  The paper derives the inverse and forward kinematic equations of a spatial
three-degree-of-freedom parallel mechanism, which is the parallel module of a
hybrid serial-parallel 5-axis machine tool. This parallel mechanism consists of
a moving platform that is connected to a fixed base by three non-identical
legs. Each leg is made up of one prismatic and two pair spherical joint, which
are connected in a way that the combined effects of the three legs lead to an
over-constrained mechanism with complex motion. This motion is defined as a
simultaneous combination of rotation and translation.
