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\u2019s 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