Advertisement

Motion Space of Contacting Smooth Curves in Plane Using Screw Derivative

  • K. Rama KrishnaEmail author
  • Dibakar Sen
Conference paper
Part of the Mechanisms and Machine Science book series (Mechan. Machine Science, volume 73)

Abstract

In this paper, the proposed formulation of the single contact motion space analysis using screws and differential screws, shows that only the geometric kinematical properties affect the second-order motion space characteristics w.r.t. a contact. The classical Eulery-Savary equation derived through the present approach established its necessity and sufficiency for the second-order roll-slide motion. Geometrical interpretations of the motion space of curves in a point contact help in defining composition rules for analyzing the cases with multiple contacts. The theory is illustrated through two examples.

Keywords

Freedom analysis Curvature theory Form-closure 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Reuleaux F.: The Kinematics of Machinery, Dover, NY (1963).Google Scholar
  2. 2.
    Mason, M. T.: Mechanics of Robotic Manipulation. MIT press, Cambridge (2001).CrossRefGoogle Scholar
  3. 3.
    Rimon, E., Burdick, J.: A configuration space analysis of bodies in contact-II. 2nd order mobility. Mech. Mach. Theory, 30(6), pp. 913-928 (1995).CrossRefGoogle Scholar
  4. 4.
    Ramakrishna, K., Sen, D.: Curvature based mobility analysis and form closure of smooth planar curves with multiple contacts. Mech. Mach. Theory, 75, pp. 131-149 (2014).CrossRefGoogle Scholar
  5. 5.
    Bottema, O., Roth, B.: Theoretical Kinematics. North-Holland Publ. Comp., Amsterdam (1979).Google Scholar
  6. 6.
    Bokelbeg, E. H., Hunt, K. H., Ridley, P. R.: Spatial Motion-I: Points of inflection and the differential geometry of screws. Mech. Mach. Theory, 27(1), pp. 1-15 (1992).Google Scholar
  7. 7.
    Do Carmo, M. P.: Differential Geometry of Curves and Surfaces. Prentice-Hall, Englewood Cliffs, NJ, pp. 27-29 (1976).Google Scholar
  8. 8.
    Griffis, G.: A study of curvature for single point contact. Mech. Mach. Theory, 38(12), pp. 1391-1411 (2003).MathSciNetCrossRefGoogle Scholar
  9. 9.
    Ramakrishna, K.: Motion Space Analysis of Smooth Contacting Objects. Ph.D. Thesis, Indian Institute of Science (2018)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Indian Institute of Technology DelhiNew DelhiIndia
  2. 2.Indian Institute of ScienceBangaloreIndia

Personalised recommendations