An interval-based method for workspace analysis of planar flexure-jointed mechanism

This paper addresses the problem of certifying the performance of a precision flexure-base mechanism design with respect to the given constraints. Due to the stringent requirements associated with flexure-based precision mechanisms, it is necessary to be able to evaluate and certify the performance at the design stage, taking into account the possible sources of errors: such as fabrication tolerances and the modeling inaccuracies in flexure joints. An interval-based method is proposed to certify whether various constraints are satisfied for all points within a required workspace. Unlike the finite-element methods that are commonly used today to evaluate a design, where material properties are used for evaluation on point-to-point sampling basis, the proposed technique offers a wide range of versatility in the design criteria to be evaluated and the results are true for all continuous values within the certified range of the workspace. This paper takes a pedagogical approach in presenting the interval-based methodologies and the implementation on a planar 3RRR parallel flexure-based manipulator.