Influence of cables layout on the dynamic workspace of a six-DOF parallel marine manipulator

Dynamic Analysis of a Tension Leg Platforms (TLPs) Inspired by Parallel Robotic Manipulators

“…Modeling can be carried out when considering the platform as a rigid body supported by mooring lines with known stiffness [1], [2]. As with any dynamic system, a TLP can be described by the equation of motion.…”

“…In FIGURE 1, P = x y z T is the position vector of the moving platform with respect to the base frame; Roll (ψ), pitch (θ ) and yaw (ϕ) are represented the Euler rotation angles between the moving (u, v, and w) and base ψ (X, Y, and Z) frames. Equation 17introduces the TLP Jacobean matrix as (1) xu (1) T u (2)T b (2) xu (2) T . .…”

“…forces along with the X, Y and Z directions and external moments about the X, Y and Z directions [35]; τ = τ (1) τ (2) , • • • , τ (n) T is the vector of internal mooring line forces and n is the mooring lines' number.…”

“…k is the mooring line stiffness, a i is the vector between the TLP base center and the bottom mooring lines anchor locations, and L i is the mooring line change length between two positions. Using mooring line stiffness k 1 = 30 * 10 3 N/m [1], [2] dynamic analysis is conducted on the TLP with the existence of the external forces which are due to the sea waves. The surge, sway, heave, roll, pitch and yaw responses of the TLP are shown in Figure 5.…”

“…Predominantly, rigid body dynamics have been employed, considering the floating marine platform as a single rigid body having six degrees of freedom about a given inertial reference coordinate system. The floating platform motion can be divided into horizontal platform dynamics (surge, sway and yaw motions), which occur at the water wave frequency, and the vertical platform dynamics (heave, roll and pitch), which occur at high frequencies [2].…”