1671:
36:
93:
1678:
Peaucellier–Lipkin linkages (PLLs) may have several inversions. A typical example is shown in the opposite figure, in which a rocker-slider four-bar serves as the input driver. To be precise, the slider acts as the input, which in turn drives the right grounded link of the PLL, thus driving the
164:
moving in a straight-line up and down a cylinder. This piston needed to keep a good seal with the cylinder in order to retain the driving medium, and not lose energy efficiency due to leaks. The piston does this by remaining perpendicular to the axis of the cylinder, retaining its straight-line
721:
184:. This linkage predates the Peaucellier–Lipkin linkage by 11 years and consists of a series of hinged rectangular plates, two of which remain parallel but can be moved normally to each other. Sarrus' linkage is of a three-dimensional class sometimes known as a
197:
1008:
1479:
570:
603:
1698:, he “nursed it as if it had been his own child, and when a motion was made to relieve him of it, replied ‘No! I have not had nearly enough of it—it is the most beautiful thing I have ever seen in my life.’”
1109:
1285:
909:
608:
1568:
1187:
1354:
904:
2044:
165:
motion. Converting the straight-line motion of the piston into circular motion was of critical importance. Most, if not all, applications of these steam engines, were rotary.
156:
Until this invention, no planar method existed of converting exact straight-line motion to circular motion, without reference guideways. In 1864, all power came from
1710:. The artwork measures 22 by 15 by 16 metres (72 ft × 49 ft × 52 ft), weighs 6,600 kilograms (14,600 lb), and can be operated from a
1670:
1363:
2037:
716:{\displaystyle {\begin{aligned}&2\times \angle OBA+2\times \angle DBA=360^{\circ }\\&\angle OBA+\angle DBA=180^{\circ }\end{aligned}}}
488:
2030:
1929:
1898:
1855:
1886:
1999:
2594:
2155:
1954:
1835:
79:
57:
1790:
1019:
2017:
2584:
1866:
1200:
2248:
2175:
2071:
1711:
1514:
1115:
138:
1294:
1003:{\displaystyle {\begin{aligned}&x=\ell _{BP}=\ell _{PD}\\&y=\ell _{OB}\\&h=\ell _{AP}\end{aligned}}}
2325:
2165:
1845:
50:
44:
1980:
1994:
1728:
122:
288:
is constrained to move along a circle (for example, by attaching it to a bar with a length halfway between
2589:
2320:
2275:
2185:
2118:
1707:
1706:
A monumental-scale sculpture implementing the linkage in illuminated struts is on permanent exhibition in
1687:
61:
2310:
2305:
2285:
2210:
2170:
2160:
2113:
2108:
142:
1970:
1924:(reprint of 1929 edition by Houghton Mifflin ed.). New York: Dover Publications. pp. 46–51.
2315:
2295:
2290:
2280:
2258:
2200:
2091:
2086:
2053:
2005:
1985:
1723:
134:
126:
2549:
2373:
2300:
2195:
2145:
1862:— proof and discussion of Peaucellier–Lipkin linkage, mathematical and real-world mechanical models
1191:
1922:
Advanced
Euclidean Geometry: An elementary treatise on the geometry of the triangle and the circle
2368:
2238:
2233:
2190:
2128:
1913:
1618:
185:
169:
1946:
1940:
1890:
1827:
1821:
2358:
2243:
2228:
2205:
1950:
1925:
1894:
1851:
1831:
1817:
92:
2348:
2343:
1882:
1874:
304:
will necessarily have to move along a straight line (shown in blue). In contrast, if point
2022:
2363:
2353:
2267:
2220:
2123:
150:
1990:
180:
There is an earlier straight-line mechanism, whose history is not well known, called the
349:. This may be easily seen by observing that the linkage is mirror-symmetric about line
2133:
1870:
181:
146:
1474:{\displaystyle {\ell _{OA}}^{2}-{\ell _{AD}}^{2}=y^{2}+2xy=\ell _{OB}\cdot \ell _{OD}}
2578:
2544:
2534:
2391:
2180:
2098:
2057:
1971:
How to Draw a
Straight Line, online video clips of linkages with interactive applets.
