Abstract
A steady-state dynamic model of a cable in air is put forward by using some tensor relations. For the dynamic motion of a long-span Cable-Driven Parallel Robot (CDPR) system, a driven cable deployment and retrieval mathematical model of CDPR is developed by employing lumped mass method. The effects of cable mass are taken into account. The boundary condition of cable and initial values of equations is founded. The partial differential governing equation of each cable is thus transformed into a set of ordinary differential equations, which can be solved by adaptive Runge-Kutta algorithm. Simulation examples verify the effectiveness of the driven cable deployment and retrieval mathematical model of CDPR.
Highlights
Cable systems arise in many practical applications, such as bridges, underwater systems, aircraft decoy systems, and tethered satellite systems
T is the tension at the right end of cable’s element, M is the diagonal inertia matrix of the concentrated mass, d2r s, t /dt[2] is accelerate, and F is the total external force, both corresponding at the unit of cable length, including gravity, damping force, and aerodynamic drag forces
A computational dynamics model is developed to simulate the dynamics of variable length cable-driven parallel robot CDPR system
Summary
Cable systems arise in many practical applications, such as bridges, underwater systems, aircraft decoy systems, and tethered satellite systems. Cable-driven mechanisms have received attention and have been recently studied since the 1980s 3. Dynamical characteristics of this type of mechanism have been well studied, such as the manipulation problem of load by multiple wires 7, 8 , and the cables are considered to be massless. Cable-body systems have been modeled using continuum models based on partial differential equations for strings, as well as lumped mass method in 10. The lumped mass method representation is usually the preferred choice for detailed simulation work 11 and is employed in our work. We present a deployment and retrieval cable mathematical model using a lumped parameter representation. According to the 50 m scaled model Figure 1 , based on the inverse kinematics analysis, the inverse dynamic formulation of deployment and retrieval CDPR is established.
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