Excerpt from Dynamics and Modern Geometry, Vol. 4: A New Chapter in the Theory of ScrewsThe only restrictions which we shall impose are thus stated: -(1). The material system consists of a single rigid body.(2). The body has two degrees of freedom.(3). The investigation only applies while the body remains in or near to its original position.It will be observed that the forces are generally unrestricted, though in some cases it will be found that they should belong to what is often known as a 'conservative' system. Nor is the nature of the constraints prescribed in any way, except that they shall so limit the body that any position it is capable of assuming can he specified by two co-ordinates. The third condition expresses the well-known limit to the operation of the Theory of Screws. The effect of this condition is to confine our inquiries to four departments, as follows: - 1st. The kinematics of small movements, 2nd. The theory of equilibrium, 3rd. The theory of impulsive forces, 4th. The theory of small oscillations.I refer to the Theory of Screws for the demonstrations of the fundamental theorems that are required. I commence by reciting three laws which govern the displacements of a body which has two degrees of freedom.(1). A body with two degrees of freedom can twist about all the screwsof a singly infinite system.(3). Each screw has a specific pitch appropriate to its situation on thecylindroid.2. Representation of the Cylindroid by a Circle. - The essence of the present Memoir lies in the geometrical representation of a screw by a point.About the PublisherForgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.comThis book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully, any imperfections that remain are intentionally left to preserve the state of such historical works.