Clifford, Kinematic, book iii.).
Under the general heading "Geometry" occur the subheadings "Foundations," with the topics principles of geometry, non-Euclidean geometries, hyperspace, methods of analytical geometry; "Elementary Geometry," with the topics planimetry, stereometry, trigonometry, descriptive geometry; "Geometry of Conics and Quadrics," with the implied topics; "Algebraic Curves and Surfaces of Degree higher than the Second," with the implied topics; "Transformations and General Methods for Algebraic Configurations," with the topics collineation, duality, transformations, correspondence, groups of points on algebraic curves and surfaces, genus of curves and surfaces, enumerative geometry, connexes, complexes, congruences, higher elements in space, algebraic configurations in hyperspace; "Infinitesimal Geometry: applications of Differential and Integral Calculus to Geometry," with the topics kinematic geometry, curvature, rectification and quadrature, special transcendental curves and surfaces; "Differential Geometry: applications of Differential Equations to Geometry," with the topics curves on surfaces, minimal surfaces, surfaces determined by differential properties, conformal and other representation of surfaces on others, deformation of surfaces, orthogonal and isothermic surfaces.
No better testimony to the value of the quaternion method could be desired than the constant use made of its notation by mathematicians like Clifford (in his Kinematic) and by physicists like ClerkMaxwell (in his Electricity and Magnetism).
There is a corresponding kinematic peculiarity, in that the connection is now not strictly rigid, an infinitely small relative displacement being possible.
From the purely kinematic point of view, the t of our formulae may be any continuous independent variable, suggested (it may be) by some physical process.
It follows, by the preceding kinematic theory, that the mass-centre G of thc system will move exactly as if the whole, mass were concentrated there and were acted on by the extraneous forces applied paralle to their original directions.
In the Reiileaux system of analysis of mechanisms the principle of comparative motion is generalized, and mechanisms apparently very diverse in character are shown to be founded on the same sequence of elementary combinations forming a kinematic chain.
Kinematic pairs in which contact takes place along a line only are classified as higher pairs.
A kinematic link of the simplest form is made by joining up the halves of two kinematic pairs by means of a rigid link.
In order that a kinematic chain may be made the basis of a mechanism, every point in any link of it must be completely constrained with regard to every other link.
These principles may be applied to examine any possible combination of links forming a kinematic chain in order to test its suitability for use as a mechanism.
Compound chains are formed by the super-position of two or more simple chains, and in these more complex chains links will be found carrying three, or even more, halves of kinematic pairs.
The Joy valve gear mechanism is a good example of a compound kinematic chain.
The piece A~ togethef with the pin B4 therefore form a kinematic link A1B4.
The Reuleaux system, therefore, consists essentially of the analysis of every mechanism into a kinematic chain, and since each link of the chain may be the fixed frame of a mechanism quite diverse mechanisms are found to be merely inversions of the same kinematic chain.
81.* Centrodes, Instantaneous Centres, Velocity Image, Velocity Diagram.Problems concerning the relative motion of the several parts of a kinematic chain may be considered in two ways, in addition to the way hitherto used in this article and based on the principle of 34.
Reuleaux has shown that the relative motion of any pair of nonadjacent links of a kinematic chain is determined by the rolling together of two ideal cylindrical surfaces (cylindrical being used here in the general sense), each of which may be assumed to be formed by the extension of the material of the link to which it corresponds.
To find the instantaneous centre for a particular link corresponding to any given configuration of the kinematic chain, it is only necessary to know the direction of motion of any two points in the link, since lines through these points respectively at right angles to their directions of motion.
Following the method indicated above for a kinematic chain in general, there will be obtained a velocity diagram similar to that of fig.
Acceleration Image.Although it is possible to obtain the acceleration of points in a kinematic chain with one link fixed by methods which utilize the instantaneous centres of the chain, the vector method more readily lends itself to this purpose.
Then other conditions consequent upon the fact that, the link forms part of a kinematic chain operate to enable b tobe fixed.