Romansy 16 pp 113-120 | Cite as

Estimation of Leg Stiffness Parameters of a 6DOF Parallel Mechanism

  • Józef Knapczyk
  • Michał Maniowski
Part of the CISM Courses and Lectures book series (CISM, volume 487)


The paper describes a novel algorithm for estimation of the stiffness parameters of a 6DOF parallel mechanism with a known topology and geometry. The mechanism is composed of a platform guided by six or more legs with Spherical-Prismatic-Universal joints. A substitute compliance of each leg is modelled by linear springs in the P-joints. Such structure has a broad application in robotics, machining tools, and car suspension systems. The stiffness parameters of the legs are considered as unknown or hard to measure directly. These parameters are estimated using as an input data the spatial displacements of the platform from an initial pose, measured under specified quasi-static loads. The presented method is exemplified on a five-rod wheel guiding mechanism of an actual passenger car. Results of the mechanism measurements carried out on a test stand are used. Five static rates of elastomeric bushings installed in the mechanism rods are determined taking into account the influence of the measurement noise.


Machine Tool Stiffness Parameter Spatial Displacement Dimensional Synthesis Spring Rate 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Carbone, G., and Ceccarelli, M. (2004). A procedure for Experimental Evaluation of Cartesian Stiffness Matrix of Multibody Robotic Systems. In Proc. ROMANSY, Montreal, Canada, 1–9.Google Scholar
  2. Daney, D., and Emiris, I.Z. (2004). Identification of Parallel Robot Kinematic Parameters under Uncertainties by Using Algebraic Methods. Proc. of the 11 th World Congress in Mechanism and Machine Science, Tianjin, China.Google Scholar
  3. Davidson, K., and Hunt, K. (2004). Robots and Screw Theory. Oxford University Press.Google Scholar
  4. Knapczyk, J., and Dzierżek, S. (1995). Displacement and force analysis of five-rod suspension with flexible joints. Trans. ASME, Journal of Mech. Design, Vol. 117, 532–538.Google Scholar
  5. Knapczyk, J., and Maniowski, M. (2006-a). Synthesis of a five-rod suspension for given load-displacement characteristics. Proc. Instn. Mech. Engrs, Part D: J. Automobile Eng, paper submitted for publication.Google Scholar
  6. Knapczyk, J., and Maniowski, M. (2003). Dimensional synthesis of a five-rod guiding mechanism for car front wheels. The Archive of Mechanical Engineering, Vol. 50, No 1, 89–116.Google Scholar
  7. Knapczyk, J., and Maniowski, M. (2006-b). Elastokinematic modeling and study of five-rod suspension with subframe. Mechanism and Machine Theory, paper accepted for publication in vol. 41.Google Scholar
  8. Maggiolaro, M.A., Dubowski S., and Mavroidis C. (2005). Geometric and elastic error calibration of a high accuracy patient positioning system. Mechanism and Machine Theory, 29, 415–427.CrossRefGoogle Scholar
  9. Thomas, M., Yuan-Chou, H.C., and Tesar, D. (1985). Optimal Actuator stiffness distribution for robotic manipulators based on local dynamic criteria. Proc. of IEEE Int. Conf. on Robotics and Automation, 275–281.Google Scholar
  10. Using MATLAB, Version 6 (2000). The Math Works Inc.Google Scholar
  11. Scheaffer, R., and McClave J. (1986). Probability and Statistics for Engineers. PWS-KENT, Boston.Google Scholar

Copyright information

© CISM, Udine 2006

Authors and Affiliations

  • Józef Knapczyk
    • 1
  • Michał Maniowski
    • 1
  1. 1.Institute of Automobiles and Internal Combustion EnginesCracow University of TechnologyPoland

Personalised recommendations