Abstract
The cable sagging problem of cable-driven parallel robots (CDPRs) is very complicated, because several models for calculating cable sag based on the well-known catenary equation have been studied, but time and computational efficiency are a problem to be solved. There is still no simple mathematical model to calculate cable sag by considering all relevant conditions due to the complexity and nonlinearity of the cable sagging model, which involves many dominant variables and their influence on the position accuracy of CDPRs. In this study, we proposed an ANFIS (adaptive neuro-fuzzy inference system) architecture to estimate cable sag for large-sized CDPRs. The ANFIS model can be used to solve nonlinear functions and detect nonlinear factors online in the control system; this characteristic is consistent with the nonlinear model of cable sag. The trained data for ANFIS models were taken from calculation results by Trust-Region-Dogleg algorithm based on two cable tension calculation algorithms as Dual Simplex Algorithm and Force Distribution in Closed Form. Cable sagging data obtained from ANFIS and Trust-Region-Dogleg algorithm are compared and evaluated by statistical factors of evaluations consisting of root-mean-square error, correlation coefficients, and scatter index. The analytical results show that the ANFIS gave computed results with small errors and can be applied to predict cable sagging for any CDPR configuration, with the advantage of fast calculation time and high precision. The results of these models are also applied on a CDPR that contains two redundant actuators.
Highlights
Mechanical Structure AnalysisE relationship of the cable lengths (variable joints) and the poses of the moving platform of cable-driven parallel robots (CDPRs) were represented by the kinematics problems
Riehl et al [11] studied the problem of the effect of cable mass on the model of inverse and forward kinematics of underconstrained cable-driven parallel robots (CDPRs). e inverse and forward kinematics of the large-workspace 3DOF CDPRs driven by 3 cables were calculated based on the elastic catenary model described by Irvine. is paper showed that for high-load or large-workspace CDPRs, the influence of cable mass on the sag of cables and accuracy of CDPRs is significant. erefore, it needs to be analyzed when designing and controlling the robot to achieve the desired accuracy
Assuming that the catenary model is only affected by its gravity, the effects of external forces such as wind or nonuniform mass distribution along the cable are ignored. e cable sag model between two points B and M is shown in Figure 8, where B and M are the attachment points of cables on the base frame and moving platform, respectively, LS is the distance between points B and M, L denotes the length between B and M taking into account sag of the cable, g is the gravity acceleration, τ is the cable tension at point M, and τx and τz is the component cable tension of τ in the x and z
Summary
E relationship of the cable lengths (variable joints) and the poses of the moving platform of CDPRs were represented by the kinematics problems. E joint variables of the CDPRs are represented by li, which are the length of the driven cables i. Inverse kinematics of CDPRs can be obtained as follows: [6, 15, 18]. Li ai − r − Rbi. Rotation matrix R can be obtained based on the rollpitch-yaw convention as follows: cccβ ccsβsα − sccα ccsβcα + scsα
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
