Using Redundancy to Optimize Manipulability of Stewart Platforms

Apply fuzzy interpolation method to calibrate parallel machine tools

“…Generally, it is difficult to derive a forward kinematic model for parallel manipulators since there is no closed form solution, and some numerical algorithms must be used to find the "true" forward kinematic parameters [3][4][5][6][7].…”

“…If e x is W; e y is N; and e z is U; then ee x is P x1 ; ee y is P y 1 ; and ee z is P z1 ; and ee a is a 1 ; ee b is b 1 ; and ee g is g 1 : P 1 ð Þ If e x is W; e y is N; and e z is L; then ee x is P x3 ; ee y is P y 3 ; and ee z is P z3 ; and ee a is a 3 ; ee b is b 3 ; and ee g is g 3 : P 3 ð Þ If e x is W; e y is S; and e z is U; then ee x is P x5 ; ee y is P y 5 ; and ee z is P z5 ; and ee a is a 5 ; ee b is b 5 ; and ee g is g 5 : P 5 ð Þ If e x is W; e y is S; and e z is L; then ee x is P x7 ; ee y is P y 7 ; and ee z is P z7 ; and ee a is a 7 ; ee b is b 7 and ee g is g 7 : P 7 ð Þ If e x is E; e y is N; and e z is U; then ee x is P x2 ; ee y is P y 2 ; and ee z is P z2 ; and ee a is a 2 ; ee b is b 2 ; and ee g is g 2 : P 2 ð Þ If e x is E; e y is N; and e z is L; then ee x is P x4 ; ee y is P y 4 ; and ee z is P z4 ; and ee a is a 4 ; ee b is b 4 ; and ee g is g 4 : P 4 ð Þ If e x is E; e y is S; and e z is U; then ee x is P x6 ; ee y is P y 6 ; and ee z is P z6 ; and ee a is a 6 ; ee b is b 6 ; and ee g is g 6 : P 6 ð Þ If e x is E; e y is S; and e z is L; then ee x is P x8 ; ee y is P y8 ; and ee z is P z8 ; and ee a is a 8 ; ee b is b 8 and ee g is g 8 : P 8 ð Þ…”

“…This membership function is determined by the real position errors at the 8-neighboring grid points in the x direction, P x1 ∼P x8 . This membership function determines the degree to which the current position input belongs to each different real error output based on the eight control rules defined in (4) in the x direction, and it is equivalent to the universe of discourse or a weighing factor. Substituting (7) and (8) into (6), one obtains:…”

“…In recent years, parallel machine tools (PMTs) have drawn more and more interest in the academia and industry for their applications [1][2][3][4][5]. PMTs have the advantage of great operational accuracy due to their high rigidity.…”

Physiological hemostasis based intelligent integrated cooperative controller for precise fault-tolerant control of redundant parallel manipulator

“…Roberts et al (2008) investigated the worst-case relative manipulability index to design the optimally faulttolerant control systems, which can be applicable to both serial and parallel manipulators. Meanwhile, many scholars used kinematical redundancy to optimise fault-tolerant capability (Yi, McInroy, and Chen 2006;Hassan and Notash 2007), torque recovery capability (Notash 2011) and manipulability (Ukidve, McInroy, and Jafari 2008) of the parallel manipulators. The control scheme designs usually use backup active joint to replace the fault ones and modify the kinematic layout.…”