Direct Linearization Method Kinematic Variation Analysis

Velocity and acceleration analysis is an important tool for predicting the motion of mechanisms. The results, however, may be inaccurate when applied to manufactured products due to the process variations that occur in production. Small changes in mechanism dimensions can accumulate and propagate, causing a significant variation in the performance of the mechanism. A new application of statistical analysis is presented for predicting the effects of variation on mechanism kinematic performance. The new method is an extension of the direct linearization method developed for static assemblies. This method provides a solution that is a closed form. It may be applied to two-dimensional mechanisms to predict variation in velocity and acceleration due to dimensional variations. It is also shown how form, orientation, and position variations may be included in the analysis to analyze variations that occur within the joints. Only two assemblies are analyzed to characterize the distribution: The first determines the mean, and the second estimates the variance. The system is computationally efficient and well suited for design iteration.