Three-dimensional static and dynamic stiffness analyses of the cable driven parallel robot with non-negligible cable mass and elasticity

Analysis on variable stiffness of a cable-driven parallel–series hybrid joint toward wheelchair-mounted robotic manipulator

“…Because x 2 is an elliptic integral, there is no analytical solution but numerical solution. At this point, substitute the three equilibrium equations obtained from the static analysis into equations (15) and (16) to derive the values of T 1 , T 2 , F 1 , F 2 , and M.…”

“…Generally, there are three different models of cable, namely, ideal lines which have no mass and no flexibility, a massless spring, and the sagging cable model that considers cable mass and elasticity. 15,16 The first model is the simplest cable model used in the theoretical analysis of CDM. The second model is valid and efficient for light-weight, 18 lowspeed, 15 and small-size robots.…”

“…15,16 The first model is the simplest cable model used in the theoretical analysis of CDM. The second model is valid and efficient for light-weight, 18 lowspeed, 15 and small-size robots. 22,23 The third model is used for high-speed, large-dimension, or heavy-load CDM.…”

“…16,[23][24][25][26][27][28] Previous researches have shown that the sagging cable model is divided into two-dimensional inclined cable [16][17][18][19]29 and three-dimensional inclined cable. 15,23,30 Riehl et al 29 analyzed the influence of the sagging cable model on the end-effector positioning, the control lengths of the cables, and the cable tensions. They pointed out that for large working volume manipulators, this aspect needs to be taken into account at the design level in order to achieve good positioning and accuracy.…”

“…Actually, cables as massless springs just consider axial stiffness of cables; however, if the cable profile is a sagging curve and it needs to consider transversal stiffness, Jacobian matrix cannot be used to calculate the Cartesian stiffness matrix. 16 Amare et al 15 made SSA and DSA of the CDM in three-dimensional inclined plane with external forces exerted by hydraulic cylinder on the system. Yuan and colleagues 16,17 studied the variation of pose error with external load for evaluating the static stiffness performance of CDM and used dynamic stiffness matrix method to identify the system natural frequencies to solve the vibration problems of structures.…”