This text is devoted to the statics of rigid laminas on a plane and to the first-order instantaneous kinematics (velocities) of rigid laminas moving over a plane. Higher-order instantaneous kinematic problems, which involve the study of accelerations (second-order properties) and jerk (third-order properties) are not considered.

This text is influenced by the book Elementary Mathematics from an Advanced Standpoint: Geometry, written by the famous German geometer Felix Klein. It was published in German in 1908 and the third edition was translated into English and published in New York by the Macmillan Company in 1939. The book was part of a course of lectures given to German High School Teachers at Göttingen in 1908. Klein was admonishing the teachers for not teaching geometry correctly, and he was essentially providing a proper foundation for its instruction.

The present text stems from the undergraduate course “The Geometry of Robot Manipulators,” taught in the Mechanical Engineering Department at the University of Florida. This course is based on Klein's development of the geometry of points and lines in the plane and upon his elegant development of mechanics: “A directed line-segment represents a force applied to a rigid body. A free plane-segment, represented by a parallelogram of definite contour sense, and the couple given by two opposite sides of the parallelogram, with arrows directed opposite to that sense, are geometrically equivalent configurations, i.e., they have equal components with reference to every coordinate system.”