before the industrial revolution w hen m anufacturing techniques ing, IISc and is engaged in w ere not as good as they are today. H ence, craftsm en of that tim e research on optim al design explored alternate m eans for g e n e r a t i n g a straight line. A particu- and m echanics concerning larly vexing problem encountered by craftsm en of the m id 18th m achines and structures, m icrosystem s, biological century w as guiding a piston inside a cylinder of a steam engine. cells, and proteins. T he first person to com e up w ith a solution, although approxim ate but good enough for practical purposes, w as Jam es W att. Acknow ledgem ents: Professors A shitava G hosal (IIS c), A m itaba T he approxim ate straight-line linkage that Jam es W att developed G hosh (IIT-Kanpur), G regory is know n today as the W att’s linkage. T his and other inventions of Pennock (Purdue), and Anupam W att defined a field called linkage synthesis and occupied the Saxena (IIT-Kanpur) read this m inds of m any engineers, scientists, and m athem aticians since m anuscript and suggested im - provem ents. The authors are then. T hus, Jam es W att w as not just an inventor w ho played a key grateful to all of them . role in ushering in the industrial revolution but w as also the one w ho played a key role in transform ing the im age of able craftsm en K e y w o r d s into engineers and scientists. B y discussing his contributions to Jam es Watt, straight-line link- linkages, w e present a profile of W att that is m uch m ore than the age, centrifugal governor, sculpt- person w ho im proved N ew com en’s steam engine and m ade steam ing m achine. pow er generation portable.

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GENERAL GENERAL ARTICLE 

Watt’s Straight-line Linkage Straight-line Watt’s

Let us turn to the question of why Watt required a straight-line linkage or other linkages that he that linkages other or linkage straight-line a required Watt why of question the to turn us Let 1a,b show a linkage (see engine (see steam the linkage in invented. a show are) Figures 1a,b linkages what know to Box 1 that was invented by Thomas Newcomen in 1712 – almost 24 years before James Watt was born. was Watt James before years 24 almost – 1712 in Newcomen Thomas by invented was that which is simply a lever driven by steam power, steam by driven lever a linkage, simply This is which of out water pump to used was mines. It had a wooden beam pinned to a base with sectors attached at its either end. Iron chains Iron end. either its at attached sectors with base a to pinned beam wooden a had It mines. tangentially hung from the sectors and held a pump-rod and a piston-rod. Since a chain hanging chain a Since piston-rod. a and pump-rod a held and sectors the from hung tangentially from one point remains vertical due to gravity, the rods could be guided vertically. But a chain a But vertically. guided be could rods the gravity, to due vertical remains point one from will be straight only when it is pulled. We cannot push through with a chain. In a double-acting a In chain. a with through push cannot We pulled. is it when only straight be will steam engine that Watt invented, there was a need to push and pull on the piston-rod. the on pull and push to need a was there invented, Watt that engine steam Manufacturing a snugly fitting and yet freely movable piston-cylinder assembly is one option. one is assembly piston-cylinder movable freely yet and fitting snugly a Manufacturing But it was not practicable at that time. Watt did have access to an able ironmaster, John ironmaster, able an to access have did Watt time. that at practicable not was it But Wilkinson, who could bore the best cylindrical hole at that time for as large a diameter as 50 in. 50 as diameter a large as for time that at hole cylindrical best the bore could who Wilkinson, But it was expensive and Watt wanted a better solution than this. So, he set out to find a linkage a find to out set he So, this. than solution better a wanted Watt and expensive was it But that would give straight-line motion. It is important that such a linkage should only have pin have only should linkage a such that important is It motion. straight-line give would that joints and no sliding joints because a sliding joint again takes one back to the problem of not of problem the to back one takes again joint sliding a because joints sliding no and joints being able to machine a perfectly straight slider. straight perfectly a machine to able being

Watt’s solution to this problem was as remarkable as his other significant contributions to steam to contributions significant other his as remarkable as was problem this to solution Watt’s engines such as a separate condenser and double-acting cylinder were. His creative thought took thought creative His were. cylinder double-acting and condenser separate a as such engines

(a) (b)

Figure 1. (a) N ew com en w ater-pum ping steam engine [1]; (b) a sketch of the sim ple linkage involved i n i t .

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GENERAL GENERAL  ARTICLE

Box 1. Linkages 1. Box

A linkage is an assembly of rigid bodies. A rigid body does not change its shape upon application of forces. of application upon shape its change not does body rigid A bodies. rigid of assembly an is linkage A A solid metal rod can be considered to be a rigid body even though nothing is perfectly rigid. If we want we If rigid. perfectly is nothing though even body rigid a be to considered be can rod metal solid A to rotate it about a point, we use a pin joint and connect it to a base. Now, we take another rigid rod and rod rigid another take we Now, base. a to it connect and joint pin a use we point, a about it rotate to connect it to the other end of the first rod. We then take a third one and connect it to the free end of the of end free the to it connect and one third a take then We rod. first the of end other the to it connect second rod. To complete the assembly, we connect the free end of the third rod to the base. All connections All base. the to rod third the of end free the connect we assembly, the complete To rod. second are with pin joints. What we now have is an assembly of four bodies (three rods and the base). See See base). the and rods (three bodies four of assembly an is have now we What joints. pin with are Figure A(i). Such an assembly is a a is assembly an Such A(i). a is it particular, linkage In . any of linkage consist four-bar can linkage A . number of bodies and connections as well as a variety of connection, besides pin joints. Other types of types Other joints. pin besides connection, of variety a as well as connections and bodies of number connections include: a sliding joint, a ball-and-socket joint, a gear-pair, a cam-and-follower, chains- cam-and-follower, a gear-pair, a joint, ball-and-socket a joint, sliding a include: connections A(ii) shows the familiar slider-crank linkage with a sliding joint and three and joint sliding a with etc. linkage belt-pulley, slider-crank sprocket, familiar the shows Figure A(ii) pin joints. pin

