Static and dynamic stiffness analyses of cable-driven parallel robots with non-negligible cable mass and elasticity

Dynamic and Oscillatory Motions of Cable-Driven Parallel Robots Based on a Nonlinear Cable Tension Model

“…Therefore, a 265 trapezoidal-velocity trajectory is chosen to analyze the influence of the cable modulus of elasticity on the CDPR dynamic behavior. The lack of smoothness of the trajectory is chosen here to excite the end-effector on its fundamental rigid-body mode frequencies [16]. The shape of the cable linear velocities at the pulley entrance is defined such as the motion is uniformly accelerated until the linear cable velocities achieve the limit value V max (Fig.…”

“…The dynamic and elastic modulus, the phase angle ϕ and the loss factor η are given for each DMA test in Table 1. Table 1: Frequency dependency of the modulus of elasticity of the steel wire cable at loading frequencies between 0.1 and 20 Hz We can see that the stiffness and damping are highly dependent on frequency for a given preload, over a representative 160 frequency range of the CDPR behavior [16]. The elastic modulus increases significantly at very low frequencies, from 120.5 ± 2.8 GPa at 0.1 Hz to 137.3 ± 3.3 GPa at 1Hz (Table 1).…”

Vibration analysis of cable-driven parallel robots based on the dynamic stiffness matrix method

“…Although there are a lot of previous works on the vibration analysis and 30 control of rigid-link parallel robots, e.g. [14,15,16,17,18,19,20,21,22], only few studies are dedicated to the vibration analysis of CDPRs [23,24,25,26,27,28,29,30]. Vibrations can notably be induced by (brutal) end-effector velocity changes, wind disturbance, and/or friction of the cables around pulleys [24].…”

“…Besides, an oscillating model developed using Lagrangian approach in conjunction with the Dynamic Stiffness Matrix (DSM) method was presented in our previous work [29]. This modeling framework does not allow the computation of the time-domain response (motion) of the CDPR along a trajectory as the aforementioned modeling methods, but its advantages include mathematical convenience, simplicity in numerical implementation and computation.…”

“…Compared to our previous work [29], with the intention to evaluate the effect of the cable natural modes on the robot vibrations, the present paper focuses on 95 a dynamic stiffness analysis where the calculation of the Frequency Response Functions (FRFs) are explicated. The FRFs represent the input-output relationships between an excitation force and a system response (position, velocity or acceleration).…”