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Mechanical structures which can vibrate about a state of mean rotation or translation may constitute gyroscopic dynamic systems that are related by the mathematical similarity of their governing equations of motion. Considering as examples a rotating circular ring and an axially travelling string, the analogy of those systems is demonstrated. The linear vibrations obtained by superposing small perturbations on the stationary solution are analyzed. Assuming time-varying speeds, the effect of non-constant stress resultants on the dynamic stability of gyroscopic systems is investigated and the results are compared to those found in literature where the stress resultants of axially moving continua are commonly taken as constant. Governing EquationsThe shape of a one-dimensional continuum is described by a function x(ξ, t) indicating the position vector x at time t of a material point ξ along the axis of the continuum. Neglecting rotary inertia and distributed loading, the planar motion of an inextensible continuum of cross section A and mass density ρ is governed by the balances of linear and angular momentum ρAwhere the notation D/Dt indicates the material time derivative, the vector e t denotes the unit tangent vector and the symbol ∧ is used to indicate the outer product of two vectors in the plane. The stress resultants are the internal force F and the bending moment M . Linear vibrations are obtained by superposing small perturbations on a stationary solution, x(ξ, t) =x(ξ) + u(ξ, t), in which the displacement vector is represented by its components in tangential and normal directions as u = u tēt + u nēn . Since the considered continuum is assumed to be inextensible, the displacement components are coupled bywithκ denoting the curvature of the prescribed curve, such that only one component remains as a dependent variable. Rotating Circular RingIn case of a freely rotating circular ring, a Lagrangian description with the dependent variable ψ representing a small perturbation of the direction angleφ is adopted. Assuming M to satisfy the constitutive equation M = EIκ, the dynamics of a ring that rotates at constant angular velocity Ω is governed bywhere the dot and the prime symbol indicate derivatives with respect to time t and angleθ, respectively. Since the operator 4Ω∂/∂θ is skew-symmetric, the rotating circular ring represents a gyroscopic system.

Cable-driven parallel robots are being developed for rescue operations in large-scale earthquake disasters. This paper proposes an identification method of kinematic parameters for the installation, such as the position of cable fixture by initializing motion on site. This problem is unique to robots in natural fields, such as disaster sites because the environment is not structured. On the basis of identification error analysis and simulation, the optimal number of measurement points and the size of an identification reference frame are obtained.

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