Figure linkage. Figure (i) A. four-bar A linkage. slider-crank (ii) A

him in a direction that nobody had thought of before. Although linkages were known, everyone known, were linkages Although before. of thought had nobody that direction a in him until then had focused attention on the ends of the rigid bodies where joints are located. Watt located. are joints where bodies rigid the of ends the on attention focused had then until examined the motion of an interior point of the middle body called the the called body middle the of point interior an of motion the examined in 2 coupler (marked A(i)). We present the details of his approximate straight-line linkage next. linkage straight-line approximate his of details the present We Figure A(i)).

Watt’s straight-line linkage is shown in in shown is linkage bodies straight-line rigid Watt’s movable three of consists Figure It 2. labeled DE, EB and BC connected with pin joints at D, E, B and C. The pin joints at D and C and D at joints pin The C. and B E, D, at joints pin with connected BC and EB DE, labeled connect the bodies to a fixed base-frame while the joints at E and B can freely move about in a in about move freely can B and E at joints the while base-frame fixed a to bodies the connect plane. Point F is the midpoint of BE. The lengths of DE and BC are equal. As BC is rotated about rotated is BC As equal. are BC and DE of lengths The BE. of midpoint the is F Point plane. C, point F traces an approximate vertical straight line in a small segment of its locus. its of segment small a in line straight vertical approximate an traces F point C,

Note that point F, being the midpoint of EB will traverse a vertical line if the horizontal motions horizontal the if line vertical a traverse will EB of midpoint the being F, point that Note of points B and C are equal and opposite. It is quite evident from from evident quite is It opposite. and equal are C and B points of moves B when Figure that 2 to the right, E moves to the left. For a short range of motion of this linkage, the horizontal the linkage, this of motion of range short a For left. the to moves E right, the to movements of B and E are almost equal in magnitude. Thus, an approximate straight-line approximate an Thus, magnitude. in equal almost are E and B of movements linkage is obtained. is linkage

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Figure 2. Watt’s approximate straight-line linkage. straight-line approximate Watt’s 2. Figure The curve shown is the locus of point F. It has a has It F. point of locus the is shown curve The short vertical segment that approximates a straight a approximates that segment vertical short line.

2 also shows the locus of the midpoint of midpoint the of locus the shows Figure also 2 BE. It is called a a called is It BE. curve the coupler EB, because middle body of a four-bar linkage, is called a called is linkage, four-bar a of body middle . The coupler curve of Watt’s linkage is linkage Watt’s of curve coupler coupler The . 2. Half of the coupler curve is shown as a solid line and the other half in dashes. in half other the and line solid a as shown is curve coupler in the shown of Half Figure 2. This is because a transition occurs in the linkage at the points where dashed and solid lines meet. lines solid and dashed where points the at linkage the in occurs transition a because is This To understand this, we need to know more about the nature of this curve. This curve has many has curve This curve. this of nature the about more know to need we this, understand To interesting properties and is one of the most fascinating planar curves. The variety of shapes this shapes of variety The curves. planar fascinating most the of one is and properties interesting curve can assume is available in an atlas created by Hrones and Nelson, which is in use even use in is which Nelson, and Hrones by created atlas an in available is assume can curve today by linkage designers. Watt was the first one to have thought of using this curve. One of One curve. this using of thought have to one first the was Watt designers. linkage by today the properties of this curve is that it cannot have a perfectly straight segment. More bodies are bodies More segment. straight perfectly a have cannot it that is curve this of properties the necessary to get an exact straight-line motion. Perhaps Watt did not know this property but he but property this know not did Watt Perhaps motion. straight-line exact an get to necessary was able to get a novel solution to the problem he was facing. Watt’s approximate straight-line approximate Watt’s facing. was he problem the to solution novel a get to able was linkage aroused interest in many great mathematicians and geometers such as Chebyshev and Chebyshev as such geometers and mathematicians great many in interest aroused linkage 3 for developments on straight-line linkages using only pin points). It led It points). pin only using linkages (see straight-line on Sylvester Figure developments for 3 to the fascinating field of kinematic analysis and synthesis of linkages. of synthesis and analysis kinematic of field fascinating the to

