Kinematic Analysis and Trajectory Planning of the Orthoglide 5-axis

TL;DR

This paper presents the kinematic analysis and trajectory planning methods for the Orthoglide 5-axis, a hybrid parallel kinematic machine, emphasizing models suitable for high-frequency control and illustrating with test trajectories.

Contribution

It provides simplified kinematic models and Jacobian matrices for the Orthoglide 5-axis, tailored for high-speed control applications, and demonstrates their application through trajectory examples.

Findings

Kinematic models can be expressed in quadratic form due to hybrid architecture.

Test trajectories illustrate joint angle, velocity, and acceleration profiles.

Models support control loop frequencies above 1.5 MHz.

Abstract

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.