Key Takeaways & Executive Findings
- •• Introduces a semi-analytical stiffness model for the novel (R(RPS&RP))&2-UPS parallel mechanism, explicitly considering compliances of all elastic elements and over-constraint characteristics. • Proposes 'local' stiffness performance indices based on four special reference configurations, offering accurate evaluation of overall stiffness with significantly improved computational efficiency. • Demonstrates that the proposed indices achieve excellent accuracy and efficiency when applied to Tricept and Trimule mechanisms, validating their generalizability. • Reveals that the stiffness performance of the Trifree mechanism closely resembles that of the well-known Tricept and Trimule mechanisms, indicating its potential for similar applications.
Abstract
The average stiffness performance indices throughout the workspace are commonly used as global stiffness performance indices to evaluate the overall stiffness performance of parallel mechanisms, which involves an analysis of the stiffness performance of numerous discrete points in the workspace. This necessitates time-consuming and inefficient calculation, which is particularly pronounced in the optimization design stage of the mechanism, where the variations in the global stiffness performance indices versus various dimensional and structural parameters need to be analyzed. This paper presents a semi-analytical approach for stiffness modeling of the novel (R(RPS&RP))&2-UPS parallel mechanism (referred to as the Trifree mechanism) and proposes “local” stiffness performance indices as alternatives to global indices. Drawing on the screw theory, the Cartesian stiffness matrix of the Trifree mechanism is formulated explicitly by considering the compliances of all elastic elements and the over-constraint characteristics inherent in the mechanism. Based on the spherical motion pattern of the Trifree mechanism, four special reference configurations are extracted within the workspace. This yields “local” stiffness performance indices capable of accurately evaluating the overall stiffness performance of the mechanism and effectively improving the computational efficiency. The variations in global and “local” stiffness performance indices versus key design parameters are investigated. Furthermore, the proposed indices are applied to the Tricept and Trimule mechanisms. The results demonstrate that the proposed indices exhibit excellent computational accuracy and efficiency in evaluating the overall stiffness performance of these spherical parallel mechanisms. Moreover, the stiffness performance of the novel parallel mechanism investigated in this study closely resembles that of the well-known Tricept and Trimule mechanisms. This research proposes a semi-analytic stiffness model of the Trifree mechanism and “local” stiffness performance indices to evaluate the overall stiffness performance, thereby substantially improving the computational efficiency without sacrificing accuracy.
1. Introduction
In recent years, hybrid kinematic machines (or hybrid robots) that employ a 1T2R (T: translation, R: rotation) parallel mechanism as the main body and integrate a two- or three-degree-of-freedom (2- or 3-DOF) serial module have gradually become an important technology choice for the highly efficient manufacturing of large complex parts in high-end manufacturing fields such as aerospace and rail transportation. This is owing to their relatively large envelope against footprint, high rigidity, accuracy, and dynamic response [1, 2]. Hybrid robots can be divided into two types. The first family, exemplified by the well-known Tricept robot [3] and Trimule robot [4], consists of a properly constrained active/passive Limb and multiple 6-DOF active limbs [5]. The parallel mechanisms belonging to the second family consist of three lower-mobility limbs. Typical examples of this family are the Exechon robot [6] and the Sprint Z3 head [7]. These robots can be built as plug-and-play modules and mounted on long reference tracks or Automated Guided Vehicles (AGVs) to efficiently complete the in-situ manufacturing and assembly of large complex parts [8, 9], for example, drilling and polishing of aircraft elevators, milling on wing ribs, and friction stir welding of automobile bodies.
Given that hybrid robots of this type are primarily used for high-speed machining and/or forced assembly tasks (where both high accuracy and rigidity are critical), stiffness has emerged as an important factor in performance. Consequently, numerous effective investigations have been conducted on the stiffness modeling and performance evaluation of parallel mechanisms within these hybrid robots. Currently, the available methods for stiffness modeling include finite element analysis (FEA) [10, 11], matrix structural analysis (MSA) [12–14], and analytical and semi-analytical approaches [15–18]. The FEA method relies on the FEA software to accurately calculate the stiffness of the mechanism. However, this method...
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Minghao Wang, Manxin Wang, Hutian Feng, Chuhan Wu (2025). Stiffness Modeling and Performance Evaluation of a (R(RPS&RP))&2-UPS Parallel Mechanism. Chinese Journal of Mechanical Engineering. https://doi.org/10.1186/s10033-025-01347-y
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Frequently Asked Questions
What is the Trifree mechanism?
The Trifree mechanism is a novel (R(RPS&RP))&2-UPS parallel mechanism with spherical motion, designed for high-speed machining and assembly tasks. It offers high rigidity and accuracy, similar to well-known mechanisms like Tricept and Trimule.
What are 'local' stiffness performance indices?
Local stiffness performance indices are proposed as alternatives to global indices. They are derived from four special reference configurations within the workspace, allowing accurate evaluation of overall stiffness performance with significantly reduced computational effort.
How is the stiffness model formulated?
The stiffness model is formulated using screw theory, explicitly considering the compliances of all elastic elements and the over-constraint characteristics inherent in the mechanism, resulting in a semi-analytical Cartesian stiffness matrix.
What are the main advantages of the proposed method?
The proposed method substantially improves computational efficiency without sacrificing accuracy, making it particularly useful in the optimization design stage where numerous parameter variations need to be analyzed.
How does the Trifree mechanism compare to Tricept and Trimule?
The stiffness performance of the Trifree mechanism closely resembles that of the Tricept and Trimule mechanisms, indicating it can serve as a viable alternative in applications requiring high stiffness and accuracy.
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