Kinematics, a term coined by André-Marie Ampere ( Ampere André-Marie by coined term a Kinematics, roots Greek from cinematique derived meaning to move), is an area of study where motion is motion where or study of motion area kinema an meaning is move), to kinein meaning analyzed without regard to the forces that cause it. It is essentially geometry in motion. in geometry essentially is It it. cause that forces the to regard without analyzed Understanding the changing geometry of a linkage needs kinematic analysis. Kinematic analysis. kinematic needs linkage a of geometry changing the Understanding synthesis or linkage synthesis entails conceiving an arrangement of assembled bodies and bodies assembled of arrangement an conceiving entails synthesis linkage or synthesis determining their sizes to get the desired motion. That is exactly what Watt did to generate a generate to did Watt what exactly is That motion. desired the get to sizes their determining straight line using only pin joints. Thus, Watt is deservedly credited with the initiation of an of initiation the with credited deservedly is Watt Thus, joints. pin only using line straight orderly study of kinematic synthesis of linkages. of synthesis kinematic of study orderly

From Watt’s correspondence, it is evident that Watt himself had realized the importance of his of importance the realized had himself Watt that evident is it correspondence, Watt’s From invention of the straight-line linkage. Apparently, he thought that this was one of his most his of one was this that thought he Apparently, linkage. straight-line the of invention significant accomplishments: he wrote to his son several years after this invention, “ invention, this after years several son his to wrote he accomplishments: significant am I though not over anxious after fame, yet I am more proud of the parallel motion than of any other any of than motion parallel the of proud more am I yet fame, after anxious over not mechanical invention I have ever made ever have I invention the mechanical as known was linkage Watt’s .” motion parallel during his time but not now. Immediately after conceiving this idea in 1784, he had he 1784, in idea this conceiving after Immediately now. not but time his linkage during written to his friend and business partner Matthew Boulton: “ Boulton: Matthew partner business and friend his to written method a of glimpse a got have I

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GENERAL GENERAL  ARTICLE

Figure 3. Watt’s straight-line linkage straight-line Watt’s 3. Figure and the others that it inspired. The inspired. it that others the and pictures in the left column show the show column left the in pictures linkages in one position and the right the and position one in linkages in many positions. many in

of causing the piston-rod to move to piston-rod the causing of up and down perpendicularly…I down and up think it a very probable thing to thing probable very a it think succeed, and one of the most inge- most the of one and succeed, nious simple pieces of mechanisms of pieces simple nious I have contrived have I suc- did Watt ”. cessfully use this linkage in his sub- his in linkage this use cessfully sequent engines. sequent

Watt’s mechanical inventiveness mechanical Watt’s and practical bent of mind were mind of bent practical and clear from the way he combined he way the from clear this linkage with a a with linkage this pantograph to achieve compactness in the engine. the in compactness achieve A pantograph is a linkage consist- linkage a is pantograph A ing of a parallelogram that helps in helps that parallelogram a of ing duplicating the scaled motion of motion scaled the duplicating one of its points to another of its of another to points its of one points. This idea of Watt is highly is Watt of idea This points. appreciated by kinematicians and kinematicians by appreciated we describe it briefly here. briefly it describe we

4 shows Watt’s double-act- Watt’s Figure shows 4 ing steam engine where Watt’s where engine steam ing straight-line linkage was used. At used. was linkage straight-line the top, one can notice a beam pinned at its midpoint. This beam was called a a called was beam This midpoint. its at pinned beam a notice can one top, the beam great and existed in Newcomen’s engine. As the piston reciprocates due to the steam action, the great the action, steam the to due reciprocates piston the As engine. Newcomen’s in existed beam oscillates about its pin joint. This oscillatory motion is transmitted to a rotating wheel at wheel rotating a to transmitted is motion oscillatory This joint. pin its about oscillates beam the right through a rod. Let us understand how Watt’s straight-line linkage was combined with combined was linkage straight-line Watt’s how understand us Let rod. a through right the a pantograph linkage in this engine. this in linkage pantograph a

5a shows a sketch with the great beam pivoted at C and Watt’s straight-line linkage straight-line Watt’s and C at pivoted beam great the with sketch a Figure shows 5a consisting of bodies DE, EB and BC. Body BC is extended up to H and thus BH is the great the is BH thus and H to up extended is BC Body BC. and EB DE, bodies of consisting

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Figure 4. Watt’s double-acting steam double-acting Watt’s 4. Figure engine that incorporated his straight- his incorporated that engine line linkage along with a pantograph a with along linkage line [2]. The schematic of the linkage is linkage the of schematic The [2]. overlaid for clarity. The two fixed pin fixed two The clarity. for overlaid joints are filled with gray colour while colour gray with filled are joints the other five are shown in white. in shown are five other the

beam. The cap symbol at the pin joint C indicates that BC and CH are part of the same rigid body. rigid same the of part are CH and BC that indicates C joint pin the at symbol cap The beam. The piston is to be connected to point F through a rod. As the piston reciprocates vertically, so vertically, reciprocates piston the As rod. a through F point to connected be to is piston The does point F. This straight-line motion of F is converted to oscillating rotary motion of BC by BC of motion rotary oscillating to converted is F of motion straight-line This F. point does the Watt’s linkage. While this linkage serves the purpose, the design is not compact since D is D since compact not is design the purpose, the serves linkage this While linkage. Watt’s the located at quite a distance away from the central portion. One can scale down the Watt’s linkage, Watt’s the down scale can One portion. central the from away distance a quite at located 5b but it would reduce the motion of F thus restricting the stroke the restricting in thus F shown of as motion half, the by say reduce would it Figure but 5b length of the piston. the of length

