Geometric modeling with small defects of over-constrained Parallel Kinematic Machine

• Published in: Mechanism and machine theory Vol. 179; p. 105120
• Main Authors: Guyon, Jean-Baptiste, Chanal, Hélène, Boudon, Benjamin, Blaysat, Benoît
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.01.2023; Elsevier
• Subjects: Engineering Sciences; Geometric defects; Geometric model; Identification; Over-constrained mechanism; Stationarity analysis; Over-constrained mechanism; Identification; Geometric model; Stationarity analysis; Geometric defects; geometric model; identification; geometric defects; over-constrained mechanism; stationarity analysis
• ISSN: 0094-114X; 1873-3999
• DOI: 10.1016/j.mechmachtheory.2022.105120

In the case of over-constrained mechanisms, the system can only be assembled or move under strict geometric conditions. A crucial step is to identify these conditions from the geometric model. Classically, the geometric model of a robot is computed from the Denavit–Hartenberg formalism. However, when imperfect mechanisms are studied, this formalism does not introduce exhaustively small geometric defects. In this article, a formalism based on kinematic joint invariants is preferred to describe the geometric behavior. The efficiency of this formalism is demonstrated for the accuracy improvement of a serial robot. A stationarity analysis of the geometric model is then performed to determine the geometric constraints induced by the over-constrained systems and to reduce the number of geometric parameters initially introduced. The methodology is first illustrated on an over-constrained slider–rod–crank system. Then, it is applied to the over-constrained mechanism of the Tripteor X7, a Parallel Kinematic Machine-tool. The benefit of our methodology is validated by a comparison of the geometric model obtained with a CAD model and a previous geometric model proposed in the literature. Finally, the identification of the parameters of the defined geometric model is conducted in order to quantify the potential accuracy benefit. •Method to identify geometric constraints of over-constrained mechanisms.•Used geometric formalism based on robot joints invariants.•Identification of geometric constraints with a stationarity analysis.•Identification of the geometric constraints of a rod–crank system.•Identification of the geometric constraints of Exechon like PKM.