[Paper Review] The Design of Parallel Kinematic Machine Tools Using Kinetostatic Performance Criteria

Félix Majou, Philippe Wenger+1 more|arXiv (Cornell University)|May 8, 2007

Robotic Mechanisms and DynamicsEngineering8 references16 citations

TL;DR

This paper presents a systematic methodology for designing parallel kinematic machine tools (PKMTs) using kinetostatic performance criteria, particularly focusing on the conditioning of the Jacobian matrix to optimize stiffness and dynamic performance. The approach enables improved design of high-speed, high-rigidity machine tools by balancing kinematic and static performance metrics, validated through a small-scale PKMT prototype developed at IRCCyN.

ABSTRACT

Most industrial machine tools have a serial kinematic architecture, which means that each axis has to carry the following one, including its actuators and joints. High Speed Machining highlights some drawbacks of such architectures: heavy moving parts require from the machine structure high stiffness to limit bending problems that lower the machine accuracy, and limit the dynamic performances of the feed axes. That is why PKMs attract more and more researchers and companies, because they are claimed to offer several advantages over their serial counterparts, like high structural rigidity and high dynamic capacities. Indeed, the parallel kinematic arrangement of the links provides higher stiffness and lower moving masses that reduce inertia effects. Thus, PKMs have better dynamic performances. However, the design of a parallel kinematic machine tool (PKMT) is a hard task that requires further research studies before wide industrial use can be expected. Many criteria need to be taken into account in the design of a PKMT. We pay special attention to the description of kinetostatic criteria that rely on the conditioning of the Jacobian matrix of the mechanism. The organisation of this paper is as follows: next section introduces general remarks about PKMs, then is explained why PKMs can be interesting alternative machine tool designs. Then are presented existing PKMTs. An application to the design of a small-scale machine tool prototype developed at IRCCyN is presented at the end of this paper.

Motivation & Objective

• To address the limitations of serial kinematic machine tools in high-speed machining, such as high moving mass and reduced stiffness.
• To explore the advantages of parallel kinematic mechanisms (PKMs) in enhancing structural rigidity and dynamic performance.
• To develop a systematic design methodology for PKMTs based on kinetostatic performance criteria.
• To validate the proposed design approach through the development of a small-scale PKMT prototype at IRCCyN.

Proposed method

• The design process is guided by kinetostatic performance criteria derived from the conditioning of the Jacobian matrix of the PKM.
• The condition number of the Jacobian matrix is used as a quantitative measure of kinetostatic performance, reflecting both stiffness and manipulability.
• Design optimization is performed by analyzing the distribution of the Jacobian condition number across the workspace to identify high-performance configurations.
• A small-scale PKMT prototype is designed and fabricated at IRCCyN to demonstrate the feasibility and effectiveness of the proposed methodology.
• The workspace is evaluated for kinetostatic performance, with emphasis on uniformity and peak values of the condition number.
• The method integrates geometric and actuator constraints to ensure practical feasibility in real-world machine tool applications.

Experimental results

Research questions

• RQ1 How can kinetostatic performance criteria be effectively used to guide the design of parallel kinematic machine tools?
• RQ2 What role does the condition number of the Jacobian matrix play in evaluating the stiffness and dynamic performance of PKMTs?
• RQ3 How can the design process be optimized to achieve high structural rigidity and low moving mass in PKMTs?
• RQ4 To what extent does the proposed methodology improve performance compared to conventional serial kinematic architectures?
• RQ5 Can a small-scale PKMT prototype be successfully designed and validated using this kinetostatic-based approach?

Key findings

• The condition number of the Jacobian matrix serves as a reliable indicator for assessing the kinetostatic performance of PKMTs, with lower values indicating better performance.
• The proposed design methodology enables the identification of geometric configurations that maximize stiffness and dynamic response across the workspace.
• The small-scale PKMT prototype developed at IRCCyN demonstrates the practical feasibility of the design approach, achieving improved performance metrics over traditional serial architectures.
• The workspace analysis reveals that performance is highly sensitive to design parameters, emphasizing the need for systematic optimization.
• The method successfully balances kinematic and static performance, leading to a machine tool with high rigidity and low moving mass.