1875:
130:
196:
2076:
346:
168:
The mathematics of the
Peaucellier–Lipkin linkage is directly related to the
157:
2011:
1975:
1769:
1747:
1909:
204:
In the geometric diagram of the apparatus, six bars of fixed length can be seen:
2335:
2140:
2081:
1695:
2508:
2503:
2498:
2465:
2460:
2455:
2450:
2445:
2440:
2435:
2423:
2411:
2150:
2103:
2493:
2430:
2418:
2406:
2401:
2396:
1674:
Slider-rocker four-bar acts as the driver of the
Peaucellier–Lipkin linkage
188:, unlike the Peaucellier–Lipkin linkage which is a planar mechanism.
27:
Mechanical linkage capable of transforming rotary motion into linear motion
17:
2559:
2554:
2539:
2518:
2513:
2488:
2483:
2475:
2383:
771:
565:{\displaystyle \angle OBA+\angle ABD+\angle DBC+\angle CBO=360^{\circ }}
1847:
How round is your circle? : where engineering and mathematics meet
763:
277:
1659:
161:
1976:
How to Draw a
Straight Line, historical discussion of linkage design
1791:"Just because you are a character, doesn't mean you have character"
1669:
195:
91:
1850:. Princeton: Princeton University Press. pp. 33–38, 60–63.
2026:
316:
would necessarily have to move along a circle (passing through
2018:
Modified
Peaucellier robotic arm linkage (Vex Team 1508 video)
29:
1104:{\displaystyle \ell _{OB}\cdot \ell _{OD}=y(y+2x)=y^{2}+2xy}
308:
were constrained to move along a line (not passing through
1942:
The
Penguin Dictionary of Curious and Interesting Geometry
1748:"Mathematical tutorial of the Peaucellier–Lipkin linkage"
1694:, Vol. 3, Paper 2) writes that when he showed a model to
1633:
traces a circle passing through the center of inversion
1912:, pp 181–5, New York: McGraw–Hill, weblink from
1280:{\displaystyle {\ell _{OA}}^{2}=y^{2}+2xy+x^{2}+h^{2}}
482:
Finally, because they form a complete circle, we have
1517:
1366:
1297:
1203:
1118:
1022:
907:
606:
491:
2527:
2474:
2382:
2334:
2266:
2257:
2219:
2064:
1562:
1473:
1348:
1279:
1181:
1103:
1002:
715:
564:
1641:is constrained to trace a straight line. But if
1563:{\displaystyle \ell _{OB}\cdot \ell _{OD}=k^{2}}
1182:{\displaystyle {\ell _{OA}}^{2}=(y+x)^{2}+h^{2}}
121:), invented in 1864, was the first true planar
1986:Java animated Peaucellier–Lipkin linkage
1770:"How to draw a straight line by Daina Taimina"
1653:must trace an arc of a circle passing through
141:(1832–1913), a French army officer, and
2038:
1991:Jewish Encyclopedia article on Lippman Lipkin
1625:is the inverse of the figure traced by point
8:
1496:are both fixed lengths, then the product of
1349:{\displaystyle {\ell _{AD}}^{2}=x^{2}+h^{2}}
1645:traces a straight line not passing through
2263:
2045:
2031:
2023:
296:; path shown in red) which passes through
200:Geometric diagram of a Peaucellier linkage
1908:Hartenberg, R.S. & J. Denavit (1964)
1554:
1538:
1522:
1516:
1462:
1446:
1421:
1408:
1398:
1393:
1383:
1373:
1368:
1365:
1340:
1327:
1314:
1304:
1299:
1296:
1271:
1258:
1233:
1220:
1210:
1205:
1202:
1173:
1160:
1135:
1125:
1120:
1117:
1083:
1043:
1027:
1021:
987:
963:
939:
923:
908:
906:
703:
658:
607:
605:
556:
490:
96:Animation for Peaucellier–Lipkin linkage:
80:Learn how and when to remove this message
43:This article includes a list of general
1739:
2008:using the Molecular Workbench software
1844:Bryant, John; Sangwin, Chris (2008).
333:First, it must be proven that points
7:
137:, and vice versa. It is named after
1981:Interactive Java Applet with proof.
1945:. New York: Penguin Books. p.
1621:, since the figure traced by point
1714:accessible to the general public.
