[Paper Review] Design of a Three-Axis Isotropic Parallel Manipulator for Machining Applications: The Orthoglide

Philippe Wenger, Damien Chablat|arXiv (Cornell University)|May 9, 2007

Robotic Mechanisms and Dynamics10 references19 citations

TL;DR

This paper presents the Orthoglide, a three-axis isotropic parallel manipulator designed for high-precision machining with a cubic Cartesian workspace, fixed orientation, and homogeneous kinetostatic performance. It achieves isotropy through orthogonal linear actuators and parallelogram linkages, enabling uniform velocity and force transmission across a regular, singularity-free workspace, validated by a small-scale prototype with 200 mm×200 mm×200 mm workspace and 1.2 m/s speed at the isotropic point.

ABSTRACT

The orthoglide is a 3-DOF parallel mechanism designed at IRCCyN for machining applications. It features three fixed parallel linear joints which are mounted orthogonally and a mobile platform which moves in the Cartesian x-y-z space with fixed orientation. The orthoglide has been designed as function of a prescribed Cartesian workspace with prescribed kinetostatic performances. The interesting features of the orthoglide are a regular Cartesian workspace shape, uniform performances in all directions and good compactness. A small-scale prototype of the orthoglide under development is presented at the end of this paper.

Motivation & Objective

• To design a 3-DOF parallel manipulator with isotropic kinetostatic performance for machining applications.
• To achieve a regular, cubic Cartesian workspace free of singularities and self-collisions.
• To ensure uniform velocity and force transmission factors across the entire workspace.
• To combine the performance homogeneity of serial PPP machines with the dynamic advantages of parallel kinematics.
• To develop a compact, scalable prototype suitable for high-speed, high-accuracy machining.

Proposed method

• The Orthoglide uses three orthogonal prismatic joints actuated by linear or rotary motors with ball screws.
• Each chain consists of a PRPaR architecture: prismatic (P), revolute (R), and parallelogram (Pa) joints to maintain fixed orientation.
• The mobile platform is connected via three identical parallelograms of length L, ensuring pure translation in x, y, and z directions.
• The design is optimized using two criteria: Jacobian conditioning for isotropy and manipulability ellipsoid for joint limit and link length optimization.
• The workspace size is determined by solving joint limit constraints based on maximum allowable velocity transmission factor variation (1/2 ≤ ψi ≤ 2).
• The prototype is fabricated using rotary motors with ball screws, and its kinematic parameters are derived from prescribed workspace and performance requirements.

Experimental results

Research questions

• RQ1 Can a 3-axis parallel manipulator be designed with a regular, cubic Cartesian workspace and isotropic performance?
• RQ2 How can isotropy and uniform kinetostatic performance be achieved in a parallel manipulator for machining?
• RQ3 What design parameters (link lengths, joint limits) ensure a prescribed workspace size while maintaining acceptable transmission factors?
• RQ4 How does the Orthoglide compare in compactness and performance to existing PKMs for machining?
• RQ5 Can a small-scale prototype be built that achieves high speed and accuracy within a defined cubic workspace?

Key findings

• The Orthoglide achieves a cubic Cartesian workspace of 200×200×200 mm³ with high regularity and no singularities.
• The Jacobian matrix is isotropic near the center, ensuring uniform performance across the workspace.
• The velocity transmission factors remain within the range 1/2 ≤ ψi ≤ 2 across the workspace, indicating consistent dynamic performance.
• The required parallelogram length is L = 310 mm to achieve the prescribed workspace size and performance.
• The actuated joint range is Δρ = 257 mm, yielding a ratio r = 0.78 of joint range to workspace size, which is favorable compared to other mechanisms.
• The prototype achieves a maximum speed of 1.2 m/s and an acceleration of 14 m/s² at the isotropic point with a 4 kg payload.