Flexibility optimization of a hexapod machine tool. (English) Zbl 1330.70025

Summary: Lightweigth structures like Stuart platforms for manufacturing processes and space application require low flexibility in order to guarantee high motion accuracy. In this paper two methods of flexibility optimization are presented and applied to design variants of a hexapod machine tool. The first one is based on a multibody system simulation (MBS). Here, the hexapod is modeled as a rigid multibody system under consideration of joint elasticities. Actuator amplitudes in the links associated with desired end-effector trajectories are computed by inverse kinematics. Hence, dynamic forces and torques are not considered and, as there is no closed-loop control realized so far in the model and the built machine, the actual rotational and translational positions of the end-effector deviate from the desired pose due to machining loads. These deviations serve as objective functions during the optimization. Further, the obtained results are verified by considering the linearized elastostatic behavior. As a second method, a more general optimization approach based on the tangential stiffness matrix is introduced. Here, the flexibility behavior of the machine is optimized considering the whole workspace. The results are then compared with the results from the MBS-based optimizations which consider only the poses on a sample trajectory.


70B15 Kinematics of mechanisms and robots
74K99 Thin bodies, structures
Full Text: DOI


[1] D. Bestle Analyse und Optimierung von Mehrkörpersystemen. Berlin: Springer, 1994. · Zbl 0817.70002
[2] Bestle, Analyzing and Optimizing Multibody Systems, Mechanics of Structures and Machines 20 pp 67– (1992)
[3] D. Bestle P. Eberhard NEWOPT/AIMS 2.2. Ein Programmsystem zur Analyse und Optimierung von mechanischen Systemen. Manual AN-35. Institute B of Mechanics, University of Stuttgart, 1994.
[4] D. Bestle P. Eberhard Dynamic System Design via Multicriteria Optimization. In Multiple Criteria Decision Making. Proc. of the Int. Conf. on MCDM, Hagen 1995, pp. 467-478. Berlin: Springer, 1997. · Zbl 0898.90068
[5] Bischof, ADIFOR 2.0: Automatic Differentiation of Fortran 77 programs, IEEE Computational Science & Engineering 3 pp 18– (1996) · Zbl 05092146
[6] C. Boör L. Molinari-Tosatti K. Smith Parallel Kinematic Machines: Theoretical Aspects and Industrial Requirements (Advanced Manufacturing). London: Springer, 1999.
[7] Dasgupta, Force Redundancy in Parallel Manipulators: Theoretical and Practical Issues, Mechanisms and Machine Theory 33 (6) pp 727– (1998) · Zbl 1049.70601
[8] F. Dignath Zur Optimierung mechatronischer Systeme mit nichtdifferenzierbaren Kriterien. VDI-Verlag (accepted for publ.), 2004.
[9] F. Dignath D. Hempelmann Grundlagenuntersuchungen zum thermischen Einfluss - Bericht 2002. Report ZB-131. Institute B of Mechanics, University of Stuttgart, 2002.
[10] Eberhard, Zur Mehrkriterienoptimierung von Mehrkörpersystemen, VDI-Fortschritt-Berichte 11 (227) (1996)
[11] P. Eberhard D. Bestle Integrated Modeling, Simulation and Optimization of Multibody Systems. In G. Johannsen (Ed.), Integrated Systems Engineering, pp. 35-40. Oxford: Pergamon, 1994.
[12] Eberhard, Parallel Evolutionary Optimization of Multibody Systems with Application to Railway Dynamics, Multibody System Dynamics 9 pp 143– (2003) · Zbl 1041.70006
[13] R. Fletcher Practical Methods of Optimization. Chichester: John Wiley & Sons, 1987. · Zbl 0905.65002
[14] Gosselin, Singularity Analysis of Closed-Loop Kinematic Chains, IEEE Transactions on Robotics and Automation 6 (3) pp 281– (1990)
[15] U. Heisel Precision Requirements of Hexapod-Machines and Investigation Results. In Proceedings of the First European-American Forum on Parallel Kinematic Machines. Mailand, 1998.
[16] Heisel, Auslegung von Maschinenkonstruktionen mit GelenkstabKinematik-Grundaufbau, Tools, Komponentenauswahl, Methoden und Erfahrungen, wt - Werkstatttechnik 88 (4) pp 75– (1998)
[17] E. Kreuzer G. Leister Programmsystem NEWEUL’90. Manual AN-24. Institute B of Mechanics, University of Stuttgart, 1991. 1181 L. Kübler, C. Henünger, and P. Eberhard. Multi-Criteria Optimization of a Hexapod Machine. In J. Ambrosio (Ed.), Advances in Computational Multibody Dynamics, ECCOMAS Lisbon 2003. Doordrecht: Kluwer (accepted for publication).
[18] J. Liu Kinematics and Dynamics of Spatial Hexapod Motions with Thermal Disturbances. Report IB-38. Institute B of Mechanics, University of Stuttgart, 2001.
[19] Merlet, Singular Configurations of Parallel Manipulators and Grassmann Geometry, Journal of Robotics Research 8 (5) pp 45– (1989) · Zbl 05422374
[20] J.-P. Merlet Parallel Robots. Dordrecht: Kluwer, 2000.
[21] R. Neugebauer Parallel Kinematic Machines in Research and Practice - The 4th Chemnitz Parallel Kinematics Seminar, Fraunhofer Institute for Machine Tools and Forming Technology IWU, Chemnitz, April 2004.
[22] O’Brien, Redundant Actuation for Improving Kinematic Manipulability, In Proceedings of the 1999 IEEE International Conference on RoboticsAutomation 2 pp 1520– (1999)
[23] W. Schiehlen Technische Dynamik. Stuttgart: B.G. Teubner, 1986.
[24] Takeda, Kinematic and Static Characteristics of In-Parallel Actuated Manipulators at Singular Points and in Their Neighborhood, JSME International Journal, Series C 39 (1) pp 85– (1996)
[25] Takeda, Kinematic Synthesis of In-Parallel Actuated Mechanisms Based on the Global Isotropy Index, Journal of Robotics and Mechatronics 11 (5) pp 404– (1999)
[26] L.-W. Tsai Robot Analysis: the mechanics of serial and parallel manipulators. New York: John Wiley, 1999.
[27] M. ValNasek Z. Sika V. Bauma T. Vampola Design Methodology for Redundant Parallel Robots. In Proc. of AED 2001, 2nd Int. Conf. on Advanced Engineering Design, pp. 243-248. Glasgow, 2001.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.