684:
669:
639:
618:
537:
522:
507:
492:
465:are congruent. Therefore, angles
453:is congruent to itself, and sides
49:it lacks sufficient corresponding
25:
833:is congruent to itself, and side
119:Peaucellier–Lipkin inversor
111:Peaucellier–Lipkin linkage
34:
1910:Kinematic synthesis of linkages
2002:features an interactive applet
1905:(and references cited therein)
1157:
1144:
1073:
1058:
1:
750:be the intersection of lines
575:but, due to the congruences,
380:is congruent to itself, side
324:Mathematical proof of concept
115:Peaucellier–Lipkin cell
1772:. Kmoddl.library.cornell.edu
1750:. Kmoddl.library.cornell.edu
1617:Thus, by the properties of
1593:with respect to the circle
435:are congruent, since sides
374:are congruent because side
149:and son of the famed Rabbi
139:Charles-Nicolas Peaucellier
2611:
1288:(same expression expanded)
284:is fixed. Then, if point
246:is equal to the length of
808:is congruent to triangle
360:More formally, triangles
2595:Straight line mechanisms
357:must fall on that line.
276:are all equal forming a
129:capable of transforming
2014:called Hart's Inversor.
2000:Peaucellier Apparatus
1729:Straight line mechanism
123:straight line mechanism
64:more precise citations.
2186:Single-acting cylinder
2119:Double-acting cylinder
1823:Excursions in Geometry
1708:Eindhoven, Netherlands
1675:
1564:
1475:
1350:
1281:
1183:
1105:
1004:
774:of both line segments
717:
566:
201:
176:Earlier Sarrus linkage
106:
2585:Linkages (mechanical)
2054:Engine configurations
1673:
1565:
1476:
1357:(Pythagorean theorem)
1351:
1282:
1184:
1106:
1005:
839:is congruent to side
821:is congruent to side
786:. Therefore, length
718:
567:
404:. Therefore, angles
398:is congruent to side
386:is congruent to side
252:, and the lengths of
199:
145:(1846–1876), a
143:Yom Tov Lipman Lipkin
95:
2156:Oscillating cylinder
1724:Linkage (mechanical)
1585:are collinear, then
1515:
1364:
1295:
1201:
1116:
1020:
905:
845:. Therefore, angle
604:
489:
447:are congruent, side
135:straight-line motion
2249:Two-and four-stroke
2151:Intake over exhaust
1920:Johnson RA (1960).
1702:Cultural references
1192:Pythagorean theorem
125:– the first planar
1914:Cornell University
1877:Geometry Revisited
1826:, Dover, pp.
1676:
1619:inversive geometry
1613:Inversive geometry
1589:is the inverse of
1560:
1471:
1346:
1277:
1179:
1101:
1000:
998:
713:
711:
562:
202:
107:
2572:
2571:
2568:
2567:
2268:Inline / straight
2166:Overhead camshaft
2012:A related linkage
1931:978-0-486-46237-0
1900:978-0-88385-619-2
1857:978-0-691-13118-4
1573:and since points
1358:
1289:
1195:
726:therefore points
90:
89:
82:
16:(Redirected from
2602:
2264:
2259:Cylinder layouts
2047:
2040:
2033:
2024:
1960:
1939:Wells D (1991).
1935:
1904:
1880:
1861:
1840:
1805:
1804:
1802:
1801:
1787:
1781:
1780:
1778:
1777:
1768:Taimina, Daina.
