On Structure Equations and Constraint Manifolds in Kinematic Analysis and Mechanism Geometry

This study consists of five chapters. In the first chapter, basic kinematic concepts are reviewed, which will be discussed in detail in the following chapter. In addition to planar motion, basic concepts such as rotation/ translation, degrees of freedom, manifold, mechanism and kinematic chains are introduced. The Jacobian matrix and Denavit-Hartenberg parameters are also discussed. In the second part, the mobility of the mechanism is analyzed and the formulas for the number of parameters and degrees of freedom used to determine its configuration in the plane, on a spherical surface and in space are discussed. In the third section, the general structural equations are presented and then these equations are specialized to the planar, spherical and spatial chain cases. In the fourth section, the constraint manifolds of 2R and 3R planar and spherical open chains and 2C and 3C spatial open chains are considered. By eliminating common variables, these manifolds are found to be defined by quadratic forms. This reduces the derivation of the constraint manifolds of closed 4R, 5R and 6R planar and spherical chains to the intersection of quadric surfaces. The constraint manifolds of spatial chains 4C, 5C and 6C have the same form as those of closed spherical chains 4R, 5R and 6R but written in terms of dual numbers. The fifth section is reserved for the conclusion