Synthesis of precision flexible mechanisms using screw theory and beam constraints

Abstract

The design of flexible parallel stages has recently been systematised for the three-dimensional space using screw theory. The relationships between the twists (motions), the wrench actuations, and constraint wrenches spaces can be manipulated by linear algebra. The use of flexible beams to constraint small motions leads to simple precision mechanisms. In a previous work by the authors, an analytical enumeration of twists and their reciprocal wrenches for any degree of freedom with zero and infinite pitches was presented and validated using finite element analysis. This work extends the methodology to account for screws with finite non-null pitches. Two synthesis problems are analytically calculated and validated using finite element analysis.