Summary
The present paper investigates the properties of the angular velocity tensor ϕ and the angular acceleration tensor Ψ for rigid body motion. Three vectorial invariants of rigid body kinematics are presented. In case of tensor Ψ being non-singular, its inverse Ψ−1 is inferred. A novel procedure for automatic computation of tensor ϕ and Ψ based on measured velocity and acceleration data is developed. Depending of the type of available data, three algorithms are suggested. Numerical examples show the application of the method.
Similar content being viewed by others
References
Angeles, J.: Automatic computation of the screw parameters of rigid-body motion. Part II: Infinitesimally separated positions. Trans. ASME J. Dynamic Systems, Measurement and Control108, 39–43 (1986).
Angeles, J.: Rational kinematics. New York Berlin Heidelberg: Springer 1988.
Angeles, J.: Fundamentals of robotic mechanical systems. New York Berlin Heidelberg: Springer 1997.
Angeles, J.: The angular acceleration tensor of rigid-body kinematics and its properties. Arch. Appl. Mech.69, 204–214 (1999).
Béda, G., Kozák, I., Verhás, J.: Continuum mechanics. Budapest: Académiai Kiadó 1995
Bottema, O., Routh, B.: Theoretical kinematics. Amsterdam New York Oxford: North Holland 1988.
Condurache, D.: On the acceleration field of a rigid body under general motion. Bul Inst. Polit. Iaşi,XLIV (XLVIII), 1–2, s. I, 67–73 (1998).
Condurache, D.: New generalization of Poisson formulae. Bul. Inst. Polit. Iaşi,XLIV (XLVIII), 3–4, s. I, 74–87 (1988).
Géradim, M., Rixen, D.: Parameterisation of finite rotations in computational dynamics: a review. Rev. Européenne des Eléments Finis4, 497–553 (1995).
McCarthy, M. J.: An introduction to theoretical kinematics. Cambridge: MIT Press 1990.
Segel, L. A.: Mathematics applied to continuum mechanics. New York: Dover 1987.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Condurache, D., Matcovschi, M. Computation of angular velocity and acceleration tensors by direct measurements. Acta Mechanica 153, 147–167 (2002). https://doi.org/10.1007/BF01177449
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01177449