Page 103 - 4624
P. 103

IX KINEMATICS

              Introduction
              Kinematics is the branch of  dynamics which describes the
         motion of bodies without reference to the forces which  either cause
         the  motion or are  generated as a result of the  motion. Kinematics
         treats only the  geometric aspects of  the motion.  Some engineering
         applications of kinematics include the design of cams, gears, linkages,
         and  other machine elements  to control  or produce certain desired
         motions, and the calculation of flight trajectories for aircraft, rockets,
         and spacecraft.
              The motion of  particles (or rigid bodies) can be described by
         using coordinates measured from fixed reference axes (absolute-
         motion  analysis)  or by using  coordinates measured from moving
         reference axes  (relative-motion  analysis). Both descriptions  will be
         developed and applied in the articles which follow.

              38  Kinematics of Particle

              We begin our study of kinematics  by  first discussing  in this
         chapter the motions of points or particles. A particle is a body whose
         physical dimensions are so small compared with the  radius of
         curvature of its path that we may treat the motion of the particle as
         that of a point.  For  example, the  wingspan  of a  jet transport flying
         between Los Angeles and New York is of no consequence compared
         with the radius of curvature of its flight path, and thus the treatment of
         the airplane as a particle or point is an acceptable approximation.
              We can describe the motion of a particle in a number of ways,
         and the choice of the most convenient or appropriate way depends a
         great deal on experience and on how the data are given. Let us obtain
         an overview of the  several methods  developed  in this chapter by
         referring to Fig. 2-1,  which shows  a particle  P  moving  along some
         general path in space. If the particle is confined to a specified path, as
         with a  bead sliding along a  fixed wire, its motion  is said  to be
         constrained. If there are no physical guides, the motion is said to be
         unconstrained. A small rock tied to the end of a string and whirled in
         a circle undergoes constrained motion until the string breaks, after
         which instant its motion is unconstrained.
                                                                      103
   98   99   100   101   102   103   104   105   106   107   108