Dynamics Analysis And Chaos Identification Of One Decoupled Parallel Mechanism

Distinguished from generally parallel mechanisms, the decoupled parallel mechanisms(DPMs) present more special characteristics such as easier to control, easier to acquire trajectory planning, higher kinematic accuracy, possessing preferable isotropy etc. Chaos motions(or other motions like this) usually appear in deterministic system and normally possess unpredictability and randomness, which generally also exits in nonlinear dynamic system. With the continuing development of the Chaos theory, which also becomes more mature, if decoupled parallel mechanisms and Chaos theory were combined together to explore DPMs’ non-linear dynamics, then a more overall overview and details may be obtained, which can also guide and support the application of DPMs. Aiming at one category of fully decoupled parallel mechanisms with clearances, chaos-phenomenon of mechanism was recognized and studied, Main contents of this paper are as follows:Building mechanism’s mathematical model is the primary condition to theoretically study mechanism’s chaos-motion. Therefore, in this paper, primarily for the fully decoupled mechanisms of PU-RCRR-CRRR under the ideal condition, its kinematics analysis was obtained. Then according to the second kind of Lagrange’s equation and “contact-separation” two states force model, dynamic model of mechanism with clearances was built, namely mechanism’s dynamic differential equation.For mechanisms with clearances, in line with Matlab-software, dynamic differential equations’ numerical solution was solved, based on which, dynamic space trajectory and poincare-map of revolute pairs with clearance were drew, simultaneously chaotic motions’ details can be preliminarily judged, similarly according to the numerical solution, lyapunov exponent and qualitative study of mechanisms’ chaos motions can be confirmed, especially to investigate how changes of mechanisms’ parameters affects chaos motions.At last, by the Dynamics Simulation Software(ADAMS), dynamic model of the fully PU-RCRR-CRRR decoupled paralleled mechanisms with clearance was established, relevant dynamic characters were also analyzed. Simultaneously, deriving data from previous simulation and the max-Lyapunov exponent can be acquired, which accordingly demonstrated the mechanisms’ chaos motions’ conclusion studied by the theory before.