Abstract
The pseudoinverse of a rectangular matrix of modified screws is used to compute the least-squares fit of a set of points that have been measured along a line-profile. Tolerances on line profiles are used to control cross-sectional shapes of parts, such as turbine blades. The specified profile is treated as a moving platform of a hypothetical, redundant, and planar in-parallel-actuated robot, and all the measured points are presumed to be fixed in it. The locations of the linear actuators are represented with screw coordinates, and these are arranged in a matrix equation that relates the three small displacements of the platform to the corresponding deviations (treated as small displacements) of the measured points.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
American National Standard ASME Y14.5M, Dimensioning and Tolerancing. Amer. Soc. Mech. Engs, NY (2009)
Mani, N., Shah, J.J., Davidson, J.K.: Standardization of CMM fitting algorithms and development of inspection maps for use in statistical process control. In: ASME Int. Manuf. Sci. Eng. Conf. Corvallis, OR, USA, June 13-17, vol. 2, MSEC2011Â 50152 (2011)
Choi, W., Kurfess, T.R.: Dimensional measurement data analysis, part 1: A zone fitting algorithm. J. Manuf. Sci. Eng. 121, 238–245 (1999)
Carr, K., Ferreira, P.: Verification of form tolerances part I: Basic issues, flatness, and straightness. Prec. Eng. 17, 131–143 (1995)
Carr, K., Ferreira, P.: Verification of form tolerances part II: Cylindricity and straightness of a median line. Prec. Eng. 17, 144–156 (1995)
Choi, W., Kurfess, T.R.: Dimensional measurement data analysis, part 2: Minimum zone evaluation. J. Manuf. Sci. Eng. 121, 246–250 (1999)
Barari, A., ElMaraghy, H.A., Knopf, G.K.: Evaluation of Geometric Deviations in Sculptured Surfaces Using Probability Density Estimation. In: Davidson, J.K. (ed.) Models for Computer-Aided Tolerancing in Design and Manufacturing, Proc., 9th CIRP Int’l Seminar on CAT, Tempe, AZ, USA, April 10-12, 2005, pp. 45–54. Springer, Dordrecht (2007)
Dowling, M.M., Griffin, P.M., Tsui, K.L., et al.: A comparison of the orthogonal least squares and minimum enclosing zone methods for form error estimation. Mfg. Rev. 8, 120–138 (1995)
Choi, S.C.: Introductory applied statistics in science, pp. 23–35. Prentice-Hall, Englewood Cliffs (1978)
Ben-Israel, A., Greville, T.N.E.: Generalized inverse: Theory and application, 2nd edn. Springer, New York (2003)
Davidson, J.K., Hunt, K.H.: Robots and screw theory: Application of kinematics and statics to robotics, Oxford (2004)
Strang, G.: Linear Algebra and Its Applications, 4th edn. Thomson Brooks/Cole (2006)
Davidson, J.K., Shah, J.J.: Modeling of geometric variations for line-profiles. J. Comp. Inform. Sc. Eng. 12, 041004 (2012)
Coxeter, H.S.M.: Introduction to geometry, 2nd edn. Wiley, New York (1969)
Davidson, J.K., Savaliya, S.B., He, Y., et al.: Methods of robotics and the pseudoinverse to obtain the least-squares fit of measured points on line-profiles. In: ASME Des. for Mfg. & Life Cycle Conf., Chicago, IL, USA, August 12-15, DETC2012-70203 (2012)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Davidson, J.K., Savaliya, S., Shah, J.J. (2013). Screws and Robotics for Metrology. In: Kumar, V., Schmiedeler, J., Sreenivasan, S., Su, HJ. (eds) Advances in Mechanisms, Robotics and Design Education and Research. Mechanisms and Machine Science, vol 14. Springer, Heidelberg. https://doi.org/10.1007/978-3-319-00398-6_5
Download citation
DOI: https://doi.org/10.1007/978-3-319-00398-6_5
Publisher Name: Springer, Heidelberg
Print ISBN: 978-3-319-00397-9
Online ISBN: 978-3-319-00398-6
eBook Packages: EngineeringEngineering (R0)