[Paper Review] Kinematic and Dynamic Analysis of the 2-DOF Spherical Wrist of Orthoglide 5-axis

Raza Ur-Rehman, Stéphane Caro+2 more|ArXiv.org|Apr 1, 2009

Robotic Mechanisms and Dynamics17 references6 citations

TL;DR

This paper presents a comprehensive kinematic and dynamic analysis of the 2-DOF spherical wrist in the Orthoglide 5-axis machine tool, a parallel kinematic mechanism combining a Delta-type 3-DOF translational manipulator with a spherical wrist. Using CAD-derived geometric and inertial parameters, the study evaluates performance under various trajectories, cutting forces, and tool lengths, concluding with a preliminary actuator selection based on required torques and velocities for dynamic trajectories.

ABSTRACT

This paper deals with the kinematics and dynamics of a two degree of freedom spherical manipulator, the wrist of Orthoglide 5-axis. The latter is a parallel kinematics machine composed of two manipulators: i) the Orthoglide 3-axis; a three-dof translational parallel manipulator that belongs to the family of Delta robots, and ii) the Agile eye; a two-dof parallel spherical wrist. The geometric and inertial parameters used in the model are determined by means of a CAD software. The performance of the spherical wrist is emphasized by means of several test trajectories. The effects of machining and/or cutting forces and the length of the cutting tool on the dynamic performance of the wrist are also analyzed. Finally, a preliminary selection of the motors is proposed from the velocities and torques required by the actuators to carry out the test trajectories.

Motivation & Objective

• To analyze the kinematic and dynamic behavior of the 2-DOF spherical wrist in the Orthoglide 5-axis machine tool.
• To evaluate the wrist's performance under realistic machining conditions, including cutting forces and varying tool lengths.
• To determine the geometric and inertial parameters of the wrist using CAD software for accurate modeling.
• To identify actuator requirements (torque and velocity) for executing test trajectories under dynamic loading.
• To support preliminary motor selection based on dynamic performance demands of the wrist mechanism.

Proposed method

• Modeling the spherical wrist using precise geometric and inertial parameters extracted from CAD software.
• Performing forward and inverse kinematics analysis to determine position, velocity, and acceleration of the wrist's end-effector.
• Applying dynamic modeling to compute actuator torques and forces under various test trajectories.
• Simulating the effects of external cutting forces and tool length variations on wrist dynamics.
• Evaluating performance across multiple test trajectories to assess workspace, dexterity, and dynamic response.
• Using the results to estimate required actuator output, enabling preliminary motor selection.

Experimental results

Research questions

• RQ1 How do cutting forces and tool length affect the dynamic performance of the 2-DOF spherical wrist?
• RQ2 What are the required actuator torques and velocities to accurately follow predefined test trajectories?
• RQ3 How does the wrist’s kinematic structure influence its dexterity and workspace characteristics?
• RQ4 What is the impact of geometric and inertial parameter accuracy on dynamic modeling results?
• RQ5 How can actuator requirements be estimated for real-time control and machine tool integration?

Key findings

• The wrist’s dynamic performance is significantly affected by both cutting forces and the length of the cutting tool.
• Trajectory-dependent actuator torques and velocities were computed, enabling a preliminary selection of suitable motors.
• The CAD-derived geometric and inertial parameters enabled accurate kinematic and dynamic modeling of the wrist.
• Performance evaluation across test trajectories revealed variations in dynamic loads, particularly under high-force conditions.
• The study demonstrates that tool length and external forces must be considered in actuator sizing for precision machining.
• The dynamic model provides a foundation for control system design and real-time performance optimization in the Orthoglide 5-axis machine.