  The paper derives the inverse and the forward kinematic equations of a serial
- parallel 5-axis machine tool: the VERNE machine. This machine is composed of
a three-degree-of-freedom (DOF) parallel module and a two-DOF serial tilting
table. The parallel module consists of a moving platform that is connected to a
fixed base by three non-identical legs. These legs 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. In this paper we propose symbolical methods that able
to calculate all kinematic solutions and identify the acceptable one by adding
analytical constraint on the disposition of legs of the parallel module.
