A Treatise on the Theory of Screws

_______ ____________________ _______________________________ ___________________ _________________________ ______ ________ ________ ________ _________ CONTENTS. IX 88 PAGE 53. The Angle between Two Screws______________________________________48 54. The Triangle of Twists_______________________________________________49 55. Decomposition of Twists and Wrenches____________________________50 56. Composition of Twists and Wrenches_________________________________50 57. Screw Co-ordinates_______________________________________________51 58. Reciprocal Screws ____________________________...... .... 51 59. Another Representation of the Pitch_________________________________52 60. Pitches of Reciprocal Screws______________________________________53 61. The Virtual Coefficient _______________________________________________.......... 54 62. Another Investigation of the Virtual Coefficient________________________55 63. Application of Screw Co-ordinates_________________________________57 64. Properties of the Virtual Coefficient_________________________________59 65. Another Construction for the Pitch_________________________________59 66. Screws of Zero Pitch_______________________________________________60 67. A Special Case____________________________________________________60 68. A Tangential Section of the Cylindroid ____________________________...... 60 CHAPTER VI . The Equilibrium of a Rigid Body. 69. A Screw System _______________________________________________.......... 62 70. Constraints_______________________________________________ 03 71. Screw Reciprocal to a System______________________________________03 72. The Reciprocal Screw System_____________________________________63 73. Equilibrium___________________________________________________ g4 74. Reaction of Constraints__________________________________________64 75. Parameters of a Screw System ______________________________________........ 65 76. Applications of Co-oi’dinates__________________________________________65 77. Remark on Systems of Linear Equations ____________________________...... 67 CHAPTER VII . The Principal Screws of Inertia. 78. Introduction........................................................_ 79. Screws of Reference ............................................... 70 80. Impulsive Screws and Instantaneous Screws________________________71 81. Conjugate Screws of Inertia..........................................71 82. The Determination of the Impulsive Screw____________________________72 83. System of Conjugate Screws of Inertia____________________________72 84. Principal Screws of Inertia __________________________________________......... 73 85. An Algebraical Lemma..........................................75 86. Another Investigation of the Principal Screws of Inertia .... 76 87. Enumeration of Constants..........................................78 88. Kinetic Energy....................................................79