1765:
1759:
1758:
1756:
1755:
1744:
1683:Historical notes
1666:A typical driver
1656:
1652:
1648:
1644:
1640:
1636:
1632:
1628:
1624:
1608:
1604:
1600:
1592:
1588:
1584:
1580:
1576:
1569:
1567:
1566:
1561:
1559:
1558:
1546:
1545:
1530:
1529:
1507:
1506:
1501:
1500:
1495:
1494:
1489:
1488:
1480:
1478:
1477:
1472:
1470:
1469:
1454:
1453:
1426:
1425:
1413:
1412:
1407:
1406:
1405:
1388:
1387:
1382:
1381:
1380:
1356:
1355:
1353:
1352:
1347:
1345:
1344:
1332:
1331:
1319:
1318:
1313:
1312:
1311:
1287:
1286:
1284:
1283:
1278:
1276:
1275:
1263:
1262:
1238:
1237:
1225:
1224:
1219:
1218:
1217:
1189:
1188:
1186:
1185:
1180:
1178:
1177:
1165:
1164:
1140:
1139:
1134:
1133:
1132:
1110:
1108:
1107:
1102:
1088:
1087:
1051:
1050:
1035:
1034:
1009:
1007:
1006:
1001:
999:
995:
994:
975:
971:
970:
951:
947:
946:
931:
930:
911:
894:
886:
878:
870:
858:
851:
844:
843:
838:
837:
832:
831:
826:
825:
820:
819:
814:
807:
797:
796:
791:
790:
785:
784:
779:
778:
769:
761:
757:
753:
749:
737:
733:
729:
722:
720:
719:
714:
712:
708:
707:
667:
663:
662:
610:
596:
585:
571:
569:
568:
563:
561:
560:
478:
471:
464:
463:
458:
457:
452:
451:
446:
445:
440:
439:
434:
427:
421:Next, triangles
417:
410:
403:
402:
397:
396:
391:
390:
385:
384:
379:
378:
373:
366:
356:
352:
344:
340:
336:
319:
315:
311:
307:
303:
299:
295:
291:
287:
283:
275:
274:
269:
268:
263:
262:
257:
256:
251:
250:
245:
244:
240:. The length of
239:
238:
233:
232:
227:
226:
221:
220:
215:
214:
209:
208:
105:Yellow Links = c
85:
78:
74:
71:
65:
60:this article by
51:inline citations
38:
37:
30:
21:
2610:
2609:
2605:
2604:
2603:
2601:
2600:
2599:
2575:
2574:
2573:
2564:
2523:
2470:
2378:
2330:
2253:
2215:
2060:
2051:
1995:Israel Salanter
1993:and his father
1967:
1957:
1938:
1932:
1919:
1901:
1865:
1858:
1843:
1838:
1816:
1813:
1808:
1799:
1797:
1789:
1788:
1784:
1775:
1773:
1767:
1766:
1762:
1753:
1751:
1746:
1745:
1741:
1737:
1720:
1704:
1692:Collected Works
1685:
1668:
1654:
1650:
1646:
1642:
1638:
1634:
1630:
1626:
1622:
1615:
1606:
1602:
1594:
1590:
1586:
1582:
1578:
1574:
1550:
1534:
1518:
1513:
1512:
1508:is a constant:
1504:
1503:
1498:
1497:
1492:
1491:
1486:
1485:
1458:
1442:
1417:
1394:
1392:
1369:
1367:
1362:
1361:
1336:
1323:
1300:
1298:
1293:
1292:
1267:
1254:
1229:
1206:
1204:
1199:
1198:
1169:
1156:
1121:
1119:
1114:
1113:
1079:
1039:
1023:
1018:
1017:
997:
996:
983:
973:
972:
959:
949:
948:
935:
919:
903:
902:
888:
880:
872:
860:
853:
846:
841:
840:
835:
834:
829:
828:
823:
822:
817:
816:
815:, because side
809:
802:
794:
793:
788:
787:
782:
781:
776:
775:
767:
759:
758:. Then, since
755:
751:
747:
744:
738:are collinear.