(a)

(b)

Figure 5. (a) Watt’s linkage with one body acting as the great beam. (b) An attempt to reduce the size, the reduce to attempt An (b) beam. great the as acting body one with linkage Watt’s (a) 5. Figure which reduces the stroke length of the piston. the of length stroke the reduces which

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In order to overcome the reduced stroke reduced the overcome to order In length, Watt made use of a pantograph a of use made Watt length, linkage (see (see BD and AC linkage Links . Figure 6) are such that BD/AC = OB/OA. If FE If OB/OA. = BD/AC that such are were to be absent, points D and C would C and D points absent, be to were trace arbitrary paths on the plane unlike A unlike plane the on paths arbitrary trace and B which can only trace arcs of a of arcs trace only can which B and circle. If we somehow ensure that D, C D, that ensure somehow we If circle. and O remain collinear and OC/OD is a is OC/OD and collinear remain O and constant, then the path traced by D is a is D by traced path the then constant, Figure 6. A pantograph linkage. pantograph A 6. Figure scaled version of the path traced by C. by traced path the of version scaled The scaling is about O by a factor of OD/OC. In order to achieve collinearity and constant ratio, constant and collinearity achieve to order In OD/OC. of factor a by O about is scaling The we only need to ensure that AC and BD remain parallel. This follows from a theorem of theorem a from follows This parallel. remain BD and AC that ensure to need only we geometry concerning similar triangles. This parallelism is achieved by introducing FE so that so FE introducing by achieved is parallelism This triangles. similar concerning geometry FEBA is a parallelogram. a is FEBA

7 shows the pantograph linkage combined with Watt’s straight-line linkage. The motion The linkage. straight-line Watt’s with combined linkage pantograph the Figure shows 7 5b) is scaled back at point G through the pantograph shown in the figure. the in shown pantograph the through G (of point F at point back of scaled is Figure 5b) Thus, Watt was able to put his clever invention to practical use through an elegant (certainly not (certainly elegant an through use practical to invention clever his put to able was Watt Thus, simple for his times) modification. This trait was visible in many other inventions of Watt where Watt of inventions other many in visible was trait This modification. times) his for simple he was able to cleverly adapt and improve upon existing knowledge. existing upon improve and adapt cleverly to able was he

A graph representation of this linkage in terms of the number of bodies and joints is known as known is joints and bodies of number the of terms in linkage this of representation graph A Watt’s six-bar chain (see ( (see chain chain six-bar six-bar eponymous Watt’s another is There Figure 8a). Figure 8b) credited to Robert Stephenson, son of George Stephenson – the father of railways. Watt’s and Watt’s railways. of father the – Stephenson George of son Stephenson, Robert to credited Stephenson’s six-bar chains are the only possible assemblies of six bodies that have completely have that bodies six of assemblies possible only the are chains six-bar Stephenson’s determined motion with only a single actuator. We next examine a few other linkages that Watt that linkages other few a examine next We actuator. single a only with motion determined developed.

Figure 7. Watt’s solution to the to solution Watt’s 7. Figure straight-line guidance problem. The problem. guidance straight-line sketch shows how the straight-line the how shows sketch linkage and pantograph were com- were pantograph and linkage bined without reducing the stroke the reducing without bined and by avoiding an over-sized link- over-sized an avoiding by and age.

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Figure 8. (a) A graph of Watt’s six- Watt’s of graph A (a) 8. Figure bar chain; referring to Figure 7, body 7, Figure to referring chain; bar 1 is ABCH, body 2 is AG, body 3 is 3 body AG, is 2 body ABCH, is 1 GE, body 4 is BE, body 5 is ED, and ED, is 5 body BE, is 4 body GE, body 6 is the fixed frame DC, (b) a (b) DC, frame fixed the is 6 body graph of Stephenson’s six-bar Stephenson’s of graph chain; a linkage based on this was this on based linkage a chain; used in a valve mechanism in a in mechanism valve a in used steam locomotive. The historic ship historic The locomotive. steam Titanic had this valve in its engine. its in valve this had Titanic

Rotary Engine Linkages Engine Rotary

Newcomen’s engine and Watt’s early engines moved the piston back and forth along a straight a along forth and back piston the moved engines early Watt’s and engine Newcomen’s line using steam power. This reciprocating motion is useful for some applications but not all. not but applications some for useful is motion reciprocating This power. steam using line Continuous rotary motion of a wheel was necessary to drive many machines of that time just as just time that of machines many drive to necessary was wheel a of motion rotary Continuous it is now. Conversion of linear reciprocating motion to rotary motion, although trivial today, trivial although motion, rotary to motion reciprocating linear of Conversion now. is it was not obvious or practical in those times. A practical solution of that time was to pump the pump to was time that of solution practical A times. those in practical or obvious not was water up into a reservoir and let it fall on a water-wheel. But this was cumbersome. So, Watt and Watt So, cumbersome. was this But water-wheel. a on fall it let and reservoir a into up water other engineers worked on other means to convert linear motion to rotary motion. rotary to motion linear convert to means other on worked engineers other

