Research On Probabilistic Design Of Spherical Mechanism

With the spherical mechanisms has got wide application in the engineering practical, to improve kinematic accuracy and kinematic performance becomes a hot problem. However the uncertainty, including dimension variables, joint clearance, bar deformation, is ubiquitous in mechanisms, which has a great influence on kinematic and dynamic performance of mechanism. For analyzing and reducing the influence of uncertainty, a probabilistic method has presented to develop the reliability analysis and synthesis under uncertainty for spherical mechanisms in this paper. The main works are described as followings:1. Based on the analysis of kinematics and movement performance, and combine with the impact of dimension variables and structure error, a model of output motion error for spherical linkages is deduced. Then a numerical example is provided to analysis. The analysis results show that randomness of dimension variables has an obvious influence on kinematic accuracy.2. Probability and statistic theory is utilized to evaluate the influence of randomness of dimension variables on kinematic reliability and reliability sensitivity. Point kinematic reliability and time-independent kinematic reliability model of spherical mechanism are deviation by First order second moment and first-passage Poisson method respectively. Moreover, analysis result of Monte Carlo Simulation(MCS) is presented to compare. The result of the compare indicates that probability is characterized in certain point for point kinematic reliability, while probability is characterized in entire time interval for time-independent kinematic reliability, and time-independent kinematic reliability is less than the former. This means that time-independent kinematic reliability can reflect the reliability accuracy for the entire kinematic range.3. Deterministic optimal synthesis(DOS), probabilistic optimal synthesis(POS) and robust synthesis(RS) model for spherical mechanism are proposed to study the influence of randomness of dimension variables with uncertainty. The synthesis result of three methods is demonstrated by a numerical example. The result shows that design quality of robust synthesis superior to the others.4. Posture error analysis of spherical parallel mechanism is researched with manufacture error. The kinematics, the velocity Jacobian matrix and model of posture are established, and software MATLAB is taken to simulate based on normal distribution. Then curve of output posture error and its statistic distribution of mechanism are obtained.