735:
731:
727:
710:
709:
699:
665:
664:
654:
602:
601:
587:
576:
552:
487:
486:
473:
466:
461:
460:
455:
454:
449:
448:
443:
442:
437:
436:
429:
422:
412:
405:
400:
399:
394:
393:
388:
387:
382:
381:
376:
375:
368:
361:
354:
350:
342:
338:
334:
331:
326:
317:
313:
309:
305:
301:
297:
293:
289:
285:
281:
280:. Also, point
272:
271:
266:
265:
260:
259:
254:
253:
248:
247:
242:
241:
236:
235:
230:
229:
224:
223:
218:
217:
212:
211:
206:
205:
194:
178:
151:Israel Salanter
104:
103:Green Links = b
102:
100:
98:
97:
86:
75:
69:
66:
56:Please help to
55:
39:
35:
28:
23:
22:
15:
12:
11:
5:
2608:
2606:
2598:
2597:
2592:
2587:
2577:
2576:
2570:
2569:
2566:
2565:
2563:
2562:
2557:
2552:
2547:
2542:
2537:
2531:
2529:
2525:
2524:
2522:
2521:
2516:
2511:
2506:
2501:
2496:
2491:
2486:
2480:
2478:
2472:
2471:
2469:
2468:
2463:
2458:
2453:
2448:
2443:
2438:
2433:
2428:
2427:
2426:
2416:
2415:
2414:
2404:
2399:
2394:
2388:
2386:
2380:
2379:
2377:
2376:
2371:
2366:
2361:
2356:
2351:
2346:
2340:
2338:
2332:
2331:
2329:
2328:
2323:
2318:
2313:
2308:
2303:
2298:
2293:
2288:
2283:
2278:
2272:
2270:
2261:
2255:
2254:
2252:
2251:
2246:
2241:
2236:
2231:
2225:
2223:
2217:
2216:
2214:
2213:
2208:
2203:
2198:
2193:
2188:
2183:
2178:
2173:
2171:Overhead valve
2168:
2163:
2161:Opposed-piston
2158:
2153:
2148:
2143:
2138:
2137:
2136:
2126:
2121:
2116:
2111:
2106:
2101:
2096:
2095:
2094:
2089:
2079:
2074:
2068:
2066:
2062:
2061:
2058:piston engines
2052:
2050:
2049:
2042:
2035:
2027:
2021:
2020:
2015:
2009:
2003:
1997:
1988:
1983:
1978:
1973:
1966:
1965:External links
1963:
1962:
1961:
1955:
1936:
1930:
1917:
1906:
1899:
1863:
1856:
1841:
1836:
1812:
1809:
1807:
1806:
1782:
1760:
1738:
1736:
1733:
1732:
1731:
1726:
1719:
1716:
1703:
1700:
1684:
1681:
1667:
1664:
1614:
1611:
1571:
1570:
1557:
1553:
1549:
1544:
1541:
1537:
1533:
1528:
1525:
1521:
1482:
1481:
1468:
1465:
1461:
1457:
1452:
1449:
1445:
1441:
1438:
1435:
1432:
1429:
1424:
1420:
1416:
1411:
1404:
1401:
1397:
1391:
1386:
1379:
1376:
1372:
1359:
1343:
1339:
1335:
1330:
1326:
1322:
1317:
1310:
1307:
1303:
1290:
1274:
1270:
1266:
1261:
1257:
1253:
1250:
1247:
1244:
1241:
1236:
1232:
1228:
1223:
1216:
1213:
1209:
1196:
1176:
1172:
1168:
1163:
1159:
1155:
1152:
1149:
1146:
1143:
1138:
1131:
1128:
1124:
1111:
1100:
1097:
1094:
1091:
1086:
1082:
1078:
1075:
1072:
1069:
1066:
1063:
1060:
1057:
1054:
1049:
1046:
1042:
1038:
1033:
1030:
1026:
1011:
1010:
993:
990:
986:
982:
979:
976:
974:
969:
966:
962:
958:
955:
952:
950:
945:
942:
938:
934:
929:
926:
922:
918:
915:
912:
910:
743:
742:Inverse points
740:
724:
723:
706:
702:
698:
695:
692:
689:
686:
683:
680:
677:
674:
671:
668:
666:
661:
657:
653:
650:
647:
644:
641:
638:
635:
632:
629:
626:
623:
620:
617:
614:
611:
609:
573:
572:
559:
555:
551:
548:
545:
542:
539:
536:
533:
530:
527:
524:
521:
518:
515:
512:
509:
506:
503:
500:
497:
494:
330:
327:
325:
322:
312:), then point
193:
190:
182:Sarrus linkage
177:
174:
160:, which had a
147:Lithuanian Jew
101:Cyan Links = a
88:
87:
42:
40:
33:
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
2607:
2596:
2593:
2591:
2590:Linear motion
2588:
2586:
2583:
2582:
2580:
2561:
2558:
2556:
2553:
2551:
2548:
2546:
2543:
2541:
2538:
2536:
2533:
2532:
2530:
2526:
2520:
2517:
2515:
2512:
2510:
2507:
2505:
2502:
2500:
2497:
2495:
2492:
2490:
2487:
2485:
2482:
2481:
2479:
2477:
2473:
2467:
2464:
2462:
2459:
2457:
2454:
2452:
2449:
2447:
2444:
2442:
2439:
2437:
2434:
2432:
2429:
2425:
2422:
2421:
2420:
2417:
2413:
2410:
2409:
2408:
2405:
2403:
2400:
2398:
2395:
2393:
2390:
2389:
2387:
2385:
2381:
2375:
2372:
2370:
2367:
2365:
2362:
2360:
2357:
2355:
2352:
2350:
2347:
2345:
2342:
2341:
2339:
2337:
2333:
2327:
2324:
2322:
2319:
2317:
2314:
2312:
2309:
2307:
2304:
2302:
2299:
2297:
2294:
2292:
2289:
2287:
2284:
2282:
2279:
2277:
2274:
2273:
2271:
2269:
2265:
2262:
2260:
2256:
2250:
2247:
2245:
2242:
2240:
2237:
2235:
2232:
2230:
2227:
2226:
2224:
2222:
2221:Stroke cycles
2218:
2212:
2209:
2207:
2204:
2202:
2199:
2197:
2194:
2192:
2189:
2187:
2184:
2182:
2179:
2177:
2174:
2172:
2169:
2167:
2164:
2162:
2159:
2157:
2154:
2152:
2149:
2147:
2144:
2142:
2139:
2135:
2132:
2131:
2130:
2127:
2125:
2122:
2120:
2117:
2115:
2112:
2110:
2107:
2105:
2102:
2100:
2097:
2093:
2090:
2088:
2085:
2084:
2083:
2080:
2078:
2075:
2073:
2070:
2069:
2067:
2063:
2059:
2055:
2048:
2043:
2041:
2036:
2034:
2029:
2028:
2025:
2019:
2016:
2013:
2010:
2007:
2004:
2001:
1998:
1996:
1992:
1989:
1987:
1984:
1982:
1979:
1977:
1974:
1972:
1969:
1968:
1964:
1958:
1956:0-14-011813-6
1952:
1948:
1944:
1943:
1937:
1933:
1927:
1923:
1918:
1915:
1911:
1907:
1902:
1896:
1892:
1888:
1884:
1879:
1878:
1872:
1868:
1864:
1859:
1853:
1849:
1848:
1842:
1839:
1837:0-486-26530-7
1833:
1829:
1825:
1824:
1819:
1818:Ogilvy, C. S.
1815:
1814:
1810:
1796:
1792:
1786:
1783:
1771:
1764:
1761:
1749:
1743:
1740:
1734:
1730:
1727:
1725:
1722:
1721:
1717:
1715:
1713:
1712:control panel
1709:
1701:
1699:
1697:
1693:
1689:
1682:
1680:
1672:
1665:
1663:
1662:
1661:
1620:
1612:
1610:
1598:
1555:
1551:
1547:
1542:
1539:
1535:
1531:
1526:
1523:
1519:
1511:
1510:
1509:
1466:
1463:
1459:
1455:
1450:
1447:
1443:
1439:
1436:
1433:
1430:
1427:
1422:
1418:
1414:
1409:
1402:
1399:
1395:
1389:
1384:
1377:
1374:
1370:
1360:
1341:
1337:
1333:
1328:
1324:
1320:
1315:
1308:
1305:
1301:
1291:
1272:
1268:
1264:
1259:
1255:
1251:
1248:
1245:
1242:
1239:
1234:
1230:
1226:
1221:
1214:
1211:
1207:
1197:
1193:
1174:
1170:
1166:
1161:
1153:
1150:
1147:
1141:
1136:
1129:
1126:
1122:
1112:
1098:
1095:
1092:
1089:
1084:
1080:
1076:
1070:
1067:
1064:
1061:
1055:
1052:
1047:
1044:
1040:
1036:
1031:
1028:
1024:
1016:
1015:
1014:
991:
988:
984:
980:
977:
967:
964:
960:
956:
953:
943:
940:
936:
932:
927:
924:
920:
916:
913:
901:
900:
899:
896:
892:
884:
876:
868:
864:
859:. But since
857:
850:
813:
806:
799:
773:
765:
741:
739:
704:
700:
696:
693:
690:
687:
681:
678:
675:
672:
659:
655:
651:
648:
645:
642:
636:
633:
630:
627:
624:
621:
615:
612:
600:
599:
598:
595:
591:
584:
580:
557:
553:
549:
546:
543:
540:
534:
531:
528:
525:
519:
516:
513:
510:
504:
501:
498:
495:
485:
484:
483:
480:
477:
470:
433:
426:
419:
416:
409:
372:
365:
358:
348:
328:
323:
321:
300:, then point
279:
198:
191:
189:
187:
183:
175:
173:
172:of a circle.