Slider-crank linkages (see (see linkages 15th the in Slider-crank Vinci da Leonardo of to Figure (ii) A known were Box 1) century. Perhaps they existed much before that. But several accomplished engineers of the of engineers accomplished several But that. before much existed they Perhaps century. steam engine era believed that a simple piston-crank linkage would not serve well because of the of because well serve not would linkage piston-crank simple a that believed era engine steam irregularity of generated power or because of the fear that a crank will not be able to bear the bear to able be not will crank a that fear the of because or power generated of irregularity loads. This opinion was shared by John Smeaton, who had contributed a lot to the development the to lot a contributed had who Smeaton, John by shared was opinion This loads. of steam engines and is the father of the civil engineering profession, for whom Watt had a lot a had Watt whom for profession, engineering civil the of father the is and engines steam of of admiration. Perhaps because of that or due to fear of infringement of a patent by his by patent a of infringement of fear to due or that of because Perhaps admiration. of contemporaries, Watt too did not stick to a slider-crank linkage although he had experimented had he although linkage slider-crank a to stick not did too Watt contemporaries, with it. Historical reports say that James Pickard, who had employed Mathew Wasborough to Wasborough Mathew employed had who Pickard, James that say reports Historical it. with build an engine for his flour mill, had a patent that involved a crank. So, Watt explicitly avoided explicitly Watt So, crank. a involved that patent a had mill, flour his for engine an build a crank and attempted new designs. One of them was the sun-planet gear linkage, which is a is which linkage, gear sun-planet the was them of One designs. new attempted and crank a somewhat roundabout solution when we think about it today. it about think we when solution roundabout somewhat

9a shows the photograph of the sun-planet or epicyclic gear linkage. linkage. gear epicyclic or sun-planet the of photograph the Figure shows 9a the Figure shows 9b schematic of the linkage. It has two gears that mesh with each other. One gear is fixed to a base- a to fixed is gear One other. each with mesh that gears two has It linkage. the of schematic frame with a pin joint and turns with the shaft from which power can be tapped for any for tapped be can power which from shaft the with turns and joint pin a with frame application. This gear is the sun gear because the second gear – called the planet gear – revolves – gear planet the called – gear second the because gear sun the is gear This application. around the sun gear. The planet gear is rigidly connected using two pin joints to a connecting rod connecting a to joints pin two using connected rigidly is gear planet The gear. sun the around

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Figure 9. Watt’s sun-planet gear linkage for converting reciprocating linear motion into continuous into motion linear reciprocating converting for linkage gear sun-planet Watt’s 9. Figure rotary motion. (a) Photograph [1]. (b) Schematic. (b) [1]. Photograph (a) motion. rotary

which in turn is attached to the great beam. The planet in this linkage does not spin about its about spin not does linkage this in planet The beam. great the to attached is turn in which centre. By making the radii of the planet and gear the same, Watt made it possible to rotate the rotate to possible it made Watt same, the gear and planet the of radii the making By centre. sun gear twice for every cycle of the steam engine. This made the required size of the flywheel the of size required the made This engine. steam the of cycle every for twice gear sun small because it rotates twice as fast as otherwise. A flywheel was added to smooth out the out smooth to added was flywheel A otherwise. as fast as twice rotates it because small periodic bursts of forces coming from a steam engine. steam a from coming forces of bursts periodic

Today, the invention of the sun-planet gear linkage is sometimes credited to Watt’s loyal Watt’s to credited sometimes is linkage gear sun-planet the of invention the Today, employee and an inventive engineer, William Murdoch. But in a letter written by Watt to Watt by written letter a in But Murdoch. William engineer, inventive an and employee I have tried a model of one of my old plans of plans old my of one of model a tried have I “… says: Watt 1782, 3rd, January on Boulton rotative engines revived and executed by W.M(urdock) and which merits being included as a as included being merits which and W.M(urdock) by executed and revived engines rotative …”. Here, Watt was alluding to the methods of converting linear reciprocating linear converting of methods the to alluding method was Watt fifth Here, …”. motion into continuous rotary motion. The other four were: (i) a two-cylinder engine with engine two-cylinder a (i) were: four other The motion. rotary continuous into motion cranks that were out of phase with counterweights on the shaft to overcome the difficulties of difficulties the overcome to shaft the on counterweights with phase of out were that cranks a dead-centre position when a sliding piston cannot transmit power to the rotating shaft; (ii) a (ii) shaft; rotating the to power transmit cannot piston sliding a when position dead-centre a modification of a rack arrangement; (iii) the internally-geared connecting rod; and (iv) the (iv) and rod; connecting internally-geared the (iii) arrangement; rack a of modification swash plate and crown-cam motion. It is believed that the fifth method of sun-planet gear sun-planet of method fifth the that believed is It motion. crown-cam and plate swash method was added in the 1782 patent upon a suggestion of Murdock. It was one of the simplest the of one was It Murdock. of suggestion a upon patent 1782 the in added was method and most practicable of all the five methods described in the patent specifications. patent the in described methods five the all of practicable most and

