A novel approach of input tolerance design for parallel mechanisms using the level set method

Input uncertainties inevitably result in the output error for parallel mechanisms, which will lead to significant influence on good work performance. To control the output error within the specification boundary, this article proposes a novel approach of input tolerance design based on the level set method for the driving joint. The implementation of the proposed method can be divided into two subtasks. First, using the level set method, the exact input error boundary is determined by means of evolving an initial input error interface with a defined normal speed field, thereby transforming the problem of exploring the exact boundary into solving a partial differential equation with initial value. On this basis, according to the equal and scaled principles, the tolerance width of each input is evaluated in an intuitionally geometrical manner, that is, searching the maximum geometry corresponding to the principle inside the exact input error boundary. Finally, two planar parallel mechanisms with different degrees of freedom are introduced as numerical examples to demonstrate the execution and effectiveness of the proposed method.