Abstract
The pose of the moving platform in parallel robots is possible thanks to the strong coupling, but it consequently is very difficult to obtain its forward displacement. Different methods establishing forward displacement can obtain different numbers of variables and different solving speeds with nonlinear equations. The nonlinear equations with nine variables for forward displacement in the general 6-6 type parallel mechanism were created using the rotation transformation matrix R, translation vector P and the constraint conditions of the rod length. Given the problems of there being only one solution and sometimes no convergence when solving nonlinear equations with the Newton method and the quasi-Newton method, the Euler equation for free rotation in a rigid body was applied to a chaotic system by using chaos anti-control and chaotic sequences were produced. Combining the characteristics of the chaotic sequence with the mathematical programming method, a new mathematical programming method was put forward, which was based on chaos anti-control with the aim of solving all real solutions of nonlinear equations for forward displacement in the general 6-6 type parallel mechanism. The numerical example shows that the new method has some positive characteristics such as that it runs in the initial value range, it has fast convergence, it can find all the possible real solutions that be found out and it proves the correctness and validity of this method when compared with other methods.
Highlights
The pose of the moving platform in parallel robots can be realized thanks to the strong coupling, this means it is very difficult to obtain its forward displacement
In the problem of the forward displacement of parallel robots, we need to solve a class of strongly nonlinear algebraic equations with many variables which are extremely difficult to solve
The nonlinear equations with nine variables for forward displacement in the general 6‐6 type parallel mechanism were built up using the rotation transformation matrix R, translation vector P and the constraint conditions of the rod length
Summary
The pose of the moving platform in parallel robots can be realized thanks to the strong coupling, this means it is very difficult to obtain its forward displacement. The chaotic sequence method is a new method, in which the initial point of the Newton iteration is generated using the chaotic and hyper‐chaotic system and all the real solutions in the mechanism synthesis can be effectively solved [28,29,30,31,32]. Nonlinear equations with nine variables on forward displacement in the general 6‐6 type parallel mechanism were created using the rotation transformation matrix R , translation vector P and the constraint conditions of the rod length and the mathematical programming method based on chaos anti‐ control was proposed as a means to solve forward displacement in the general 6‐6 type parallel mechanism. The numerical example shows that the new method has fast convergence, it can find all the possible real solutions that be found out and it proves the correctness and validity of this method when compared with other methods
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have