Centrifugal Governor Centrifugal

A third important linkage that is attributed to James Watt is the the is Watt James to attributed is that linkage important third A governor Watt’s neither Watt . invented it nor patented its use but many believe that he used a centrifugal governor in a steam a in governor centrifugal a used he that believe many but use its patented nor it invented engine for the first time. A centrifugal governor, shown in in shown governor, centrifugal A time. first the for engine in schematic a with Figure 10a Figure 10b, is a marvelous example of automatic control. It was used in mills to regulate the distance the regulate to mills in used was It control. automatic of example marvelous a is 10b,

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Figure 10. Watt’s centrifugal governor. (a) Photograph [1]. (b) Schematic. (b) [1]. Photograph (a) governor. centrifugal Watt’s 10. Figure

and pressure between the mill-stone and bed-stone as per the speed of the engine. Boulton saw Boulton engine. the of speed the per as bed-stone and mill-stone the between pressure and it in a mill and was amazed at the way it worked and wrote to Watt about it in a small paragraph small a in it about Watt to wrote and worked it way the at amazed was and mill a in it in a letter in 1788. That was all Watt needed to come up with the design shown in in shown design the with up come to needed Watt all was That 1788. in letter a in Figure 10a just five months later. Watt cleverly used it to control the throttle valve that lets the steam in. The in. steam the lets that valve throttle the control to it used cleverly Watt later. months five just governor works as follows. as works governor

It is essentially a slider-crank linkage (see (see linkage slider-crank a essentially is It the by of driven Figure is A(ii) it but Box 1) centrifugal force that a rotating body would experience. Here, a heavy ball is hung like a like hung is ball heavy a Here, experience. would body rotating a that force centrifugal pendulum from the pivot of the crank in the slider-crank linkage wherein the pivot itself can spin can itself pivot the wherein linkage slider-crank the in crank the of pivot the from pendulum around the axis of a vertical shaft but is fixed to the shaft. The pendulum rod is extended beyond extended is rod pendulum The shaft. the to fixed is but shaft vertical a of axis the around the pivot to serve as the crank in the slider-crank. The sliding pivot – a sleeve – also can spin can also – sleeve a – pivot sliding The slider-crank. the in crank the as serve to pivot the around and hence can slide. As the shaft starts rotating, the ball moves away from the centre of centre the from away moves ball the rotating, starts shaft the As slide. can hence and around centrifugal force. This makes the sleeve move down closer to the fixed pivot. fixed the to closer down move sleeve the the to makes due This shaft the force. centrifugal This movement is used to open or close the throttle valve. A prior adjustment sets the required the sets adjustment prior A valve. throttle the close or open to used is movement This opening of the valve corresponding to a speed of rotation. Thus, the rotation speed of the engine the of speed rotation the Thus, rotation. of speed a to corresponding valve the of opening shaft is used to regulate the steam that is let in. In general, another ball and the linkage are used are linkage the and ball another general, In in. let is that steam the regulate to used is shaft for symmetry and balance. and symmetry for

The centrifugal governor is yet another example of how Watt could invent and adapt anything adapt and invent could Watt how of example another yet is governor centrifugal The and everything that made the steam engine better. engine steam the made that everything and

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Pressure-indicating Linkage Pressure-indicating

Before discussing this linkage, we shall slightly digress to mention how how mention to digress slightly shall we linkage, this discussing Before the be to came watt (W) unit for power rating in modern times. Measuring the capacity of an engine in terms of horses of terms in engine an of capacity the Measuring times. modern in rating power for unit was not new in Watt’s time. It was only natural to do that because horses used to do the work the do to used horses because that do to natural only was It time. Watt’s in new not was before steam engines came along. Watt went further and estimated the power a horse contrib- horse a power the estimated and further went Watt along. came engines steam before utes. He observed that a mill-horse walks in a circular path of 24 ft diameter 2.4 times in a in times 2.4 diameter ft 24 of path circular a in walks mill-horse a that observed He utes. minute. He measured that a horse exerts a pull of 180 lb. So, the work done by a horse per minute per horse a by done work the So, lb. 180 of pull a exerts horse a that measured He minute. × 24 × 2.4 × 180 = 32572 ft.lb/min. It appears that Watt, for convenience, rounded it off to off it rounded convenience, for Watt, that appears It ft.lb/min. 32572 = 180 × 2.4 × is 24  × 33,000 ft.lb/min or 550 ft.lb/s, which is used even today as the old unit of power, the the power, of unit old the as today even used is which ft.lb/s, 550 or ft.lb/min 33,000 horse or HP to rate engines. One HP is equal to 746 W. The watt unit for power was adopted was power for unit watt The W. 746 to equal is HP One engines. rate to HP power or by the Second Congress of the British Association for the Advancement of Science in 1889, and 1889, in Science of Advancement the for Association British the of Congress Second the by by the General Conference on the Weights and Measures in 1960 as the unit of power in- power of unit the as 1960 in Measures and Weights the on Conference General the by corporated in the International System of Units (SI). It is a well-deserved tribute to James Watt. James to tribute well-deserved a is It (SI). Units of System International the in corporated