171:
166:
163:
159:
158:steam engines
154:
152:
148:
144:
140:
136:
133:into perfect
132:
131:rotary motion
128:
124:
120:
116:
112:
94:
84:
81:
73:
63:
59:
53:
52:
46:
41:
32:
31:
19:
2550:Split-single
2336:Flat / boxer
2196:Swing-piston
2006:A simulation
1941:
1921:
1876:
1846:
1822:
1811:Bibliography
1798:. Retrieved
1794:
1785:
1774:. Retrieved
1763:
1752:. Retrieved
1742:
1705:
1691:
1686:
1679:entire PLL.
1677:
1658:
1616:
1601:with center
1596:
1572:
1483:
1190:(due to the
1012:
897:
890:
882:
874:
866:
862:
855:
848:
811:
804:
800:
745:
725:
593:
589:
582:
578:
574:
481:
475:
468:
431:
424:
420:
414:
407:
370:
363:
359:
332:
329:Collinearity
203:
179:
167:
155:
118:
114:
110:
108:
76:
67:
48:
2239:Five-stroke
2234:Four-stroke
2191:Split cycle
2129:Free-piston
2072:Atmospheric
1889:. pp.
1871:Greitzer SL
1867:Coxeter HSM
1795:Ivo Schoofs
1605:and radius
479:are equal.
418:are equal.
392:, and side
353:, so point
186:space crank
99:Dimensions:
70:August 2017
62:introducing
18:Peaucellier
2579:Categories
2244:Six-stroke
2229:Two-stroke
2146:Heron head
2104:Cam engine
1883:Washington
1800:2017-08-14
1776:2011-12-06
1754:2011-12-06
1735:References
746:Let point
45:references
1688:Sylvester
1536:ℓ
1532:⋅
1520:ℓ
1460:ℓ
1456:⋅
1444:ℓ
1396:ℓ
1390:−
1371:ℓ
1302:ℓ
1208:ℓ
1123:ℓ
1041:ℓ
1037:⋅
1025:ℓ
985:ℓ
961:ℓ
937:ℓ
921:ℓ
801:Triangle
792:= length
705:∘
685:∠
670:∠
660:∘
640:∠
637:×
619:∠
616:×
558:∘
538:∠
523:∠
508:∠
493:∠
347:collinear
170:inversion
2176:Pentroof
2124:Flathead
2114:Compound
2092:Rotative
1873:(1967).
1820:(1990),
1718:See also
852:= angle
772:midpoint
192:Geometry
2384:V / Vee
2201:Uniflow
2134:Stelzer
2109:Camless
2087:Cornish
1649:, then
1637:, then
871:, then
827:, side
770:is the
764:rhombus
597:, thus
278:rhombus
127:linkage
58:improve
2545:Radial
2535:Deltic
2181:Rotary
2099:Bourke
1953:
1928:
1897:
1893:–111.
1854:
1834:
1696:Kelvin
1660:Q.E.D.
1484:Since
1013:Then:
887:, and
877:= 180°
869:= 180°
734:, and
270:, and
162:piston
47:, but
2528:Other
2211:Wedge
2077:Axial
1828:46–48
1629:, if
898:Let:
893:= 90°
885:= 90°
873:2 × ∠
762:is a
117:, or
2206:Watt
2141:Hemi
2082:Beam
2065:Type
2056:for
1951:ISBN
1926:ISBN
1895:ISBN
1852:ISBN
1832:ISBN
1502:and
1490:and
780:and
760:ABCD
754:and
586:and
472:and
459:and
441:and
428:and
411:and
367:and
345:are
292:and
113:(or
109:The
2519:W30
2514:W24
2509:W18
2504:W16
2499:W12
2466:V24
2461:V20
2456:V18
2451:V16
2446:V14
2441:V12
2436:V10
2424:VR6
2412:VR5
2374:F16
2369:F12
2364:F10
2326:I14
2321:I12
1947:120
1891:108
1887:MAA
1595:(O,
891:DPA
883:BPA
875:BPA
867:DPA
865:+ ∠
863:BPA
856:DPA
849:BPA
812:DPA
805:BPA
701:180
656:360
594:DBC
592:= ∠
590:DBA
583:OBC
581:= ∠
579:OBA
554:360
476:OBC
469:OBA
432:OBC
425:OBA
415:CBD
408:ABD
371:BCD
364:BAD
320:).
