Performance reliability and tolerance allocation of stochastically defined mechanical systems

Tolerances play an important role in mechanical system design. They are inevitable in manufacture, create mechanical errors and may influence the system performance. Determination of appropriate tolerances requires a systematic way of evaluating the performance. The mechanical errors for the position, velocity and acceleration are represented in terms of the expected values and standard deviations of output variables of interest. The mechanical systems under consideration are general planar pin-jointed systems which are governed by coupled dynamic and kinematic equations. Pin locations are variations in link lengths and radial clearances are treated as random variables.; A probabilistic model and methods are developed to statistically determine mechanical errors due to tolerances for planar mechanical systems. The effects of dimensional tolerances and a random pin location are considered as a net effect on the link's effective length. The model developed from this concept is referred to as the effective link model. The analytical method determines the first and second moments of output variables based on the first order Taylor series expansion with respect to the means. Position, velocity and acceleration reliabilities are defined to evaluate the system performance using joint normal approximation for the output distribution in the analytical method. The method is also applied to determine optimum allocation of tolerances. The Monte Carlo simulation is implemented to verify the analytical results. Using the analytical method and the simulation, three example cases are considered: a six-bar toggle mechanism, a slider-crank and a two-link robot manipulator.; The effective link model simplifies modeling and analysis and it is easily adopted for the analysis of velocities and accelerations. The comparison of the analytical method and the simulation establishes the range of the analytical method and credibility of the simulation model. The relative errors between the two approaches are less the 6.1% in average for means, variances, covariances and reliabilities. The analytical method provides good approximations and is straightforward to implement.