Lie Algebra Contributions to Instantaneous Plane Kinematics

Abstract

Roth and Bottema obtain the instantaneous properties of a plane motion and its inverse motion by the instantaneous invariants depending on a canonical frame which was introduced in Veldkamp's dissertation(1963). We obtain the instantaneous invariants depending on the same frame by using Lie algebra of the plane motion.

Keywords

• Geometric kinematics
• instantaneous invariants
• Lie algebra
• time independent planar motion.

References

1. [1] Bottema, O. and Roth, B. (1990) Theoretical kinematics. Dover Publications.
2. [2] Hausdorff, F. (1906). Die symbolische Exponentialformel in der Gruppentheorie. Ber. Verh. Kgl. SËA chs. Ges.Wiss. Leipzig., Math.-phys. Kl., 58, 19-48.
3. [3] McCarthy, J. M., Soh, G. S. (2010) Geometric design of linkages (Vol. 11). Springer Science and Business Media.
4. [4] Selig, J. M. (2005) Geometric fundamentals of robotics (Vol. 128). New York: Springer.
5. [5] Selig, J. M. (2007) Cayley maps for SE (3). In 12th International Federation for the Promotion of Mechanism and Machine Science World Congress (p. 6). London South Bank University.
6. [6] Selig, J. M. (2007) Centrodes and Lie algebra. In 2th IFT oMM World Congress (p. 6). London South Bank University.
7. [7] Veldkamp, G. R. (1963) Curvature theory in plane kinematics. JB Wolters.