Geometric Design of Linkages Analysis of Planar Linkages Graphical Synthesis in the Plane Planar Kinematics Algebraic Synthesis of Planar Chains Analysis of Spherical Linkages Spherical Kinematics Algebraic Synthesis of Spherical Chains Analysis of Spatial Chains Spatial Kinematics Algebraic Synthesis of Spatial Chains Platform Manipulators. to introduce these techniques and additional background is provided in appendices. The rst chapter presents an overview of the articulated systems that we will be considering in this book. The generic mobility of a linkage is dened and we separate them into the primary classes of planar spherical and spatial chains. The second chapter presents the analysis of planar chains and details their movement and classication. Chapter three develops the graphical design theory for planar linkages and introduces many of the geometric principlesthatappearintheremainderofthebook.Inparticular geometric derivations of the pole triangle and the center point theorem anticipate analytical results for the spherical and spatial cases. Chapter four presents the theory of planar displacements and Chapter ve presents the algebraic design theory. The bilinear structure of the sign equations provides a solution strategy that emphasizes the geometry underlying linear algebra. The ve position solution includes an elimi tion step that is probably new to most students though it is understood and well received in the classroom. Chapters six and seven introduce the properties of spherical linkages and detail the geometric theory of spatial rotations. Chapter eight presents the design theory for these linkages which is analogous to the planar theory. This material exercises the student’s use of vector methods to represent geometry in three dimensions. Perpendicular bisectors in the planar design theory become perpendicular bisecting planes that intersect to dene axes. The analogue provides students with a geometric perspective of the linear equations that they are solving.