Static And Dynamic Analyses Of Cable-Driven Parallel Robots

The application of cables in the parallel robots is modeled and analyzed to evaluate the mechanical properties and performance of parallel robots.Cable-driven parallel robots(CDPRs)have drawn considerable attention because of their unique abilities and advantages such as the large workspace size,which makes them well suited for broadcasting,transporting,and loading,easy to reconfigure and implement,high speed motion,and high payload to weight ratio and have good accuracy.Static and dynamic analysis is required for achieving higher efficiency and wider applications of the parallel robots.This study investigates the three-dimensional cable model,dynamic motion,static and dynamic stiffness analyses of the cable-driven parallel robot(CDPR)by considering cable's mass,elasticity and mass of end-effector.The dynamic analysis of the CDPRs is presented using Lagrange's method.The static cable model is evaluated from the static equilibrium position of the parallel robot.From this model,the static deformation of the cables with the application of gravitational force is a non-linear equation.The parameters of cables are obtained from the sagging cable equations for three-dimensional by considering mass and elasticity.The dynamic cable model is determined from a small change of static equilibrium position of the system.According to the static and dynamic cable model,optimization of cable's tensions and cable lengths using fminimax solver is carried out to determine the static stiffness of the CDPR.The inclined cable is modeled at static equilibrium state of the system and obtained multi-objective non-linear equations.Multi-objective optimization is applied in cable model analysis to find an optimal solution.Considering the catenary cable model,it determines the stiffness of the robot with external forces exerted by the hydraulic cylinder on the system.Dynamic stiffness of the CDPR is calculated through force and free vibration with a varying frequency of harmonic motion.The proposed approach accounts for both inertia force and damping force effect on dynamic stiffness analysis.Based on the static and dynamic cable models,the static and dynamic stiffness of the cable-driven parallel robots are analyzed with external hydraulic force applied to the system and the stiffness of the cables are obtained with simulation.The static stiffness is determined at a given weight of the moving platform in in multi-directional inclined cable with external forces exerted by hydraulic cylinder on the system.The dynamic stiffness of cable is the frequency dependent ratio between a dynamic cable tension andthe resulting dynamic deformation.Each static and dynamic stiffness of cables is expressed with respect to the global stiffness matrix by the superposition method to determine static and dynamic stiffness of the system.For the case of very long spans,the catenary formula gives more accurate results.In these robots cables are prone to vibration even cables operate at very low velocity,degrading the positioning precision of the end-effector.The factors that can cause these vibrations are wind disturbance,initial motion of the end-effector,the friction of cables around the fixed pulleys and speed reducer backlash.Simulations are carried out to determine the effect of the mass of the end-effector on the three-dimensional inclined plane regarding static and dynamic stiffness.The dynamic analysis of the CDPRs are presented using the Lagrange's method,taking cable's mass,cable's elasticity,the second moment of inertia of the end-effector,hydraulic cylinder and drums into account.In addition,the effect of the second moment inertia and the friction between cables and drums is considered to evaluate the dynamic motion of the robot.Lagrange's equations of motion are derived and evaluated for the generalized coordinates of the system.The dynamic motion of the parallel robot is expressed by the generalized forces and generalized coordinates to completely specify the configuration of the whole mechanical system as well as every component of the system.The cables are modeled to control and design the motion of each part of a rigid body.The cable's mass and elasticity of the cable are taken into account while modeling of the cable using Newton's equation.Cable's elasticity is determined using the optical cable's tensions and lengths.Numerical results are carried out to obtain the dynamic motion of the CDPRs.The effect of cable mass on the elasticity of the cable is investigated.Experimental analyses and the effect of the mass of the end-effector on the cable's tension and elasticity are also investigated.These examples illustrate that the general motion of the rigid body is better described in terms of a set of independent coordinates.The results indicate that a better speed of the end-effector can be achieved by adding the linear and rotational motions of the electrohydraulic cylinder actuators into the traditional CDPRs.In addition,analyses in three-dimension are very important to measure the actual performance of the cables and system.This demonstrates the potential for general applicability and motion of the CDPR.