A Treatise on the Theory of Screws

____________________ XVI ___________ ____ CONTENTS. PAGE ...................................... 319 320 320 §§ 299. Cylindroid Reduced to a Plane ............................................... 300. A difficulty removed 301. Two Geometrical Theorems . CHAPTER XXII . The Geometrical Theory 302. Preliminary................................ 303. One Pair of Impulsive and Instantaneous Screws 304. An Important Exception__________________ 305. Two Pairs of Impulsive and Instantaneous Screws 306. A System of Rigid Bodies__________________ 307. The Geometrical Theory of Three Pairs of Screws 308. Another Method........................... 309. Unconstrained Motion in system of Second Order 310. Analogous Problem in a Three-system. 311. Fundamental Problem with Free Body 312. Freedom of the First or Second Order 313. Freedom of the Third Order.................. 314. General Case................................ 315. Freedom of the Fifth Order................... 316. Principal Screws of Inertia of Constrained Body 317. Third and Higher Systems.................. 318. Correlation of Two Systems of the Third Order. 319. A Property of Reciprocal Screw Systems . 320. Systems of the Fourth Order .... 321. Systems of the Fifth Order__________________ 322. Summary................................ 323. Two Rigid Bodies___________________________ 322 323 325 325 326 330 332 332 334 336 338 339 339 340 341 342 344 347 348 350 350 351 CHAPTER XXIII . Various Exercises. 324. The Co-ordinates of a Rigid Body_____________________________ 325. A Differential Equation satisfied by the Kinetic Energy . . . 326. Co-ordinates of Impulsive Screw in terms of the Instantaneous Screw 327. Another Proof of Article 303 __________________________________ 328. A more general Theorem....................................... 329. Two Three-Systems____________________________________________ 330. Construction of Homographic Correspondents___________________ 331. Geometrical Solution of the same Problem ..•••• 332. Co-reciprocal Correspondents in Two Three-systems .... 333. Impulsive and Instantaneous Cylindroids________________________ 334. The Double Correspondents on Two Cylindroids .... 335. A Property of Co-reciprocals.................................. 336. Instantaneous Screw of Zero Pitch_____________________________ 337. Calculation of a Pitch Quadric__________________________________ ____________________________________ ______________________________________________________ 355 356 356 357 357 357 358 359 360 361 363 364 365 365 _________