It is easy to imagine how James Watt would have measured the number of turns a horse would horse a turns of number the measured have would Watt James how imagine to easy is It make in a minute on a circular track of 24 ft diameter. But how did he estimate the force exerted force the estimate he did how But diameter. ft 24 of track circular a on minute a in make by a horse? All horses would not exert the same force and a given horse would not always exert always not would horse given a and force same the exert not would horses All horse? a by the same force. So, perhaps he compared the power of a steam engine that pumped water with water pumped that engine steam a of power the compared he perhaps So, force. same the that of a horse-driven pump. In order to rate the power of a steam engine he invented a pressure a invented he engine steam a of power the rate to order In pump. horse-driven a of that gauge to measure the variations of the pressure in the engine’s cylinder.James Watt called Watt cylinder.James engine’s the in pressure the of variations the measure to gauge his pressure gauge an an gauge in pressure shown his is indicator indicator Watt’s . in schematic its with Figure 11a 11b. It is a simple linkage but uses a helical spring. Its linkage structure is akin to that of that to akin is structure linkage Its spring. helical a uses but linkage simple a is It Figure 11b. the Newcomen engine but the novelty lies in the way Watt used it. An instrument of this kind this of instrument An it. used Watt way the in lies novelty the but engine Newcomen the needs calibration with known pressure. Watt knew this very well as he had devised a method to method a devised had he as well very this knew Watt pressure. known with calibration needs determine the power of pumping of power the determine engines.

Perspective-drawing Linkage Perspective-drawing

Around the time Watt conceived Watt time the Around his remarkable idea of a separate a of idea remarkable his condenser for a steam engine to engine steam a for condenser improve its efficiency, he also in- also he efficiency, its improve vented a perspective-drawing link- perspective-drawing a vented

Figure 11. Watt’s pressure indica- pressure Watt’s 11. Figure tor. (a) Photograph [1]. (b) Sche- (b) [1]. Photograph (a) tor. matic.

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age in 1765. It is shown in in shown is It 1765. in age part A Figure 12. of this linkage is similar to that of a mini- a of that to similar is linkage this of drafter used for engineering drawing. This drawing. engineering for used drafter part consists of two parallelograms in se- in parallelograms two of consists part ries, with one of them fixed to a tripod. The tripod. a to fixed them of one with ries, pencil-holder point of the second parallelo- second the of point pencil-holder gram extends further with an index. Also index. an with further extends gram attached to the tripod holding a sheet of sheet a holding tripod the to attached paper in a frame is a movable two-arm link- two-arm movable a is frame a in paper age with an eyepiece. To draw the perspec- the draw To eyepiece. an with age tive, one has to look at a building through building a at look to has one tive, the eyepiece and follow it with the index. the with it follow and eyepiece the The pencil then draws the perspective of the of perspective the draws then pencil The automatically on the paper. the on building automatically

The perspective-drawing linkage had an- had linkage perspective-drawing The other nice feature. The board was foldable was board The feature. nice other to a reasonable size to fit in a pocket. The pocket. a in fit to size reasonable a to legs of the tripod telescoped within them- within telescoped tripod the of legs selves and could be folded to form a walk- a form to folded be could and selves Figure 12. Watt’s perspective-drawing machine [1]. machine perspective-drawing Watt’s 12. Figure ing stick! Watt did not patent this apparatus this patent not did Watt stick! ing He did not patent it although he had made several made had he although it patent not did He although he had made 50-80 pieces of this of pieces 50-80 made had he although became he before much them sold and pieces and sold them. It is reported that these still these that reported is It them. sold and famous. exist in different places around the world in world the around places different in exist museums and private collections. private and museums

Sculpting Linkages Sculpting

Watt’s inventive spirit did not age with him. When he was in his late sixties to early seventies, early to sixties late his in was he When him. with age not did spirit inventive Watt’s he started to work on sculpting machines. He did this perhaps for his amusement. In the In amusement. his for perhaps this did He machines. sculpting on work to started he workshop he had in his mansion ‘Heathfield’ mansion his in had he from workshop retirement his after stayed he where , mainstream work, busts of Socrates and Aristotle were found. There were also two machines two also were There found. were Aristotle and Socrates of busts work, mainstream using which three-dimensional objects could be replicated. Published biographical accounts biographical Published replicated. be could objects three-dimensional which using and Watt’s letters indicate that Watt designed and built those machines himself. There were There himself. machines those built and designed Watt that indicate letters Watt’s and two machines: one, a proportional sculpting machine and the other, an equal-sized sculpting equal-sized an other, the and machine sculpting proportional a one, machines: two machine. latter. machine. the Figure shows 13

Watt’s equal-sized sculpting machine used a lathe-bed (see (see lathe-bed a used machine sculpting equal-sized Watt’s Two base. the for Figure 13) tetrahedral frames were mounted on it. One frame was movable on a slide while the other was other the while slide a on movable was frame One it. on mounted were frames tetrahedral

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able to rotate up and down and left and left and down and up rotate to able right. A number of linkages were added were linkages of number A right. to balance the weight of the frames and to and frames the of weight the balance to guide them. Also in it were a feeler to feeler a were it in Also them. guide follow the contour of the original object original the of contour the follow and a tool (a variety of them specially them of variety (a tool a and made for him by Murdock and others) to others) and Murdock by him for made sculpt the replica. The machine also had also machine The replica. the sculpt a treadle to power it. There was a provi- a was There it. power to treadle a sion to run it slowly or fast. Wood, ala- Wood, fast. or slowly it run to sion and other materials were used to used were materials other baster, and make replicas. By simply moving the moving simply By replicas. make feeler over the original object and push- and object original the over feeler ing the treadle, anyone could make repli- make could anyone treadle, the ing cas using this machine as it did not need not did it as machine this using cas any skill on the part of the user. the of part the on skill any

