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A three-legged compliant parallel mechanism (3L-CPM) achieves fully decoupled motions when its theoretical 6 × 6 stiffness/compliance matrix is a diagonal matrix, which only contains diagonal components, while all non-diagonal components are zeros. Because the motion decoupling capability of 3L-CPMs is essential in the precision engineering field, this paper presents the fundamental criteria for designing 3L-CPMs with fully decoupled motions, regardless of degrees-of-freedom and the types of flexure element. The 6 × 6 stiffness matrix of a general 3L-CPM is derived based on the orientation of each flexure element, e.g., thin/slender beam and notch hinge, etc., and its relative position to the moving platform. Based on an analytical solution, several requirements for the flexure elements were identified and needed to be satisfied in order to design a 3L-CPM with a diagonal stiffness/compliance matrix. In addition, the developed design criteria were used to analyze the decoupled-motion capability of some existing 3L-CPM designs and shown to provide insight into the motion characteristics of any 3L-CPM.

mathematics

Three-Legged Compliant Parallel Mechanisms: Fundamental Design Criteria to Achieve Fully Decoupled Motion Characteristics and a State-of-the-Art Review