The main function of this chapter is to provide the reader with an introduction to an important and much neglected area of the physical sciences, namely planar kinematics. It is an area giving rise to substantial illustrations of the ideas developed in this book. Moreover, planar kinematics represents a starting point for spatial kinematics, which will be of considerable future relevance, as robotics assumes a role of ever increasing significance in our daily lives. Some historical background is provided by Section 13.1, centring around a classic example drawn from the engineering literature (the four bar linkage) in which simple mechanical means are used to generate motions of a moving plane. That leads to the abstract concept of a planar motion in Section 13.2, and the associated family of trajectories traced by the points of the moving plane. The concept is illustrated in Section 13.3 by the idea of a general roulette, extending the trochoid construction of Section 3.3 and the involute construction of Section 4.4.

Historical Genesis

The historical genesis of the subject lies in the Power Revolution, which took place from the thirteenth to the sixteenth centuries. Over that period western man was gradually released from the drudgery of providing a source of power as ways became available of converting water and wind power into mechanical work.