Kinematics is the science which treats of pure motion. It involves the fundamental conceptions of space and time and takes no direct cognisance of force or mass. Strictly speaking, any kinematical problem dealing with motions that exist in nature is at bottom dynamical, and every dynamical problem is of necessity approached in the first instance on its kinematical side. Thus, to take a familiar example, Kepler's laws of planetary motion were purely geometrical and kinematical statements, from which Newton deduced the dynamical law of universal gravitation. Again, the Nautical Almanac is essentially a book of kinematical statistics, giving the positions of the important heavenly bodies at definite successive intervals of time, and not unfrequently the rates of change of position; and the calculation of these statistics has a strict dynamic basis.
Kinematics may be regarded as a geometry of position into which the idea of time or duration has been introduced. Thus, change of position, regarded as taking place continuously in time, leads to the idea of velocity, linear and angular. Velocity itself is, of course, subject to change, and this change, regarded as taking place continuously in time, leads to the idea of acceleration, linear and angular. The distinction of linear and angular as applied to velocities and accelerations is very necessary for a clear study of the kinematics of systems of points, such as plane and solid figures, rigid or deformable, or of the kinematics of fluids.
Rotation, strain, twist, vortex are important cases. The kinematics of solid figures is a subject of growing importance to the mechanician and engineer; so much so that in the kinematics of machinery we have a highly-specialised branch of the subject. A glance at any ordinary piece of mechanism, from a steam-engine to a sewing-machine, shows how various are the relative motions of the wheels, rods, cranks, belts, and other pieces that build it up. The function of a machine is dynamic—viz. to transform energy to a certain end—but this must be effected by suitable kinematical arrangements. In all modern treatises on dynamics and mechanics a section is devoted to a preliminary study of kinematics. Reuleaux's Kinematics of Machinery (trans. 1876) deserves particular mention.