  The subject of this paper is about the kinematic analysis and the trajectory
planning of the Orthoglide 5-axis. The Orthoglide 5-axis a five degrees of
freedom parallel kinematic machine developed at IRCCyN and is made up of a
hybrid architecture, namely, a three degrees of freedom translational parallel
manip-ulator mounted in series with a two degrees of freedom parallel spherical
wrist. The simpler the kinematic modeling of the Or-thoglide 5-axis, the higher
the maximum frequency of its control loop. Indeed, the control loop of a
parallel kinematic machine should be computed with a high frequency, i.e.,
higher than 1.5 MHz, in order the manipulator to be able to reach high speed
motions with a good accuracy. Accordingly, the direct and inverse kinematic
models of the Orthoglide 5-axis, its inverse kine-matic Jacobian matrix and the
first derivative of the latter with respect to time are expressed in this
paper. It appears that the kinematic model of the manipulator under study can
be written in a quadratic form due to the hybrid architecture of the Orthoglide
5-axis. As illustrative examples, the profiles of the actuated joint angles
(lengths), velocities and accelerations that are used in the control loop of
the robot are traced for two test trajectories.