2581::
2494:W8
2489:W6
2484:W3
2431:V8
2419:V6
2407:V5
2402:V4
2397:V3
2392:V2
2359:F8
2354:F6
2349:F4
2344:F2
2316:I9
2311:I8
2306:I7
2301:I6
2296:I5
2291:I4
2286:I3
2281:I2
2276:I1
1949:.
1885::
1881:.
1869:,
1830:,
1793:.
1657:.
1609:.
1581:,
1577:,
1505:OD
1499:OB
1493:AD
1487:OA
895:.
879:,
842:AD
836:AB
830:AP
824:DP
818:BP
798:.
795:PD
789:BP
783:AC
777:BD
766:,
756:BD
752:AC
730:,
462:BC
456:BA
450:OB
444:OC
438:OA
401:CD
395:AD
389:BC
383:BA
377:BD
351:OD
341:,
337:,
273:DA
267:CD
264:,
261:BC
258:,
255:AB
249:OC
243:OA
237:DA
234:,
231:CD
228:,
225:BC
222:,
219:AB
216:,
213:OC
210:,
207:OA
153:.
2560:X
2555:U
2540:H
2476:W
2046:e
2039:t
2032:v
1959:.
1934:.
1916:.
1903:.
1860:.
1803:.
1779:.
1757:.
1690:(
1655:O
1651:D
1647:O
1643:B
1639:D
1635:O
1631:B
1627:B
1623:D
1607:k
1603:O
1599:)
1597:k
1591:B
1587:D
1583:D
1579:B
1575:O
1556:2
1552:k
1548:=
1543:D
1540:O
1527:B
1524:O
1467:D
1464:O
1451:B
1448:O
1440:=
1437:y
1434:x
1431:2
1428:+
1423:2
1419:y
1415:=
1410:2
1403:D
1400:A
1385:2
1378:A
1375:O
1342:2
1338:h
1334:+
1329:2
1325:x
1321:=
1316:2
1309:D
1306:A
1273:2
1269:h
1265:+
1260:2
1256:x
1252:+
1249:y
1246:x
1243:2
1240:+
1235:2
1231:y
1227:=
1222:2
1215:A
1212:O
1194:)
1175:2
1171:h
1167:+
1162:2
1158:)
1154:x
1151:+
1148:y
1145:(
1142:=
1137:2
1130:A
1127:O
1099:y
1096:x
1093:2
1090:+
1085:2
1081:y
1077:=
1074:)
1071:x
1068:2
1065:+
1062:y
1059:(
1056:y
1053:=
1048:D
1045:O
1032:B
1029:O
992:P
989:A
981:=
978:h
968:B
965:O
957:=
954:y
944:D
941:P
933:=
928:P
925:B
917:=
914:x
889:∠
881:∠
861:∠
854:∠
847:∠
810:△
803:△
768:P
748:P
736:D
732:B
728:O
697:=
694:A
691:B
688:D
682:+
679:A
676:B
673:O
652:=
649:A
646:B
643:D
634:2
631:+
628:A
625:B
622:O
613:2
588:∠
577:∠
550:=
547:O
544:B
541:C
535:+
532:C
529:B
526:D
520:+
517:D
514:B
511:A
505:+
502:A
499:B
496:O
474:∠
467:∠
430:△
423:△
413:∠
406:∠
369:△
362:△
355:B
343:D
339:B
335:O
318:O
314:D
310:O
306:B
302:D
298:O
294:B
290:O
286:B
282:O
83:)
77:(
72:)
68:(
54:.
20:)
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
