Eigenvalue analysis and optimised numerical simulations of the space shuttle remote manipulator system

This paper extends the earlier work of various researchers and the authors and gives an analytical solution to the natural frequencies and mode shapes of the space shuttle remote manipulator system (SRMS). For optimised numerical simulations, the exact eigenmodes are replaced by simple polynomials for use in Lagrangeʹs equation. The close agreement of the lowest natural frequency by both methods for various fixed SRMS configurations, being almost independent over the range, shows that simple mode shapes can be used to determine transient vibrations induced by large angle slews of the SRMS and payload system. The use of a tangent frame formulation for each link relative to its revolute joint is the key for the formulation of the flexible link boundary conditions and is more realistic than the use of arbitrary beam functions by other authors.