For a man who had made earlier in his in earlier made had who man a For life a letter-copying machine just to avoid to just machine letter-copying a life the monotony of copying his correspon- his copying of monotony the dence, documents, and drawings, mak- drawings, and documents, dence, ing a sculpting machine was probably a probably was machine sculpting a ing small modification. James Watt had many had Watt James modification. small machine sculpting equal-sized Watt’s 13. Figure names, usually derived from Greek roots, Greek from derived could usually that this names, of variants different also had He [1]. make scaled replicas including miniaturized ones. miniaturized including replicas scaled make for these machines. One such name was name such One machines. these for polyglyptic ( do could and polyglyptic machine many his poly meaning because carved) glyptic meaning several replicas at the same time. This machine was also capable of making miniature replicas miniature making of capable also was machine This time. same the at replicas several of objects. When he informed his friend about his new machine, he lamented that he could not could he that lamented he machine, new his about friend his informed he When objects. of incorporate all of his ideas into it. into ideas his of all incorporate

Closure

H W Dickinson, who wrote a book on Watt’s life and work [2], notes that Hippocrates’s that notes [2], work and life Watt’s on book a wrote who Dickinson, W H aphorism is apt in Watt’s life: life: Watt’s in short’. apt is is life aphorism long, brevis is vita ‘art to longa ars translates which , James Watt died at the age of 83 in 1819 – perhaps his life was not long enough to try all his ideas his all try to enough long not was life his perhaps – 1819 in 83 of age the at died Watt James for linkages. for

We presented a number of linkage inventions of James Watt here but we did not mention a mention not did we but here Watt James of inventions linkage of number a presented We

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number of other things he invented just to solve problems he encountered and the scientific the and encountered he problems solve to just invented he things other of number reasoning he used in those inventions. He had observed the phenomenon of latent heat, the heat, latent of phenomenon the observed had He inventions. those in used he reasoning theory of which was propounded by his mentor and friend, Professor Joseph Black. He had He Black. Joseph Professor friend, and mentor his by propounded was which of theory guessed (some say for the first time) that water is a compound and not an element. He had He element. an not and compound a is water that time) first the for say (some guessed improved a telemeter used to measure long distances when he worked as a civil engineer to engineer civil a as worked he when distances long measure to used telemeter a improved survey canals. He had given the idea of a screw propeller to a friend. He had designed a smoke- a designed had He friend. a to propeller screw a of idea the given had He canals. survey consuming furnace. He had worked on new iron cement for sealing. He had built a mechanical a built had He sealing. for cement iron new on worked had He furnace. consuming counter for counting the number of strokes of the engine up to a few millions. He did not bother not did He millions. few a to up engine the of strokes of number the counting for counter to patent these and a few other innovations. For him, all this was simply making the tools he tools the making simply was this all him, For innovations. other few a and these patent to needed. King Solomon (who, as the legend has it, rewarded the iron worker who made his own his made who worker iron the rewarded it, has legend the as (who, Solomon King needed. tools) would have surely rewarded James Watt, the super craftsman, who not only conceived only not who craftsman, super the Watt, James rewarded surely have would tools) and made the tools he needed but also knew much more than the tools and the craft. the and tools the than more much knew also but needed he tools the made and

Watt’s life is a consummate example of a craftsman turning into an engineer and an engineer an and engineer an into turning craftsman a of example consummate a is life Watt’s turning into a scientist. Archibald Barr, in a presidential address he gave on February 15, 1925, 15, February on gave he address presidential a in Barr, Archibald scientist. a into turning to the Optical Society, accurately captured Watt’s personality: “ personality: Watt’s captured accurately Society, Optical the to on bear to brought Watt James the practice of mechanical engineering a mind trained to consider scientifically the problems the scientifically consider to trained mind a engineering mechanical of practice the that presented themselves in his practice. He was a master in scientific reasoning based on based reasoning scientific in master a was He practice. his in themselves presented that sound knowledge of the facts and laws of the physics and chemistry of his time. His many His time. his of chemistry and physics the of laws and facts the of knowledge sound inventions contributed more than the work of any other man towards laying the foundation for foundation the laying towards man other any of work the than more contributed inventions that vast and rapid development of the mechanical arts that characterized the 19th century 19th the characterized that arts mechanical the of development rapid and vast that ”.

Steam engines of the kind James Watt invented are not in use today but his contributions to contributions his but today use in not are invented Watt James kind the of engines Steam engineering at large remain relevant forever. When it comes to linkages, no student of student no linkages, to comes it When forever. relevant remain large at engineering kinematics misses to learn about Watt’s straight-line linkage or Watt’s six-bar chain. Watt’s chain. six-bar Watt’s or linkage straight-line Watt’s about learn to misses kinematics straight-line linkage is still used in some of the automobiles to prevent the undesirable the prevent to automobiles the of some in used still is linkage straight-line movement of the axle. the of movement