A Treatise on the Theory of Screws

____________ ______________________________ ________ ______ _____ CONTENTS. __________________ _______ _______________________ XVII CHAPTER XXIV . The Theoky of Sceew-chains. PAGE 338. Introduction______________________________________________________367 339. The Graphic and Metric Elements________________________________368 340. The Intermediate Screw_________________________________________368 341. The Definition of a Screw-chain____________________________________369 342. Freedom of the First Ordei'_________________________________________369 343. Freedom of the Second Order____________________________________370 344. Homography of Screw Systems____________________________________374 345. Freedom of the Third Order____________________________________375 346. Freedom of the Fourth Order____________________________________377 347. Freedom of the Fifth Order_________________________________________378 348. Application of Parallel Projections ________________________________....... 379 349. Properties of this correspondence____________________________________383 350. Freedom of the Fifth Order_________________________________________384 351. Freedom of the Sixth Order_________________________________________386 352. Freedom of the Seventh Order____________________________________386 353. Freedom of the Eighth and Higher Orders___________________________388 354. Reciprocal Screw-chains_________________________________________388 355. Twists on 6/x + l Screw-chains____________________________________390 356. Impulsive Screw-chains and Instantaneous Screw-chains .... 392 357. The principal Screw-chains of Inertia________________________________394 358. Conjugate Screw-chains of Inertia________________________________396 359. Harmonic Screw-chains_____________________________________________397 CHAPTER XXV . The Theory of Permanent Screws. 360. Introduction.........................................................._ 361. Different Properties of a Principal Axis_____________________________400 362. A Property of the Kinetic Energy of a System ____________________.... 401 363. The Identical Equation in Screw-chain Co-ordinates___________________403 364. The Converse Theorem________________________________________________404 365. 1 ransformation of the Vanishing Emanant_____________________________405 366. The General Equations of Motion with Screw-chain Co-ordinates . . 405 367. Generalization of the Eulerian Equations _____________________________...... 406 368. The Restraining Wrench-chain_______________________________________407 369. Physical meaning of the Vanishing Emanant________________________408 370. A Displacement without change of Energy________________________408 371. The Accelerating Screw-chain _______________________________________ 409 372. Another Proof....................................................._ 373. Accelerating Screw-chain and Instantaneous Screw-chain .... 410 374. Permanent Screw-chains ____________________________________________ 410 375. Conditions of a Permanent Screw-chain_____________________________411 3/6. Another identical Equation ___________________________________________......... 412