A Scale-Independent and Frame-Invariant Index of Kinematic Conditioning for Serial Manipulators

  • Jorge Angeles
Conference paper


When defining an index of kinematic conditioning based on the minimum attainable value of the condition number of a manipulator Jacobian, dimensional inhomogeneities arise. As a means to eliminate the latter, an alternate definition of the twist of the end effector—containing all information necessary to determine the velocity field of the end effector—was proposed elsewhere. This is based on the velocities of three noncollinear points, thereby eliminating the angular velocity, which is the source of the aforementioned problem. As a consequence, the Jacobian becomes dimensionally homogeneous, what thus leads to a scale-invariant index of kinematic conditioning. We show in this paper that, if the points defining end-effector twist are the vertices of a Platonic solid, then a plausible conditioning index is derived.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Angeles, J., 1988, Rational Kinematics, Springer-Verlag, Berlin-Heidelberg-New York-Tokyo.zbMATHGoogle Scholar
  2. Angeles, J. and Ldpez-Cajûn, C., 1988, “The dexterity index of serial-type robotic manipulators”, Proc. 20th Biennial Mechanisms Conference, Sept. 2528, Kissimmee, FL: 79–84.Google Scholar
  3. Angeles, J. and Rojas, A. A., 1987, “Manipulator inverse kinematics via condition-number minimization and continuation”, Int. J. Robotics and Automation, Vol. 2, pp. 61–69.Google Scholar
  4. Gosselin, C., 1990, “Dexterity indices for planar and spherical robotic manipulators”, Proc. 1990 Int. IEEE Conf. Robotics eg Automation, Cincinnati, May 13–18, pp. 650–655.Google Scholar
  5. Gosselin, C. and Angeles, J., 1988, “A new performance index for the kinematic optimization of robotic manipulators”, Proc. 20th Proc. Biennial Mechanisms Conference, Sept. 25–28, Kissimmee, FL: 441–447.Google Scholar
  6. Paul, R. P. and Stevenson, C. N. 1983, “Kinematics of robot wrists”, Int. J. Robotics Res., Vol. 2, No. 1, pp. 31–38.CrossRefGoogle Scholar
  7. Salisbury, J. K. and Craig, J. J. 1982, “Articulated hands: force control and kinematic issues”, Int. J. of Robotics Res., Vol. 1, No. 1, pp. 4–17.CrossRefGoogle Scholar
  8. Schuman, H. 1952, Leonardo da Vinci on the Human Body: The Anatomical, Physiological, and Embryological Drawings of Leonardo da Vinci, H. Schuman, New York.Google Scholar
  9. Strang, G. 1976, Linear Algebra and its Applications, Academic Press, New York.zbMATHGoogle Scholar
  10. Vinogradov, L B., Kobrinski, A. E., Stepanenko, Y. E. and Tives, L. T., 1971, “Details of kinematics of manipulators with the method of volumes”, (in Russian), Mekhanika Mashin, No. 27–28, pp. 5–16.Google Scholar
  11. Yang, D. C. and Lai, Z. C. 1985. “On the conditioning of robotic manipulators—service angle”. ASME J. of Mech.. Trans. and Automation in Design. Vol. 107. pp. 262–270.CrossRefGoogle Scholar
  12. Yoshikawa, T. 1985, “Manipulability of robotic mechanisms”. Int. J. of Robotic. Res., Vol. 4. No. 2, pp. 3–9.CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Wien 1991

Authors and Affiliations

  • Jorge Angeles
    • 1
  1. 1.Department of Mechanical Engineering & McGill Research Centre for Intelligent MachinesMcGill UniversityMontrealCanada

Personalised recommendations