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In order to improve the kinematic reliability, it is crucial to find out the influence of each error source on the kinematic reliability of the mechanism. Reliability sensitivity analysis is used to find the changing rate in the probability of reliability in relation to the changes in distribution parameters. Based on the structural response surface function method, the functional relation between the kinematic reliability of a modified Delta parallel mechanism and the original input-error vectors is described using the quadratic function with cross terms. Moreover, the partial derivatives of the functional relation with respect to the means and variances of the original input errors are derived, which can efficiently evaluate kinematic reliability sensitivity of the mechanism. The advantages of this method are as follows: First, the response surface function, which can be easily set up by the position-error model of the mechanism, is convenient for calculating the variance, partial derivative, and reliability sensitivity. Second, in this case (unlike in the traditional error-mapping model), although the input-error values are unknown, pseudorandom variables used as random input-error sources can be generated by MATLAB software. Furthermore, the kinematic reliability of the mechanism can be assessed using the Monte Carlo method.

Kinematic reliability and sensitivity analysis of the modified Delta parallel mechanism