Geometric Perspective on Kinematics and Singularities of Spatial Mechanisms

This doctoral dissertation deals with the kinematics and singularity analyses of serial and parallel manipulators with multiple working modes. The inverse kinematics of 6R architectures with non-spherical wrists were solved using simple geometric considerations; the problem was reduced to the solution of a trigonometric equation in one variable, the sixth joint angle. The direct kinematic analysis of the parallel manipulator, namely the Exechon, was conducted; it involves using a standard numerical tool to solve the system of equations in platform’s angle variables. Both kinematics analyses took advantage of the standard numerical solver to obtain the solutions. The singularities of the Exechon were studied with the geometrical interpretation. By using the theory of reciprocal screws, the input-output velocity equations were introduced. This led to the investigation of the Jacobian matrices, which is an essential part when working with any manipulator. A method for obtaining the singularity loci and the numerical example was provided. The formulations presented in this dissertation are general and effective enough to be applicable for many other similar architectures.