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-based 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 a 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 3revolute-revolute-revolute (RRR) parallel flexure-based manipulator.